Introduction

For heat exchange tools, common carrier fluids such as oil and water have been utilized. Reducing the size of heat exchanger makes its thermal performance to augment. One way can help us to design smaller equipment is utilizing nanoparticles and dispersing them into common testing fluids. The first researcher who introduced nanofluid was Choi [1]. After publishing such proposal, other researcher tried to develop various kinds of nanomaterial for various uses [2,3,4,5,6,7,8].

Wang et al. [9] reported about 70% augmentation in thermal efficiency by utilizing CNT nanoparticle with concentration of 0.05%. Alumina working fluid has been utilized by Wen and Ding [10] inside a pipe with uniform heat flux. They examined that concentration of nanoparticle has direct relation with temperature gradient. They concerned the Brownian motion impact and found that thinner boundary layer can be obtained in greater fraction of nanofluid. Sheikholeslami et al. [11] imposed new configuration of swirl flow insert inside a pipe. They inferred that entropy generation acts against Nusselt number. Nadeem et al. [12] utilized nanomaterial along a curved plate. They imposed variable viscosity. Animasaun et al. [13] observed the migration of nanoparticles because of applying magnetic force. They reported the influence of thermoelectric effect on copper oxide–water nanofluid. Sheikholeslami et al. [14] explored mesoscopic simulation for 3D laminar nanofluid MHD flow within a porous domain. Researchers developed nanofluid simulation in the presence of various external forces [15,16,17,18,19,20,21]. Sheikholeslami et al. [22] tried to find the treatment of NEPCM in the existence of V-shaped fins during solidification. Saleem et al. [23] demonstrated the hydrothermal performance of radiative nanomaterial in appearance of heat sources. Various turbulent approaches have been tested by Sekrani et al. [24] to model the alumina nanofluid behavior inside a pipe with uniform heat flux. Range of Re is 3000–20,000.

Migration of SiO2 nanoparticles inside a solar collector has been scrutinized by Yan et al. [25]. They inferred that knf enhances with rise of fraction of nanofluid. Michael and Iniyan [26] scrutinized the impact of dispersing copper oxide on convective flow. They concluded that efficiency enhances about 6.3% by involving 0.05% of mass fraction. Development of numerical approaches for heat transfer modeling is observable in recent years [27,28,29,30,31,32,33,34]. Gupta et al. [35] examined the application of alumina nanomaterial for solar energy saving. They concluded that mass flow rate has optimum values for both pure and nanofluid testing fluid.

In the current text, influence of complex shape of turbulator on hydrothermal behavior of hybrid nanofluid has been examined. Pitch ratio and Reynolds number are two active parameters, and various contours are reported for various values of them. To simulate this problem, FVM was utilized.

Physical model and explanations

The geometry of current turbulators which are inserted within the pipe with constant heat flux condition is demonstrated in Fig. 1. Main geometric parameters have been listed in the right side of geometry. The domain was divided into three zones with equal length, and the central one is test part and turbulators were situated in that zone. The carrier fluid is water-based nanofluid with hybrid nanoparticles (MWCNT and Fe3O4). All details for estimating working fluid were mentioned in previous articles [36, 37]. In Table 1, properties of hybrid nanofluid with concentration of 0.003 have been written [37]. Moreover, an example for grid is presented in Fig. 1. Boundary layer grids over the solid surfaces were involved. Mesh is greatly refined near the walls. Number of layers around solid surface is dependent on turbulent model, because utilized mesh should satisfy the limitation of Y+. As discussed in the previous publication, k–ɛ model is the best accurate mode for heat exchangers with twisted tape [38]. So, we proposed this model for the current model. In this publication, ANSYS FLUENT 18.1 is employed for simulation. The convergence criterion should be less than 10−5. All utilized settings are the same as Ref. [39]. No slip conditions have been enforced on all solid walls. Corresponding above explanations the governing equations can be listed as:

Fig. 1
figure 1

Geometry demonstration and sample grid

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Table 1 Properties of hybrid nanofluid with concentration of 0.003 [37]
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$$\frac{{\partial \left( {u_{\text{i}} } \right)}}{{\partial x_{\text{i}} }} = 0$$
(1)
$$\frac{\partial }{{\partial x_{\text{j}} }}\left( {\rho_{\text{nf}} u_{\text{i}} u_{\text{j}} } \right) = - \frac{\partial p}{{\partial x_{\text{i}} }} + \frac{\partial }{{\partial x_{\text{j}} }}\left( { - \rho_{\text{nf}} \overline{{u_{\text{j}}^{\prime } u_{\text{i}}^{\prime } }} } \right) + \frac{\partial }{{\partial x_{\text{j}} }}\left( {\left( {\frac{{\partial u_{\text{i}} }}{{\partial x_{\text{j}} }} + \frac{{\partial u_{\text{j}} }}{{\partial x_{\text{i}} }}} \right)\mu_{\text{nf}} } \right)$$
(2)
$$\frac{\partial }{{\partial x_{\text{i}} }}\left( {\rho_{\text{nf}} Tu_{\text{i}} } \right) = \frac{\partial }{{\partial x_{\text{i}} }}\left( {\left( {\varGamma + \varGamma_{\text{t}} } \right)\frac{\partial T}{{\partial x_{\text{i}} }}} \right),\quad \varGamma \left( { = \mu_{\text{nf}} /Pr_{\text{nf}} } \right),\quad \varGamma_{\text{t}} \left( { = \mu_{\text{t}} /Pr_{\text{t}} } \right)$$
(3)

\(\mu_{\text{t}}\) and \(\rho_{\text{nf}} \overline{{u_{\text{j}}^{\prime } u_{\text{i}}^{\prime } }}\) re:

$$\mu_{\text{t}} = \frac{1}{\varepsilon }k^{2} C_{\mu } \rho_{\text{nf}}$$
(4)
$$- \rho_{\text{nf}} \overline{{u_{\text{i}}^{\prime } u_{\text{j}}^{\prime } }} = \left( {\frac{{\partial u_{\text{i}} }}{{\partial x_{\text{j}} }} + \frac{{\partial u_{\text{j}} }}{{\partial x_{\text{i}} }}} \right)\mu_{\text{t}} - \frac{2}{3}\rho_{\text{nf}} k\delta_{\text{ij}} - \frac{2}{3}\mu_{\text{t}} \frac{{\partial u_{\text{k}} }}{{\partial x_{\text{k}} }}\delta_{\text{ij}} .$$
(5)

To find k and ɛ, we have:

$$\frac{\partial }{{\partial x_{\text{j}} }}\left( {\left( {\frac{{\mu_{\text{t}} }}{{\sigma_{\text{k}} }} + \mu_{\text{nf}} } \right)\frac{\partial k}{{\partial x_{\text{j}} }}} \right) - \rho_{\text{nf}} \varepsilon + G_{\text{k}} = \frac{\partial }{{\partial x_{\text{i}} }}\left( {u_{\text{i}} \rho_{\text{nf}} k} \right),\quad G_{\text{k}} = - \rho_{\text{nf}} \overline{{u_{\text{j}}^{\prime } u_{\text{i}}^{\prime } }} \frac{{\partial u_{\text{j}} }}{{\partial x_{\text{i}} }}$$
(6)
$$\frac{\partial }{{\partial x_{\text{i}} }}\left( {u_{\text{i}} \rho_{\text{nf}} \varepsilon } \right) = \frac{\varepsilon }{k}G_{\text{k}} C_{1\varepsilon } - \rho_{\text{nf}} \frac{{\varepsilon^{2} }}{k}C_{2\varepsilon } + \frac{\partial }{{\partial x_{\text{j}} }}\left( {\left( {\frac{{\mu_{\text{t}} }}{{\sigma_{\varepsilon } }} + \mu_{\text{nf}} } \right)\frac{\partial \varepsilon }{{\partial x_{\text{j}} }}} \right)$$
(7)
$$C_{1\varepsilon } = 1.42,\quad C_{\mu } = 0.0845,\quad C_{2\varepsilon } = 1.68,\quad Pr_{\text{t}} = 0.85,\quad \sigma_{\text{k}} = 1,\quad \sigma_{\varepsilon } = 1.3.$$
(8)

As mentioned, we utilized hybrid nanofluid model as same as Ref. [37] to estimate nanofluid properties.

The inlet and outlet conditions used in the calculation are velocity inlet and pressure outlet:

$$v_{\text{i}} = 0,\quad w_{\text{i}} = cte,\quad u_{\text{i}} = 0,\quad I = 0.16(Re)^{{\frac{ - 1}{8}}} ,\quad T_{\text{i}} = cte$$
(9)
$$\frac{{\partial {\text{u}}}}{{\partial {\text{z}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{z}}}} = \frac{{\partial {\text{T}}}}{{\partial {\text{z}}}} = \frac{{\partial {\text{w}}}}{{\partial {\text{z}}}} = 0.$$
(10)

Results and discussion

The numerical study explores the behavior of hybrid nanofluid within a pipe with new type of swirl flow tools which are situated at test section. Homogenous model for nanofluid and k–ɛ model for turbulent mode have been imposed. We present the contours in three sections A, B and C which are inlet, middle and outlet sections of test section zone.

Before starting simulation, we first examined the validation test. The previous published paper has been selected for comparison in which alumina nanofluid with concentration of 0.03 was testing fluid and Reynolds number is equal to 6020 [40]. Distribution of h(x) is shown in Fig. 2 in which no large deviation can be seen. So, the used code has nice accuracy. Distribution of velocity, streamline, temperature as well as contour of temperature along longitudinal cross section is illustrated in Figs. 3–7. Insertion of turbulator generates longitudinal disturbance. Heat transfer rate has direct relation with irregular disturbance. Greater value of irregular disturbance leads to thinner thermal boundary layer. As pitch ratio declines, more mixing occurs due to greater irregular disturbance. So, nanofluid can scour the wall stronger and heat transfer can be increased. As inlet velocity enhances, the intensity of the swirls produced by turbulator augments considerably, thereby enhancing the heat transfer rate. The weakening of mixing caused by greater pitch ratio reduces the Nusselt number. Greater space of swirl device is in contact with the carrier fluid for lower pitch ratio. So, pressure drop reduces with rise of pitch ratio. Thus, it is necessary to designing turbulator with higher number of evaluations. In addition, it can be inferred that pumping power has direct relationship with temperature gradient.

Fig. 2
figure 2

Verification for h values along the pipe when \(\phi = 0.03\) and Re = 6020 [40]

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Fig. 3
figure 3

Distribution of velocity, streamline, temperature at Re = 5000, P = 0.2 m

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Fig. 4
figure 4

Distribution of velocity, streamline, temperature at Re = 20,000, P = 0.2 m

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Fig. 5
figure 5

Distribution of velocity, streamline, temperature at Re = 5000, P = 0.1 m

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Fig. 6
figure 6

Distribution of velocity, streamline, temperature at Re = 20,000, P = 0.1 m

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Fig. 7
figure 7

Contour plot of temperature along cross section for various cases

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Variations in ΔP and Nu are presented in Fig. 8. Increasing irregular disturbance makes the pressure drop to enhance. So, ΔP augments with decrease in pitch ratio. Nu demonstrates an enhancing trend with changing Reynolds number, while opposite outputs were reported for pitch ratio. The smaller the pitch ratio, the smaller is the pressure loss.

Fig. 8
figure 8

a Pressure drop; b Nusselt number for various Re and P

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Conclusions

In the current publication, innovative turbulator is designed and inserted inside the heat exchanger and its influence of efficiency of pipe under turbulent regime condition is simulated. Hybrid nanomaterial moves within the pipe. Turbulators with lower pitch ratio are favorable types of turbulator, which generate the greater turbulent intensity. Thickness of the temperature boundary layer increases when the pitch ratio enhances. Worse heat transfer rate is obtained for lower pitch ratio.