Introduction

Heat exchangers are widely utilized in the automotive industry, industrial applications, and processes. Modified technologies have increased thermal loads in a compact heat exchanger, and therefore, heat transfer improvement techniques mainly focus on thermofluid research, require establishing an energy-efficient heat exchanger (HX)[1], and avoid thermal failure of the HX. Heat transfer improvement technique has broadly classified into two categories mainly active and passive. The active technique requires an external power agent like a magnetic field vibration, while the latter technique does not require any external power source and only utilizes the flow energy for heat transfer augmentation. The passive method includes the use of fin addition, geometrical modification, tube inserts, and others, while its easy installation at a lower cost makes it superior and widely used [2]. Compact heat exchangers are used for heat exchange between hot fluid and cold fluid and its thermal enhancement could be relatively enhanced using some modifications. Several studies have been studied to intensify heat transfer performance using twisted turbulator insert [TTI] along with little geometrical modification. In the following, some recent studies on turbulators will be reviewed. Eiamsa-ard et al.[3] analyzed heat transfer and thermohydraulic performance of peripheral v-cut twisted turbulator inserts and compared them to the plain tube (PT). The author revealed TTI augmented heat transfer on increased depth ratio and decreased width ratio of v-cut. Murugesan et al. [4, 5] investigated a cumulative impact on Nusselt number and friction factor on introducing twisted turbulators of peripherally v-cut configuration, rectangular-cut configuration, and trapezoidal cut twisted tapes. The author revealed that peripheral cut enhanced fluid mixing and thus improves heat transfer performance. Vaisi et al. [6] conducted an experimental investigation on the effect of discontinuous turbulator inserts with and without perforation of different shapes (circular, square, rectangular, triangular, and diamond shape) and revealed a net enhancement in heat transfer of ( 20.8, 15, 11, 8.7, and 5%, respectively) compared to without perforation. Chu et al. [7] investigated TTI in a heat exchanger obtained an enhanced Nusselt number and friction factor and successfully achieved the performance evaluation criteria (overall performance index) in the range of 1.18 to 1.23. Although TTI was also investigated in a wavy tube of different turbulator tapes by Hasanpour et al. [8], the author revealed that HX outcomes higher Nusselt number and friction factor compared to simple tape except for porous media which has lesser friction factor. Vaisi et al. [9] investigated the effect of fin on the heat transfer and pressure drop of a heat exchanger. The author revealed a net thermal enhancement of 9.3% with 19.8% lower pressure reduction obtained in the case of symmetrical fin arrangement compared to asymmetrical fin. Javaherdeh et al. [10] investigated on fin effect in a louvered fin and tube HX and obtained enhanced heat transfer. Not only twisted tape and fin alteration affects the heat transfer phenomenon but the working fluid also plays a crucial role in the thermal performance of the heat exchanger. Nanoparticles uniformly mixed to the primary fluid of order size less than 100 nm called nanofluid enhance the thermophysical characteristics of primary fluid. Furthermore, nanofluid is a better heat transfer agent compared to ordinary fluid, thus making it suitable to be used in various applications. Better thermal enhancement is possible in the presence of nanofluid due to the combined effect of various mechanisms, like nanoparticle interaction and clustering for enhanced thermal conductivity, Brownian motion of the particles in fluid flow, interfacial fluid–solid particle layering [11]. Several authors utilized nanofluid as a working fluid in different engineering applications such as refrigeration application [12], solar energy-based application[13, 14], electronic cooling systems [15, 16] Goodarzi et al. [15] investigated a micro channel heat sink as a model to the heat transfer for the elctronic device using Graphene-silver water based hybrid nanofluid and obtained 2.5% higher heat transfer at 0.06% volume fraction, heat exchangers [17], natural circulation loops [18], and automotive industry [19, 20].

Some recent research study relevant to twisted inserts with nanofluid is discussed. Salman et al. [21] numerically investigated the effect of twist ratio (2.9–4.9) and width of cut (0.5–1) on the heat transfer and friction factor of a circular tube with twisted tape using water as working fluid. Author reported with increment in twist ratio and width of cut, the heat transfer and friction factor decreases. Author reported the highest heat transfer and friction factor at 2.9 twist ratio and 0.5 width of cut in a circular tube with inserts. Furthermore, Rashidi et al. [22] numerically studied a square channel with twisted baffles of various twist ratios using nanofluid and found that lower nanoparticle volume concentration and lower twist ratio yield better thermohydraulic performance. Eiamsa-ard et al. [23] investigated a DTTI with TiO2–water as a nanofluid and revealed that a lower pitch and lower nanoparticle concentration yields a better HX. Also, Singh et al.[24] performed an experimental investigation on TTI using a hybrid nanofluid composed of Al2O3–TiO2–water and obtained enhanced overall performance. Several studies [25,26,27] revealed that twist ratio and nanoparticle concentration play a significant enhancement in HXs. Different nanofluids like Al2O3–water [28], TiO2–SiO2–water[29], TiO2–water [30], CuO–water[31] were investigated with twisted tapes and resulted in a better heat transfer medium. Therefore, combined nanofluid and turbulators improve HX performance. As per the literature review, various nanofluids of different types have been studied, at low concentration yields excellent heat transfer agent. Moreover, thermal devices like HX generate irreversibility which is also a significant parameter to identify the exergy distribution. Sheikholeslami et al. [32] investigated entropy generation in a turbulator using CuO–water nanofluid and revealed a net reduction in entropy generation due to a decrement in thermal boundary layer thickness. The author claimed nanofluid remarkably reduces the overall temperature. Bahiraei et al. [33] investigated a double-pipe HX with twisted turbulators and revealed a net lower entropy generation in cross arrangement than a parallel arrangement of turbulators. Meanwhile, several studies are available that analyze the second law of thermodynamics for nanofluids [34,35,36]. Recently, researchers [37,38,39,40,41] focused on a new type of nanofluid tri/ternary/tripartite hybrid nanofluid [TPHNF] which at lower volume concentrations yields a better overall performance index in HXs like evaporative coolers, automotive radiators. Turbulator inserts offer fluid flow destruction and boundary layer regeneration causes enhanced heat transfer, which is a motivation to select turbulators in compact heat exchangers as a thermal enhancer. From the literature review [42,43,44,45,46,47,48,49,50,51,52,53], no study is available on four E’s analysis using TPHNF’s as a working fluid to the turbulator inserts in HX as well as scant study available for the suitable selection of TPHNF as a working fluid to be utilized in a compact heat exchanger. The present investigation deals with four E’s (energy, exergy, economic, and environmental) comparative analysis of compact heat exchangers using TPHNF’s as working fluid utilizing various turbulators. The novelty of the present investigation is:-

  • Four E’s analysis of six different TPHNF utilizes as a hot working fluid in tube side in a compact HX.

  • Effect of turbulator inserts (TTI, PTTI, and DTTI) in HX with TPHNF as working fluids effects on the four E’s.

  • The combined effect of TPHNF’s and turbulators inserts on thermohydraulic parameters [performance evaluation criteria, sustainability index, performance index, and second law analysis] of compact HX.

  • CO2 discharge and running cost analysis for sagacious selection of turbulators and TPHNF’s to be used as working fluid.

Modeling and simulation

The theoretical performance-based analysis is studied on a wavy finned tube heat exchanger, cross unmixed fluid flow type, with dimensional detail as shown in Fig. 1. Air passes through the fin gap and hot fluid (termed as coolant) passes through staggered tubes. Meanwhile, a detailed dimension of the HX on both sides, air, and coolant was measured in the laboratory and tabulated in Table 1. Also, geometrical modifications inserts of TTI, PTTI, and DTTI inserts in tubes with dimensional details are shown in Fig. 2 and tabulated in Table 2. The present analysis focuses on exergy, energy, economic, and environmental analysis (4 E’s), with performance evaluation of a compact HX of staggered tube arrangement with turbulator inserts using different TPHNFs comprised of three different nanoparticles in terms of properties, behavior, and shapes. Also, the further investigation focuses on the effect of various inserts [TTI, PTTI, DTTI] in the coolant side of the heat exchanger on the entropy generation, irreversibility, and second law efficiency with Reynold number as varying parameter. For analysis, steady-state steady flow conditions for multi-fluid are considered along with the following general assumptions stated below.

  • The heat released by the hot fluid is gained by air (no heat loss to the environment)

  • Sink heat is ignored within HX.

  • The thermophysical properties of fluid are determined at mean temperature.

  • Inserts resistance is ignored.

Fig. 1
figure 1

Unmixed cross fluid flow compact heat exchanger

Full size image
Table 1 Dimensional details of selected compact heat exchanger
Full size table
Fig. 2
figure 2

Dimensional and pictorial configuration of modified turbulators inserts (TTI, PTTI, and DTTI)

Full size image
Table 2 Detail dimensions of studied turbulator inserts
Full size table

Available dimension of the compact heat exchanger of tube internal diameter of 8 mm and the length of HX is 340 mm measured in the laboratory as shown in Fig. 1. From the past study, passive techniques like twisted tape inserts are used as a performance enhancer. Therefore, it motivates to use the passive technique in the form of different turbulators for different TPHNF undercooling. For investigation, twisted tape pitch of 85 mm is considered to complete 4 turns; twisted tape thickness of 0.5 mm, and width of 5 mm is selected in such a way that it seats well in 8 mm diameter. Also, from the past study, lower twisted pitch improves performance; therefore in dimpled and perforated twisted tape, to create 16 perforation and dimpled position, lower twisted pitch of 21 mm is selected for the present investigation.

Numerical model in airside analysis

Air heat exchanger analysis, airside Colburn factor, Wang et al. [42] proposed that a correlation to determine Colburn factor of HX with wavy finned staggered tube configuration is determined as:

$$CF = \frac{{1.201}}{{\ln\left( {Re_{\text{a}}^{{2.921}} } \right)}}$$
(1)

Reynolds number and mass velocity on airside are determined as,

$$MV_{\text{a}} = \frac{{m_{\text{a}} }}{{A_{\text{fr}} }}\;and\; Re_{\text{a}} = MV_{\text{a}} \;*D_{\text{a}} /\mu_{\text{a}}$$
(2)

Convective heat transfer coefficient on airside is evaluated as,

$$h_{\text{a}} = \frac{{CF*MV_{\text{a}} *cp_{\text{a}} }}{{Pr_{\text{a}}^{2/3} }}$$
(3)

Fin efficiency of wavy configuration is evaluated as,

$$\eta_{\text{fin}} = \frac{{tanh\left( {\sqrt {2*\frac{{h_{\text{a}} }}{{\alpha_{\text{fin}} t_{\text{fin}} }}} r\theta } \right)}}{{\sqrt {2*\frac{{h_{\text{a}} }}{{\alpha_{\text{fin}} t_{\text{fin}} }}} r\theta }}$$
(4)

Non-dimensional parameter and geometrical parameters that influence fin efficiency are determined as,

$$\theta = \left( {\frac{{R_{\text{eq}} }}{r} - 1} \right)*\left( {1 + 0.35\left( {\ln\frac{{R_{\text{eq}} }}{r}} \right)} \right)$$
(5)
$$\frac{{R_{\text{eq}} }}{r} = 1.27*\left( {\frac{{Y_{\text{l}} }}{{Y_{\text{m}} }} - 0.3} \right)^{0.5}$$
(6)

and

$$Y_{\text{l}} = \sqrt {\left( {\frac{{P_{\text{t}} }}{2}} \right)^{2} + \left( {\frac{{P_{\text{l}} }}{2}} \right)^{2} }$$
(7)

Heat capacity of air is evaluated as,

$$C_{\text{a}} = \rho_{\text{a}} *V_{\text{a}} *A_{\text{fr}} *cp_{\text{a}}$$
(8)

Thermophysical properties of Tripartite hybrid nanofluids [Hot Fluid]

The tripartite hybrid nanofluid composition consists of three various nanoparticles (based on shape, nature, and characteristics) well spread mixed in the primary fluid water. Heat exchanger performance depends upon the thermophysical properties of the working fluid. Therefore, density, specific heat capacity, thermal conductivity, and viscosity play a key role in heat transfer and pressure drop penalty in a heat exchanger. Thus, it is an essential task to predict the thermophysical properties accurately. To investigate the application of nanofluid in a heat exchanger, following amalgamations of ternary nanoparticles are mixed, 0.6% of total volume concentration into the primary fluid water:

  1. i.

    Al2O3 + ZnO + TiO2

  2. ii.

    Al2O3 + ZnO + Graphene

  3. iii.

    Al2O3 + ZnO + SWCNT

  4. iv.

    Al2O3 + TiO2 + Graphene

  5. v.

    Al2O3 + TiO2 + SWCNT

  6. vi.

    Al2O3 + Graphene + SWCNT

Detail thermophysical characteristics of selected nanoparticles are listed in Table 3 [38,39,40,41]. Density of the tripartite hybrid nanofluid is calculated as [38]:

$$\rho_{\text{hnf}} = \omega_{1} \rho_{1} + \omega_{2} \rho_{2} + \omega_{3} \rho_{3} + \left( {1 - \omega_{1} - \omega_{2} - \omega_{3} } \right)\rho_{\text{pf}}$$
(9)
Table 3 Nanoparticles thermophysical characteristics [40]
Full size table

Subscripts 1, 2, and 3 represent the three different nanoparticles of an individual composition tripartite hybrid nanofluid where \(\omega = \omega_{1} + \omega_{2} + \omega_{3}\) which represents the total volume fraction. Tripartite hybrid nanofluid heat capacity is expressed as[39]:

$$\begin{aligned} \left( {\rho c_{\text{p}} } \right)_{\text{hnf}} &= \omega_{1} \left( {\rho c_{\text{p}} } \right)_{1} + \omega_{2} \left( {\rho c_{\text{p}} } \right)_{2} + \omega_{3} \left( {\rho c_{\text{p}} } \right)_{3} \\&\quad + \left( {1 - \omega_{1} - \omega_{2} - \omega_{3} } \right)\left( {\rho c_{\text{p}} } \right)_{\text{pf}} \end{aligned}$$
(10)

Transport fluid properties of the tripartite hybrid nanofluid depend upon the primary fluid, nanoparticle morphology (spherical, platelet, and cylindrical), nanoparticle type, and individual volume concentration of nanoparticle. Thus, effective dynamic viscosity and effective thermal conductivity of tripartite hybrid nanofluid are evaluated as[40]:

$$\omega \tau_{\text{hnf}} = \omega_{1} \tau_{{\text{nf}},1} + \omega_{2} \tau_{nf,2} + \omega_{3} \tau_{{\text{nf}},3}$$
(11)
$$\omega \alpha_{\text{hnf}} = \omega_{1} \alpha_{{\text{nf}},1} + \omega_{2} \alpha_{nf,2} + \omega_{3} \alpha_{{\text{nf}},3}$$
(12)

where \(\tau_{{\text{nf}},i}\) and \(\alpha_{{\text{nf}},i}\) are dynamic viscosity and thermal conductivity, respectively, for the mono nanofluid for total volume fraction consisting of ith (i = 1, 2, or 3) kind of suspended nanoparticle into the base fluid. Nanofluid viscosity and conductivity of the ith kind of nanoparticle (of required shape) spread are determined by [41], respectively,

$$\tau_{{\text{nf, i}}} = \tau_{\text{pf}} \left( {1 + \beta_{\text{i}} \omega + \lambda_{\text{i}} \omega^{2} } \right)$$
(13)
$$\frac{{\alpha_{{\text{nf, i}}} }}{{\alpha_{{\text{pf}}} }} = \frac{{\alpha_{{\text{p, i}}} + \left( {\zeta_{{\text{i}}} - 1} \right)\alpha_{{\text{pf}}} + \left( {\zeta_{{\text{i}}} - 1} \right)\omega \left( {\alpha {}_{\text{p,i}} - \alpha_{\text{pf}} } \right)}}{{\alpha_{\text{p,i}} + \left( {\zeta_{{\text{i}}} - 1} \right)\alpha_{{\text{pf}}} - \omega \left( {\alpha {}_{\text{p,i}} - \alpha_{\text{p,f}} } \right)}}$$
(14)

where the enhancement coefficients for the dynamic viscosity (\(\beta\) and \(\lambda\)) and empirical shape coefficient, \(\zeta\), for different shapes of nanoparticles are enlisted in Table 4. Different shapes and sizes of the nanoparticle influence its thermophysical properties. SWCNT (Single-walled carbon nanotube) nanoparticles are cylindrical, while graphene nanoparticles are of platelet shape; meanwhile, remaining nanoparticles are of spherical morphology. Above empirical correlations are used in the entire investigation to determine the thermophysical properties of tripartite hybrid nanofluids. Also, thermophysical properties of a fluid determine applying the suitable equations are listed in Table 5.

Table 4 Enhancement and empirical morphology coefficients [41]
Full size table
Table 5 Thermophysical properties of THNF with water primary fluid
Full size table

Heat exchanger performance evaluation

Hot side total heat capacity rate is given by,

$$C_{\text{f}} = \rho_{\text{hnf}} V_{\text{f}} c_{\text{p,hnf}}$$
(15)

Hot fluid passes through tubes and under steady flow parallel tube combination pressure drop in a single tube is expressed as,

$$\Delta p_{\text{f}} = 0.5 \times f_{\text{f}} \times \frac{L}{{D_{\text{h}} }} \times \rho_{\text{hnf}} \times V^{2}$$
(16)

where Nusselt number and friction factor for plain tube fluid flow under turbulent flow regime has determined using suitable correlations proposed by Gnielinski [43];

$$f_{\text{f}} = \left[ {1.58 \times \ln ({\text{Re}}_{\text{f}} ) - 3.28} \right]^{ - 2} ,0.5 < pr_{\text{f}} < 2000,3000 < {\text{Re}}_{{\rm f}} < 5000000$$
(17)
$$Nu = \left[ {\left( {\text{Re} _{\text{f}} - 1000} \right) \times {\text{Pr}} _{\text{f}} \times 0.5 \times \left( {\frac{{f_{\text{f}} }}{{1 + 12.7 \times \left( {{\text{Pr}} _{\text{f}}^{{2/3}} - 1} \right) \times \left( {\frac{{f_{\text{f}} }}{2}} \right)^{{0.5}} }}} \right)} \right]$$
(18)

where non-dimensional parameters evaluated as, \(\mathop {{\text{Pr}} }\limits_{{\rm f}} = \frac{{\tau _{{\text{hnf}}} C_{{\text{p ,hnf}}} }}{{\alpha _{{\text{hnf}}} }}\) and \({\text{Re}}_{\text{f}} = \frac{{\rho _{{\text{hnf}}} VD_{\text{h}} }}{{\tau _{{\text{hnf}}} }}\).

Now, under the passive technique when twisted turbulator inserts introduced, Nusselt number in turbulent flow is determined from correlation proposed by Manglik et al.[44]

$$Nu_{{\mathrm{TTI}}} = 0.023\text{Re} _{\mathrm{f}}^{{0.8}} {\text{Pr}} _{\mathrm{f}}^{{0.4}} \left( {1 + 0.769\frac{{2D_{\mathrm{h}} }}{Y}} \right)\left( {\frac{\pi }{{\pi - 4{\raise0.7ex\hbox{${t_{\mathrm{i}} }$} \!\mathord{\left/ {\vphantom {{t_{\mathrm{i}} } {D_{\mathrm{h}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${D_{\mathrm{h}} }$}}}}} \right)^{{0.8}} \left( {\frac{{\pi + 2 - 2{\raise0.7ex\hbox{${t_{\mathrm{i}} }$} \!\mathord{\left/ {\vphantom {{t_{\mathrm{i}} } {D_{\mathrm{h}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${D_{\mathrm{h}} }$}}}}{{\pi - 4{\raise0.7ex\hbox{${t_{\mathrm{i}} }$} \!\mathord{\left/ {\vphantom {{t_{\text{i}} } {D_{\mathrm{h}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${D_{\mathrm{h}} }$}}}}} \right)^{{0.2}}$$
(19)

While friction factor for twisted turbulator inserts is determined using correlation of Smithberg and Landis proposed for a turbulent case with water as fluid flow [45] as,

$$f_{\text{f}} = 4\left( {0.046 + 2.1\left( {\frac{Y}{{D_{\text{h}} }} - 0.5} \right)^{{ - 1.2}} } \right)\left( {\frac{{\text{Re} _{{f}} }}{{1 + 2/\pi }}} \right)^{{ - Z}} ,\quad 0.5 < pr_{\text{f}} < 2000$$
(20)

where

$$Z = 0.2\left( {1 + 1.7\left( {\frac{Y}{{D_{\text{h}}}}} \right)^{{ - 0.5}} } \right)$$
(21)

While moving to the next turbulator, PTTI and DTTI, friction factor, and Nusselt number is determined using correlation proposed by Dagdevir and Ozeceyhan [46], respectively;

For perforated twisted turbulator inserts case,

$$f_{\text{f}} = 0.986776\text{Re} _{\text{f}}^{{ - 0.28012}} \left( {0.01 + \frac{{P_{p} }}{Y}} \right)^{{ - 0.13672}} ,2 < {\mathrm{Pr}} _{\text{f}} < 36.2,2300 < \text{Re} _{\text{f}} < 22754$$
(22)
$$Nu_{{\text{PTTI}}} = 0.034299\text{Re} _{\text{f}}^{{0.785361}} {\mathrm{Pr}} _{\text{f}}^{{0.413538}} \left( {0.01 + {\raise0.7ex\hbox{${P_{\text p} }$} \!\mathord{\left/ {\vphantom {{P_{\text p} } \text Y}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$\text Y$}}} \right)^{{ - 0.09157}} ,\quad 2 < {\mathrm{Pr}} _{\text{f}} < 36.2$$
(23)

When dimpled twisted turbulator inserts case,

$$f_{\text{f}} = 0.970112\text{Re} _{\text{f}}^{{ - 0.27091}} \left( {0.01 + \frac{{P_{\text{d}} }}{Y}} \right)^{{ - 0.13672}} ,2 < {\text{Pr}} _{\text{f}} < 36.2,2300 < \text{Re} _{\text{f}} < 22754$$
(24)
$$Nu_{{\text{DTTI}}} = 0.033199\text{Re} _{\text{f}}^{{0.800351}} {\mathrm{Pr}} _{\text{f}}^{{0.358743}} \left( {0.01 + {\raise0.7ex\hbox{${P_{d} }$} \!\mathord{\left/ {\vphantom {{P_{\text{d}} } Y}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$Y$}}} \right)^{{ - 0.19756}} ,\quad 2 < {\mathrm{Pr}} _{\text{f}} < 36.2$$
(25)

Now overall heat transfer coefficient (UA) of the HX is evaluated as,

$$\frac{1}{{UA}} = \frac{1}{{\eta _{\text{o}} h_{\text{a}} A_{\text{a}} }} + \frac{1}{{h_{\text{f}} A_{\text{f}} }} + \frac{{\ln \left( {\frac{{d_{\text{0}} }}{{d_{\text{i}} }}} \right)}}{{2\pi L\alpha _{\text{t}} }}$$
(26)

where overall surface effectiveness is determined as,

$$\eta _{\text{o}} = 1 - \frac{{A_{{\text{fin}}} }}{{A_{\text{a}} }}\left( {1 - \eta _{{\text{fin}}} } \right)$$
(27)

While the effectiveness of cross unmixed fluid flow type HX is determined as[47],

$$\varepsilon = 1 - \exp \left[ {\frac{{NTU^{0.22} }}{{C^{*} }}\exp \left( { - C^{*} NTU^{0.78} - 1} \right)} \right]$$
(28)

Net heat transfer rate across HX is evaluated as,

$$Q = \varepsilon C_{\min } \left( {T_{{\text{f}},{\text{in}}} - T_{{\text{a}},{\text{in}}} } \right)$$
(29)

Tube side pumping power, fan and tube pumping efficiency are considered as 65%, and are calculated by,

$$P{\text{pp}} = \frac{{\Delta p_{{{\text{f}} \times CFR}} }}{{\eta _{{\text{p}}} }}$$
(30)

Airside net pressure drop is determined by[48],

$$\Delta p_{\text{a}} = \frac{{MV_{\text{a}} ^{2} }}{{2\rho _{{\text{a,in}}} }}\left[ {\left( {1 + \sigma ^{2} } \right)\left( {\frac{{\rho _{{\text{a,in}}} }}{{\rho _{{\text{a,e}}} }} - 1} \right) + f_{\text{a}} \frac{{2F_{\text{d}} }}{{D_{{\text{h,a}}} }}\left( {\frac{{\rho _{{\text{a,in}}} }}{{\rho _{{\text{a,e}}} }} - 1} \right)} \right]$$
(31)

Fan power required to drive the fan is determined as,

$$F_{{{\text{PP}}}} = \frac{{A_{{{\text{fr}}}} \times V_{{{\text{a}} \times \Delta p_{{\text{a}}} }} }}{{\eta _{{\text{p}}} }}$$
(32)

After evaluation of heat transfer and power consumption, a related performance parameter index is evaluated as [49]

$$PI = \frac{Q}{{P_{{{\text{PP}} + {\text F}_{{\text{P}}} }} }}$$
(33)

Entropy analysis of wavy finned tube heat exchangers is necessary for qualitative energy analysis. Two unmixed fluids flow mainly air and hot fluid, air is considered as a compressible fluid flow while the latter one remains incompressible within the heat exchanger. Thus, entropy generation is determined as the sum of airside entropy and tube side entropy. Net entropy generation is calculated as:

$$\dot{S}_{{\text{gen}}} = \dot{m}_{\text{a}} \left[ {c_{{\text{p},\text{a}}} \ln \frac{{T_{{\text{a},\text{e}}} }}{{T_{{\text{a},\text{in}}} }} - R_{\text a} \ln \frac{{p_{{\text{a},\text{e}}} }}{{p_{{\text{a},\text{in}}} }}} \right] + \dot{m}_{\text f} \left[ {c_{{\text{p},\text{hnf}}} \ln \frac{{T_{{\text{f},\text{e}}} }}{{T_{{\text{f},\text{in}}} }} - \frac{{p_{{\text{a},\text{e}}} - p_{{\text{a},\text{in}}} }}{{\rho _{{\text{hnf}}} T_{{\text{f},\text{mean}}} }}} \right]$$
(34)

Exergy loss by hot fluid (tube side) is the addition of heat transfer with thermal entropy generation and viscous entropy generation across tube side is calculated as,

$$\Delta Ex_{\text{f}} = Q + T_{0} \left[ {\dot{m}_{\text{f}} c_{{\text{p},\text{hnf}}} \ln \left( {{{T_{{\text{f, in}}} } \mathord{\left/ {\vphantom {{T_{{\text{f, in}}} } {T_{{\text{f},\text{e}}} }}} \right. \kern-\nulldelimiterspace} {T_{{\text{f},\text{e}}} }}} \right) - \dot{m}_{\text{f}} {{\Delta p_{\text{f}} } \mathord{\left/ {\vphantom {{\Delta p_{\text{f}} } {(\rho _{{\text{hnf}}} T_{{\text{f},\text{mean}}} )}}} \right. \kern-\nulldelimiterspace} {(\rho _{{\text{hnf}}} T_{{\text{f},\text{mean}}} )}}} \right]$$
(35)

whereas cold air takes heat from the hotter fluid and exergy gain of air is evaluated as,

$$\Delta Ex_{\text{a}} = Q - T_{0} \left[ {\dot{m}_{\text{a}} c_{{\text{pa}}} \ln \left( {{{T_{{\text{a ,e}}} } \mathord{\left/ {\vphantom {{T_{{\text{a ,e}}} } {T_{{a,\text{in}}} }}} \right. \kern-\nulldelimiterspace} {T_{{a,\text{in}}} }}} \right) + \dot{m}_{\text{a}} R\ln \left( {{{p_{{\text{a,in}}} } \mathord{\left/ {\vphantom {{p_{{\text{a,in}}} } {p_{{\text{a ,e}}} }}} \right. \kern-\nulldelimiterspace} {p_{{\text{a ,e}}} }}} \right)} \right]$$
(36)

After exergy analysis of air and hotter fluid, second law efficiency or exergetic efficiency is calculated as,

$$\eta _{2} = \frac{{\Delta Ex_{{\text{a}}} }}{{\Delta Ex_{{\text{f}}} }}$$
(37)

Now, the irreversibility is given by,

$$I = T_{0} \dot{S}_{{{\text{gen}}}}$$
(38)

Entropy generation number, a non-dimensional parameter adopted by Mishra et al. [50] to study the effect of heat capacity with entropy generation, is determined as,

$$N_{{{\text{gen}}}} = \frac{{S_{{{\text{gen}}}} }}{{C_{{\max }} }}$$
(39)

To identify ultimate utilization of the resources on application sustainability index (SI) is studied which is defined by the exergy ratio [51].

$$SI = \frac{1}{{\left( {1 - \eta_{2} } \right)}}$$
(40)

Based on different turbulators used in the investigation, the heat transfer enhancement coefficient is defined as the Nusselt number ratio. It indicates the heat enhancement due to geometry modification. For different turbulators, heat transfer enhancement compared to Nusselt number with plain tube is defined as,

$$Nu_{r} = \frac{{\left( {Nu_{{\text{f}}} } \right)_{{{\text{TTI/PTTI/DTTI}}}} }}{{\left( {Nu_{{\text{f}}} } \right)_{{{\text{PT}}}} }}$$
(41)

Due to the use of different turbulators, heat enhancement occurs at the cost of pressure drop penalty; relative pressure drop penalty coefficients for different inserts are defined as,

$$f_{{\text{r}}} = \frac{{\left( {f_{{\text{f}}} } \right)_{{{\text{TTI/PTTI/DTTI}}}} }}{{\left( {f_{{\text{f}}} } \right)_{{{\text{PT}}}} }}$$
(42)

The performance evaluation criteria (PEC) combine both heat transfer enhancement coefficient and relative pressure drop coefficient ratios to determine heat transfer improvement at a given pumping power consumption. To judge the practical luxury of Turbulator inserts in HX, PEC is evaluated at equal power consumption. The mathematical formulation of pressure drop and coolant flow rate at constant power requirement for plain tube HX and turbulator inserts HX can be expressed as

$$(CFR \times \Delta p)_{\text{PT}} = (CFR \times \Delta p)_{\text{TTI/PTTI/DTTI}}$$
(43)

Further, it may be encountered as,

$$(f_{\text{f}} {\text{Re}}^{3} )_{\text{PT}} = (f_{\text{f}} {\text{Re}}^{3} )_{\text{TTI/PTTI/DTTI}}$$
(44)

On combining Eqs. (43) and (44), at a given pumping power PEC is defined by Webb et al. [52] as,

$$PEC = \frac{{Nu_{\text{r}} }}{{\left( {f_{\text{r}} } \right)^{{\left( \frac{1}{3} \right)}} }}$$
(45)

The utilization of various inserts and TPHNFs in heat exchangers enhances performance at cost of pumping power. Power consumption in terms of CO2 discharge will be a major criterion for analysis. Coal-based power generation supplies electricity to the main power substation. CO2 discharge analysis can be claimed to utilize carbon emission factors. CO2 discharge [53] is evaluated as:

$$Dis_{{\text{CO}_{2} }} = \frac{{f_{{\text{CO}_{2} }} P_{{\text{Net}}} t_{{\text{run}}} }}{{10^{6} }}$$
(46)

where \(Dis_{{{\text{CO}}_{2} }}\) is the carbon dioxide discharge to the environment in ton per year, and\(f_{{\text{CO}}_2}\) represents the carbon discharge factor. The carbon discharge factor is taken to be 0.820 kgCO2/kWh (location based). \(P{}_\text{net}\) that represents the net power consumption in kW requires to run the equipment in an hour while \(t_\text{run}\) is the annual operating time (h/Annum) of the heat exchanger. Heat exchanger operating cost is determined by net electricity consumption and is evaluated as:

$$HX_{{{\text{Operating Cos}} t}} = P_{\text{Net}} t_{\text{run}} C_{\text{electricity}}$$
(47)

Data analysis is evaluated by assuming heat exchangers run continuously twenty-four working hours per day and a total of 180 days of the year before maintenance. The electricity price (\(C_{\text{Electricity}}\)) is considered as 8 per kWh.

Numerical procedure and model validation

The governing set of coupled equations are solved using EES (Engineering Equation Solver) to evaluate the bulk mean temperature of both fluids, internal fluid (hot fluid), and external fluid flow (air). Estimation of temperature outlets is programmed to determine fluid properties. For energy and second law analysis of wavy finned tube heat exchanger with Turbulators for various TPHNFs, simulation methodology with the help of process layout to get outcomes is demonstrated in Fig. 3.

Fig. 3
figure 3

Process layout of Numerical model

Full size image

Fluids entrance temperatures (Tf,in = 343 K, Ta,in = 303 K), Reynolds number, and various TPHNFs thermophysical properties at 0.6% volume fraction with constant air velocity 5 m s−1 are assigned as an initial inlet condition for the HX to simulated for different turbulators. Convection heat transfer coefficient for TPHNFs and air helps to determine the overall heat transfer coefficient using EES coding, following Ɛ-NTU technique. The various analysis is simulated at different Reynolds number of TPHNF for distinguishing turbulator inserts.

Nusselt number and friction factor validation of the present study results are compared to the Eiasmaard et al. [3], Nakchi et al. [31], and experimental investigation of Saysroy et al. [26] for heat transfer and pressure drop in a tube fitted with conventional twisted tapes. Comparison is performed for Reynolds number ranges 2400–15,000 in turbulent flow region. Results are shown in Fig. 4a Nusselt number, (b) friction factor with Reynolds number of twisted pitch 85 mm, and water as a working medium. It can be observed that the heat transfer and friction factor of the present study for TTI are in good agreement with experimental data [26] and show a maximum deviation of 6.2% for heat transfer and 10.15% for friction factor. Also, the present study of DTTI shows a similar increment with the Reynolds number increment and found higher heat transfer due to induction of radial flow that improves the thermal gradient and energy transfer near the tube surface. Due to the inversely proportional Reynolds number with friction factor as specified in the Moody chart for the turbulent regime, friction factor also shows a similar trend with Reynolds number for the cases studied. For PTTI, the present study friction factor has shown an acceptable mean difference of 10.1% in the entire range of Reynolds number with the numerical data of Eiasmaard [3]. Present investigations are acceptable in good agreement compared to the previous work with conventional twisted tape inserts.

Fig. 4
figure 4

Comparison with conventional twisted tape, twisted pitch 85 mm, turns = 4, a Nusselt number with Re b friction factor with Re for water

Full size image

Result and discussion

Effects of TTI, PTTI, and DTTI on Nusselt number with Reynolds number of TPHNF 6 utilized in wavy finned tube HX are compared and presented in Fig. 5. In general, the Nusselt number varies linearly with the Reynolds number. Linear variation is mainly due to amplified turbulent intensity, which is also a reason for intensified convective heat transfer coefficient. Turbulators used in air HX enhance Nusselt number significantly. However, turbulators created a radial intense mixing of the fluid which is normally absent in PT HX. The reason for the enhancement of Nusselt number in the presence of turbulators in HX is mainly due to swirl flow generation, thermal boundary layer interruption, and radial pressure gradient generation. However, among turbulators, PTTI in HX shows larger improvement than TTI, the presence of perforated holes allows an interruption in the fluid flow direction causing redevelopment of boundary layer near the perforated holes, and due to this Nusselt number improves. As dimpled shape causes to hindrance in fluid flow and creates an additional temperature gradient in radial direction, DTTI shows higher Nusselt number than TTI. Now, DTTI in HX supplements larger surface for radial thermal gradient than PTTI which results a higher Nusselt number for DTTI compared to PTTI in HX. However, larger the number of dimpled and perforated holes, higher the Nusselt number in returns due to frequent interruption in the thermal boundary layer. However, at lower Re (below 7900), due to increased resident time of fluid flow causes a higher percentage increment of Nusselt number. However, TTI shows 64.5–25.8%. PTTI 68.24–31.6%, while DTTI shows 73.23–43.98% higher Nusselt number than without any turbulators at lowest and highest Reynolds number. Therefore, friction loss caused due to the presence of with and without turbulators with Reynolds number in the range of (2400–15,000) is presented in Fig. 5. Curve trends show a similar reduction of frictional loss of turbulators inserts and the plain tube. However, the friction factor shows a progressive decrement with an increased Reynolds number. At lower Re, high frictional forces occur at the backward of twisted turbulators and thus enhance the vortices generation results in higher friction loss. The friction factor of turbulators is higher compared to plain tube. It mainly increased surface in the presence of turbulators, amplified swirl intensity, and the loss of higher viscosity vicinity to the tube surface and resulted in a blockage in fluid flow, which are several reasons for frictional factor loss. PTTI and DTTI create additional interruption near the perforation holes and dimpled positions, thus resulting in larger friction factor than TTI. However, attach flow at dimpled position results further higher loss of viscosity which is absent in PTTI. Thus, DTTI shows higher frictional loss that PTTI in HX. However, TTI shows 38.8–40%, PTTI 62.1–65%, and DTTI results in 65.1–68.2% higher frictional factor compared to plain tube HX.

Fig. 5
figure 5

Nusselt number and friction factor with Reynolds number

Full size image

Comparative effects of overall heat transfer coefficient and pressure drop across the HX of different turbulators for TPHNF 6 (Al2O3 + Graphene + SWCNT—water) with Reynolds number compared to plain tube configuration are shown in Fig. 6. Turbulators cause swirl flow generation and a relative centrifugal force created between the turbulators and tube wall. Also, fluid residence time along with an increased mixed fluid flow between tube surface and tube core area amplifies the secondary flow; therefore, in turbulators overall heat transfer coefficient is higher compared to the plain tube for each Reynolds number. Now, among turbulators, DTTI shows the highest overall heat transfer coefficient than PTTI while lowest for TTI. While at a lower Reynolds number, below 7900, a significant enhancement in the presence of turbulators is obtained. At Re 2400, the result reveals that DTTI shows 20.6%, PTTI 18.6%, and TTI shows 17.2% higher overall heat transfer coefficient when applied in HX. As TTI caused secondary flow near the twisted tape and increased the residing time of fluid flow while along with the above phenomenon perforated twisted turbulator additionally causes an interruption in the boundary layer near the perforated holes and dimpled curvature of DTTI produces additional radial flow and redevelopment of boundary layer generation of same hole diameter and pitch than PTTI which could be the reason for increased overall heat transfer coefficient. Significant enhancement occurs with a penalty in pressure drop. Pressure drop variation with Reynolds number for various inserts for THNF is represented in Fig. 6. Pressure drop variation trend for turbulators was found similar to the plain tube with Reynolds number. Pressure drop increases with increased Reynolds number. Turbulators insert shows higher pressure drop than the plain tube. Turbulators cause immense secondary flow, addition causes a high blockage of the fluid inside the tube of the tube with inserts and with high loss of viscosity which resulted in a higher pressure drop. Moreover, at lower Re, the pressure drop is lower while at higher Re, greater than 7900, it causes an immense pressure drop which is due to higher interaction among pressure force and inertial force at the boundary layer. DTTI shows 65.6–68.2% higher pressure drop, PTTI shows 62.8–65.0% higher penalty, while TTI shows 39.5–40.8% higher pressure drop penalty in HX due to higher friction factor at lowest and highest Reynolds number, respectively.

Fig. 6
figure 6

Pressure drop and overall heat transfer coefficient with Reynolds number

Full size image

Performance evaluation criteria or thermal performance factor identifies the practical use and benefits of the compact HX with various turbulator inserts. PEC evaluation requires estimating the energy utilization in the presence of various turbulators at a given input power using Eq. (44). Thermal performance factor variation with different turbulator inserts (TTI, PTTI, and DTTI) for different hot working fluids is presented in Fig. 7, Re 3600. For all the cases studied, PEC more than unity is considered as an energy saving in terms of performance enhancement. DTTI in HX attributes the highest PEC for all hybrid nanofluids studied and shows a mean of 2.29 PEC due to higher heat transfer than pressure drop. The lowest mean PEC of 1.40 obtains in the case of TTI, while PTTI in HX contributes an intermediate mean PEC of 2.24. This is because at lower Re, thermal enhancement is more dominant than friction factor in the presence of turbulators. Moreover, inspection of various hybrid working fluids utilized in HX with various inserts reveals a little but significant variation in PEC. Among several TPHNFs, TPHNF 6 achieves the highest PEC than the rest of the hybrid working fluid studied. The preferred order of hybrid working fluid based on higher PEC in terms of energy savings should be TPHNF 6 most likely preferable, while the least preferred hybrid nanofluid would be TPHNF 4 (Al2O3 + TiO2 + Graphene—Water); therefore, for exergy, entropy, and second law analysis TPHNF 6 as a working fluid has been investigated.

Fig. 7
figure 7

PEC of turbulators for TPHNFs

Full size image

Requirement of second law analysis in detail to have the minimum entropy and mean entropy principles within HX is observed. The utilization of qualitative energy in terms of exergy change of coolant and exergy change in the air of the HX under different geometrical modifications for TPHNF 6 at different Reynolds numbers is presented in Fig. 8. At lower Re, thermal entropy generation is dominant; both exergy change in air and exergy change in the coolant (hot fluid transfers energy to secondary fluid air) show a large improvement with turbulators inserts, as inserts in the plain tube cause a restriction in flow and cause blockage of flow which amplifies the residence time which causes higher exergy exchange between the fluids compared to air HX of plain tube configuration. Also, the radial direction of fluid flow dominancy in DTTI than PTTI in turbulators causes further intensification in exergy exchange, and thus, DTTI results higher exergy exchange. Beyond Re 6500, however, an enhancement in exergy exchange continued due to increment in turbulent intensification although the rate of increment remains lower due to viscous entropy generation dominancy than thermal entropy. However, DTTI in HX caused the highest (18.1–2.16%) exergy change of coolant due to high secondary flow generation than PTTI (16.23–1.51%) and lowest for TTI (15.02–1.2%) at lowest Re 2400 and highest Re 15,000, respectively. Radial heat exchange improves, as DTTI inserts cause the highest radial flow due to dimpled extruded shape; thus, exergy change of air improves. Exergy change of air also obtains highest in the case of DTTI at mean improvement of 8.1% and lowest for TTI with a mean enhancement of 5.7%, while an intermediate range of enhancement obtains for PTTI air HX.

Fig. 8
figure 8

Exergy change of coolant and air with Reynolds number

Full size image

As the overall heat transfer coefficient in the case of HX with DTTI is higher while lowest for HX without turbulator inserts for the same reason, heat transfer has also shown similar variation with Reynolds number as shown in Fig. 9. At lower Re 2400, under modified turbulators inserts, the percentage in heat transfer enhancement is highest obtained for DTTI (24.75%) and lowest for TTI (21.8%) due to higher thermal boundary layer regeneration as well as radial flow with higher resident time allows the fluid for higher heat transfer. Also, another dimensionless number entropy generation number variation with Reynolds number for various turbulator inserts is shown in Fig. 9. Entropy generation number depends upon the entropy generation and heat capacity. Increased Re increases the viscous entropy generation as well as thermal entropy generation of the fluids; however, higher Reynolds number viscous entropy generation dominates over thermal entropy generation. Thus, entropy generation number increases with Re. However, a comparison analysis reveals that DTTI shows mean increment of 5.9%, PTTI 5.0%, and TTI has 4.4% higher entropy generation number. Entropy generation number increment is comparatively still lesser than heat transfer enhancement of HX with various inserts; therefore, results suggest a better design of compact HX achieved with turbulators.

Fig. 9
figure 9

Heat transfer and entropy generation number with Reynolds number

Full size image

Effects of various six TPHNFs utilized as a working fluid on second law efficiency in HX with different turbulator inserts at lower Re 3600 are explored in Fig. 10. Second law efficiency or exergetic efficiency indicates the utilization of qualitative energy to bring up better thermal design systems. Higher efficiency conveys an improved thermal design of the HX. Therefore, different turbulators made a significant improvement in exergetic efficiency compared to HX with plain tubes and it is due to a larger increase in exergy loss by the hot fluid (TPHNFs) than exergy gain in air. However, among turbulators, as utilization of energy and exergy exchange betters in DTTI than PTTI and least for TTI, as energy utilization gets better thus, DTTI in HX, working fluid studied, showing the highest second law efficiency compared to remaining inserts while the lowest obtained for PT HX. Thus, an HX with various turbulators inserts effectively aimed at a better thermal device. Although TPHNF has also shown an impact on exergetic efficiency, the lowest percentage enhancement in the range of 1.54–2.47% of second law efficiency was obtained for the TPHNF 1 (Al2O3 + ZnO + TiO2—Water) type for TTI and DTTI in HX, respectively, while highest improvement in exergetic efficiency obtained when operated with TPHNF 6 (Al2O3 + Graphene + SWCNT—Water) in the range of 1.86–2.74% for air HX with TTI and DTTI, respectively, compared to HX with plain tube configuration. Therefore, from the second law analysis, HX operated with TPHNF 6 working fluid and DTTI turbulators performs better compared to other turbulators. However, for every turbulators studied, the preferred order of using TPHNF as a working fluid in air HX on exergetic efficiency basis to be as TPHNF 6 > TPHNF 4 > TPHNF 2 > TPHNF 5 > TPHNF 3 > TPHNF 1.

Fig. 10
figure 10

Second law efficiency variation with turbulators utilizing TPHNFs

Full size image

Also, a parameter that involves the combined effect of heat transfer and power requirement to run an HX is the performance index. The performance index of HX under different geometrical modifications and various hybrid nanofluids is presented in Fig. 11 at Re 3600. DTTI offers higher swirl generation as well as boundary layer interruption due to the presence of dimpled on twisted turbulators which enhances heat transfer more compared to PTTI and TTI in HX than pumping power required. Therefore, the performance index obtained highest when DTTI in HX is applied while among turbulators lowest obtained when HX with PTTI and TTI is used. DTTI in HX operated with different TPHNF working fluid shows the lowest increment of 4.25% PI in HX of plain tubes operated with TPHNF1 and highest PI improvement of 4.8% with TPHNF 6 due to significant thermophysical behavior and morphological change. Among various hybrid nanofluids operated, a range of 2.8–3.38% higher-performance index obtains in TTI arrangement compared to plain tube HX for TPHNF 1 and TPHNF 6, respectively. However, different geometrical modifications with different hybrid nanofluid show a significant improvement in performance index and the order of performance index enhancement to prioritize a working fluid should follow as TPHNF 6 > TPHNF 4 > TPHNF 2 > TPHNF 5 > TPHNF 3 > TPHNF 1 in any turbulators inserts in HX compared to plain tube HX.

Fig. 11
figure 11

Performance index with TPHNFs for turbulators

Full size image

Moreover, the purpose of turbulators is to enhance the heat exchange between hot fluids (TPHNFs) or coolant and air of a HX. Various inserts enable hotter fluid or coolant to transfer its heat to the air at a faster rate. So far now, lower Reynolds number shows a great improvement in heat transfer utilizing turbulator inserts. Therefore, the coolant or hot fluid (TPHNF 6) that exits temperature of HX with various turbulator inserts at lower Re (below 7900) is depicted in Fig. 12. When mass flow increased residence time decreased; therefore, temperature drop has reduced. However, turbulator inserts improved the radial fluid flow direction which allows the tube core hot fluid to strike on the tube wall from which air takes the heat. And due to the high radial temperature gradient, a higher temperature drop is possible. Due to presence of dimpled shape in the DTTI in the HX, the dimpled surface forces the fluid in normal direction of the fluid flow thus brings larger temperature drop compared to PTTI and no additional radial flow occurs in case of TTI in HX and thus results the lowest temperature reduction. Although at Re 2400, DTTI has been able to maximum 1.05 K, PTTI has 0.84 K, and TTI has managed to 0.74 K lowered hot fluid exit temperature compared to HX with plain tubes configuration.

Fig. 12
figure 12

Hot fluid exit temperature with Reynolds number

Full size image

The best way to study energy utilization can be understood in terms of entropy analysis. Higher the entropy, lesser effectively use of energy within an HX. In general, thermodynamically, HX of lower entropy should be preferred. For a fluid flow, heat exchange process, entropy causes due to thermal change as well as the pressure drop across the flow. As seen from Fig. 13, thermal change is quite appreciable in low Reynolds number and beyond that mass flow rate increment thermal change is little significant and viscous entropy gets dominant. Therefore, the entropy change of coolant remains near about the same, see Fig. 13, beyond Re 6500. More radial flow in the presence of DTTI turbulators inserts, secondary flow, and vorticity enables the larger thermal change and pressure drop than other inserts studied. Among studied turbulators, the highest entropy change of 5.3% in the case of DTTI, 4.2% intermediate for PTTI, and lowest 3.5% for TTI in HX compared to without turbulated HX at Re 6500. Also, irreversibility variation with Re for different turbulators in HX for TPHNF 6 as a working fluid is presented in Fig. 14. Irreversibility signifies the entropy generation as it is proportional to it, while entropy generation is proportional to the mass flow rate; therefore, the trend shows increased irreversibility with Re.

Fig. 13
figure 13

Entropy change of coolant with Reynolds number for various turbulators

Full size image
Fig. 14
figure 14

Irreversibility with Reynolds number for various turbulators

Full size image

Irreversibility also signifies the exergy loss difference among heat exchanging fluids. It is found that even turbulators inserts cause higher irreversibility compared to without turbulator insert. A common order of higher heat transfer and pressure drop follows as DTTI shows highest and lowest for TTI while an intermediate variation in PTTI HX of studied working fluids. This is because DTTI creates extra vorticity and produces a regeneration of boundary layer at the dimpled positions and is sufficiently more than that has produced at perforated positions. Moreover, a comparison analysis reveals that at Re 6500, DTTI turbulators inserts have caused 4.0%, followed by PTTI 3.0% and 2.4% higher irreversibility with TTI in HX compared to that of plain tube HX.

A non-dimensional parameter, SI, depends upon coolant exergy change and exergy loss, which reveals the effective energy utilization. However, a study reveals that SI increased with the increase in the mass flow rate of coolant. A variation in SI with several studied working fluids for different turbulator inserts of HX is presented in Fig. 15. HX without inserts shows relatively lower SI compared to inserts. Meanwhile, as coolant exergy change is highest in the case of DTTI, DTTI creates higher thermal change due to a higher thermal gradient normal to the fluid flow than PTTI and this extra restriction to the flow is absent in TTI. Thus, DTTI resulted to be a genuine higher SI for all working fluid cases studied among different turbulators investigated. DTTI has shown a maximum SI of 1.187 numerical value when working fluid is TPHNF 1. Although comparing increment in SI with PT HX from other tube inin terms of percentage enhancement, different tube insertsserts for the different working fluid, TPHNF 6 has maximum enhancement due to the highest thermal enhancement. So on the basis of SI in terms of percentage enhancement, different tube inserts compared to PT HX order of preferred working fluid as a coolant is THNF6 (TPHNF4 > TPHNF2 > TPHNF5 > TPHNF3 > TPHNF1). Therefore, hybrid nanofluids of different shapes are most likely to have the highest enhancement relative to like morphology.

Fig. 15
figure 15

Sustainability index of various TPHNFs with turbulators

Full size image

Power supply to the HX for pumping power of pump and fan to run continuously requires coal combustion therefore, discharge of CO2 annually and HX operating cost for various operating fluids of different tube inserts in a compact HX is shown in Fig. 16. HX operates for 180 days, causing the highest CO2 discharge requirement of 10.4 kg for DTTI HX, while a minimum 5.2 kg requirement of CO2 discharge has been obtained without inserts HX. Also, related HX operating cost investigated which shows a similar trend of variation discharge CO2 discharge varied with TPHNFs and various inserts. As DTTI creates additional vorticity due to the presence of dimple shape, vorticity strength is higher than PTTI though is absent in twisted tape inserts. Therefore, DTTI requires larger power, intermediate power requirement for PTTI, and the least requirement to run TTI in HX. For TPHNF 2, TTI requires 23.58%, PTTI 44.7%, and DTTI 47.8% higher average CO2 discharge compared to without inserts HX. Among investigated TPHNFs, compared to plain tube HX, for different tube inserts, a lesser operating cost would be preferable as TPHNF 4 > TPHNF 5 > TPHNF 6 > TPHNF 3 > TPHNF 1 > TPHNF 2. The operating cost of TPHNF 2 is highest due to a larger pressure drop compared to other hybrid nanofluids investigated. Therefore, where lower cost is a requirement TPHNF 4 should be selected as a working fluid in HX with inserts.

Fig. 16
figure 16

CO2 Discharge and HX OC with TPHNFs for various turbulators

Full size image

Conclusions

In this present investigation, compact heat exchanger device with various performance improvement techniques is studied. Tripartite hybrid water-based nanofluids are used as hot fluid instead of simple water. Different turbulator (TTI, PTTI, and DTTI) inserts are introduced in the hot side of the compact HX and compared performance parameters to the without inserts PT HX. Effect on performance parameters is studied with varied Reynolds numbers and TPHNFs. Modified turbulator inserts are compared on energy, exergy, irreversibility, entropy, exergo-economic, sustainability, and environmental aspects. The following key points are:

  • Tripartite hybrid nanofluid utilized in HX shows mild improvement, while TPHNFs with modified turbulator inserts in HX provide remarkable enhancement, as DTTI turbulator shows highest 73.23% Nusselt enhancement using TPHNF 6 working fluid.

  • The highest overall heat transfer coefficient was obtained for DTTI, at Re 2400 with a 20.6% net improvement HX.

  • The highest hot fluid exit temperature reduction is obtained at lowest Re 2400, DTTI 1.05 K, PTTI shows 0.84 K, and TTI reduces exit temperature to 0.74 K successfully compared to without inserts compact HX.

  • The highest PEC in turbulators are obtained for THNF 6 in DTTI air HX, average 3.4% higher PEC than THNF 4 working fluid.

  • Cost analysis and carbon discharge to the environment reveal TPHNF 2 to be least and THNF 4 to be most likely preferred working fluid as TPHNF 2 working fluid with DTTI requires 47.8% higher running cost in HX.

  • The DTTI modified turbulators with TPHNF 6 as a working fluid show the best choice to be used as working fluid due to higher coolant exergy change of 18.1%, second law efficiency of 2.74%, 4.8% performance index, and 0.5% higher sustainable index in HX.

  • At lowest Re 2400, the DTTI shows the highest 24.8% coolant entropy change, 16.5% irreversibility, and 22.1% entropy generation number, in HX followed by PTTI, and TTI using TPHNF 6 working fluid.