Keywords

1 Introduction

From the last few decades, the importance and research on nanotechnology are the most fundamental and effective topics of thermal engineering. At present to improve heat transfer efficiency and heat transfer rate, nanoparticles are used with base fluids. Beside this, the utilization of pumping power to get this enhancement is also less, and this is the most advantage thing to using nanoparticles in working fluids. Basically, by adding small amount of solid particles with the base or working fluid, the thermal conductivity of the fluid can be increased noticeably. And by using this concept, researchers have been made nanofluid which is the combination of base fluids (water, engine oil or ethylene glycol) and very small amount of solid particles at nanoscale size (1–100 nm). Al2O3, CuO, TiO2, SiC, SiO2, Fe2O3, MgO, etc. particles are used as nanoparticle to mix with base fluids. Different researchers carried out their investigation on nanofluids at heat transfer application. Xuan and Li 2003 [1] worked on Cu–water nanofluid through a 10-mm inward distance across tube for convective transfer of heat. The results from their investigation reveal that at turbulent, the friction factors for volume fraction 1 and 2% of nanofluids are showed similar value compared to pure water. Williams et al. 2008 [2] experimentally carried his study on the convective turbulent heat exchange of alumina–H2O and zirconium–H2O water nanofluids in a tube. They investigated that nanofluids provide enhancement of heat exchange and behavior of viscous pressure drop. Rea et al. [3] led an investigation on the convective warmth exchange and weight drop of alumina–H2O and zirconium–H2O nanofluids in a tube for laminar flow which width is 4.5 mm (inward). But from their discoveries, there is no deviation in convective heat exchange and weight drop of nanofluid has been found. Heris et al. [4] played out an exploratory investigation to decide the loss of pressure and transfer of heat qualities of Al2O3–H2O and CuO–H2O nanofluids through a triangular conduit under uniform heat flux at laminar flow area. Their outcomes demonstrated that, at similar/constant volume concentration and Reynolds number, utilizing CuO nanoparticle is less beneficial than Al2O3 nanoparticles. Yu et al. [5] worked with SiC–water nanofluid for turbulent flow and a comparison parameter the figure of the merit which is denoted by heat transfer enhancement and pumping power ratio were presented in their study. Their result showed that SiC–water nanofluid provided the value of FOM 0.8 and Al2O3–water nanofluid provided the value of FOM 0.6 which indicates that SiC–water nanofluid is more favorable in case of pumping power penalty. Yu and Dong [6] studied on convective thermal performance investigation of nanofluids (Al2O3–water and Al2O3–polyalphaolefin) for cooling applications, and their result reveals that in case of constant pumping power condition, the nanofluid’s and the base fluid’s overall effectiveness will not be changed significantly when both the hydrodynamic and thermal performances are considered. Sarkar [7] carried out his research work on performance analyses of the nanofluids Al2O3, TiO2, CuO and Cu as cooling application for cooled gas cooler (shell-and-tube) in CO2 refrigeration cycle which is transcritical. Their research shows that the effectiveness of nanofluid is preferable to use it as coolant in the gas cooler to develop and improve the performance of the cycle of CO2 refrigeration. Monjur [8] investigated on energy savings of heat exchanger, and they showed that for constant heat transfer coefficient, Al2O3–water, CuO–water and TiO2–water required less pumping power and volumetric flow rate compared to pure water. Ingole et al. [9] investigated on pumping power of car radiator by using Al2O3–water nanofluid, and they find that 2% volume concentration of Al2O3–water need 23.81% less pumping power compared to pure water.

The above maximum researches only show higher heat transfer rate by using nanofluids, but very few papers show the justification of required pumping power study to get the higher heat transfer rate and also comparison between nanofluids on the basis of required pumping power. So in the present work, the thermal performance of four nanofluids Al2O3–H2O, CuO–H2O, SiC–H2O and TiO2–H2O has been studied, and the results are compared on the basis of pumping power requirement. Moreover, the figure of merit (FOM), Nusselt number enhancement ratio, heat transfer coefficient ratio and pumping power of base fluid along with nanofluids are calculated for constant Reynolds number and (1–5%) volume fraction. Basically, the overall performance of water-based nanofluids in the forced convective laminar regime is discussed in terms of three merits criteria. They are Nusselt number enhancement ratio, heat transfer enhancement ratio and figure of merit (FOM). The first two ones are usually used to compare different fluids of heat transfer, while other can be mainly used to evaluate nanofluid’s overall energetic performance for operating condition in a real system. Meanwhile, a higher value of figure of merit represents more gain in the heat exchange enhancement compared to the pumping power increment.

2 Physical Geometry and Boundary Condition

Parallel plates with a steady heat flux on both walls are presented to examine the performance of all the nanofluids through the channel of Fig. 1 by employing numerical method using ANSYS fluent software. The distance between two horizontal plates is 4 mm, and length is 600 mm length. A constant uniform heat flux of 500 W/m2 is applied on the wall boundary of the parallel plates, and fluid is permitted to flow with constant temperature of 303 K at the opening of the parallel plates with a presumption of no slip condition on the parallel plate’s wall which are considered. All the heat exchange and fluid dynamic parameters are extricated after the thermal and hydrodynamic improvement of the fluid stream, and in this case, for taking all the measurements the standard entrance length is considered x/D = 60. For calculating the heat transfer enhancement and pressure loss, the temperatures are taken at line which is situated 590 mm from inlet, and pressures are taken at lines which are situated from 565 to 555 mm from the inlet.

Fig. 1
figure 1

Corresponding geometry of present work with mesh

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3 Numerical and Computational Method

We use ANSYS (fluent) which is commercial computational fluid dynamics software for this numerical analysis. All the governing equations for momentum, mass, energy and laminar quantities have been solved by adopting a control volume technique. A simple algorithm has been used for velocity pressure coupling purpose, and a second-order upwind method has been used to solve energy and momentum equation. At inlet laminar inlet velocity and at the outlet boundary pressure, outlet is considered. Under relaxation factors, 0.4 for pressure, 0.76 for momentum, 1 for energy and 0.9 for density equation are considered for parallel plate. All the used nanoparticles with volume fractions (1, 2, 3, 4 and 5%) are mixed with water separately and tested with a wide range of Reynolds number 400–1100 and then results are compared with base fluid water.

4 Methodology

The governing equations for continuity, momentum and energy for forced convection under laminar steady-state flow conditions are represented as follows:

Continuity equation: In steady flow, the conversations of mass eqn:

$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0$$
(1)

Momentum equation: For laminar flow, the momentum equation:

$$\rho \left( {u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y}} \right) = \mu \frac{{\partial^{2} u}}{{\partial y^{2} }}$$
(2)

Energy equation:

$$\left( {E_{in} - \, E_{out} } \right) \, = k\frac{{d^{2} T}}{{\partial x^{2} }}{\text{d}}x{\text{d}}y + k\frac{{d^{2} T}}{{\partial y^{2} }}{\text{d}}x{\text{d}}y = k\left( {\frac{{d^{2} T}}{{\partial x^{2} }} + \frac{{d^{2} T}}{{\partial y^{2} }}} \right){\text{d}}x{\text{d}}y$$
(3)

5 Thermal and Fluid Dynamics Properties

The Reynolds number for nanofluids:

$$Re = \frac{{\rho_{nf} U_{av} D_{h} }}{{\mu_{nf} }}$$
(4)

Average Nusselt number:

$$Nu = \frac{{h_{c} D_{h} }}{{K_{nf} }}$$
(5)

Rate of heat transfer

$$Q_{nf} = m_{nf} C_{{P_{nf} }} \Delta T$$
(6)

Average heat transfer coefficient \(h_{c}\):

$$h_{c} = \frac{{Q_{nf} }}{{A_{w} \left( {\Delta T} \right)}}$$
(7)

Temperature difference:

$$\Delta T = \frac{{\left( {T_{w} - T_{o} } \right) - \left( {T_{w} - T_{i} } \right) ,}}{{\ln \left( {\frac{{T_{w} - T_{o} }}{{T_{w} - T_{i} }}} \right)}}$$
(8)

Pressure difference:

$$\Delta P = \frac{{fL\rho U^{2} }}{{2D_{h} }}$$
(9)

Nusselt number enhancement ratio

$$= \frac{{Nu_{nf} }}{{Nu_{bf} }}$$
(10)

Overall heat transfer coefficient enhancement ratio

$$= \frac{{h_{nf} }}{{h_{nf} }}$$
(11)

The pumping power per unit length:

$$W = \frac{{\left( {\pi /4} \right)D^{2} U_{av} \Delta P}}{L}$$
(12)

The figure of merit,

$${\text{FOM }} = \left( {\frac{{h_{nf} }}{{h_{bf} }}} \right)\left( {\frac{{W_{bf} }}{{W_{nf} }}} \right)$$
(13)

6 Thermophysical Properties of Nanofluids

Dynamic viscosity: There are several equations for dynamic viscosity; among them, we use Pak and Cho [10] equation for TiO2, Nguyen [11] equation for CuO, Maiga [12] equation for Al2O3 and Chein [13] equation for SiC. The equation can be expressed as:

For TiO2–water nanofluid:

$$\mu_{nf} = \mu_{bf} (1.0683 + 4.70\emptyset + 167.7\emptyset^{2} )$$
(14)

For CuO–water nanofluid:

$$\mu_{nf} = \mu_{bf} (1.475 - 0.319\emptyset + 0.051\emptyset^{2} + 0.009\emptyset^{3}$$
(15)

For Al2O3–water nanofluid:

$$\mu_{nf} = \left( {1 + 7.3\emptyset + 123\emptyset^{2} } \right)\mu_{f}$$
(16)

For SiC–water nanofluid:

$$\mu_{nf} = \mu_{bf} \left[ {1 + 10.6\emptyset + \left( {10.6\emptyset } \right)^{2} } \right]$$
(17)

Thermal conductivity: There are several thermal conductivity equations; among them, we use Pak and Cho [10] equation for TiO2, CuO and Al2O3. For SiC, we use Maxwell [14] mode equation. The following formulas are:

For TiO2–water nanofluid:

$$K_{nf} = \left( {1.0084 + 2.1796\emptyset } \right)$$
(18)

For Al2O3–water nanofluid:

$$K_{nf} = K_{bf} \left( {1.0021 + 7.3349\emptyset } \right)$$
(19)

For SiC–water and CuO–water:

$$K_{nf} = \frac{{K_{p} + 2K_{bf} + 2\left( {K_{p} - K_{bf} } \right)\emptyset }}{{K_{p} + 2K_{bf} - \left( {K_{p} - K_{bf} } \right)\emptyset \times K_{bf} }}$$
(20)

Density: (Xuan and Roetzel, 2000) [15] eqn

$$\rho_{nf} = \rho_{p} \emptyset + \rho_{bf} \left( {1 - \emptyset } \right)$$
(21)

Specific Heat: Pak and Cho, 1998 [10] equation:

$$C_{nf} = \left( {1 - \emptyset } \right)C_{w} + \emptyset C_{p}$$
(22)

7 Code Validation Test

For channel flow, at uniform velocity and constant heat flux water was passed through it and a range of Reynolds number (400-1100) were considered for calculating Nusselt numbers to validate the present work with validated equation of Nusselt number for channel flow. At fully developed zone, obtaining Nusselt number is compared with the constant value of Nusselt number 8.23 at constant heat flux for parallel plate and with the Pahor and Turtor [16] theoretical equation which is shown in Fig. 2. Pahor and Turton (1959) equation:

Fig. 2
figure 2

Comparison of Nusselt number between experimental equation and current study for different Reynolds number of water

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$$\varvec{Nu} = 8.24\left( {1 + \frac{3.79}{{\varvec{Pe}^{2} }} + \ldots } \right), \quad \varvec{Pe} \gg 1 \varvec{Pe} = {\mathbf{P}}{\mathbf{\acute{e}}}{\mathbf{clet}}\,{\mathbf{number}};$$
(23)
$$\varvec{Nu} = 8.118\left( {1 - 0.031\varvec{Pe}} \right),\quad \varvec{Pe} \ll 1$$
(24)

8 Results

Displayed Fig. 3 indicates the effective heat transfer coefficient for Al2O3–water, CuO water, SiC–water and TiO2–water nanofluids at a constant volume fraction of 3%. Other percentages showed similar trends. The result indicates that for all volume fractions of Al2O3 nanoparticles, the heat transfer coefficient is higher than other nanofluids. Similar trend has been also described by Mohammed et al. [17] and Koo and Kleinstreuer, [18]. Figure 4 shows the differentiation of pumping power requirement per unit length of Al2O3–water nanofluid with different values of heat transfer coefficient and volume concentration. From graphs, it is clear that by the increment of the values of heat transfer coefficient, the pumping power becomes higher in case of same volume concentration. For ∅ = 1–5%, the pumping power for Al2O3–water nanofluids is reduced by 20–75% compared to water for same heat transfer rate. Other nanofluids provide similar trends. For CuO–water, the pumping power is reduced by 5% to 55%. For SiC–water and TiO2–water nanofluids, the pumping power reduction is almost same 4–45% compared to pure water. Figure 5 shows, the change of pumping power with different heat transfer coefficient at constant volume fraction of 3%. Hence, the results of Fig. 5 indicates that Al2O3–water requires lower pumping power in comparison to others for all volume fractions. From Fig. 6, it is analyzed that Nusselt number enhancement ratio is increasing with the increase of volume fraction. Nusselt number enhancement ratio for Al2O3 is less than other three nanofluids. From Fig. 7, it is observed that with the increase of volume fractions, heat transfer coefficient enhancement ratio is also increasing. Here, Al2O3 shows more enhancement ratio than other three nanofluids, and TiO2 gives less enhancement ratio comparatively with others. In Fig. 8, the FOM vs. volume fraction graph is shown which indicates that with increasing of volume fraction, FOM is also increasing at constant Reynolds number. For Al2O3–water, FOM is higher than other nanofluids; CuO and TiO2 show almost same result. And more value of FOM indicates more heat transfer enhancement.

Fig. 3
figure 3

Variation of heat transfer coefficient with Reynolds number of 3% volume fraction for all nanofluids

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Fig. 4
figure 4

Variation of pumping power per unit length with heat transfer coefficient for Al2O3–water nanofluid

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Fig. 5
figure 5

Differentiation of pumping power per unit length with heat transfer coefficient of nanofluids

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Fig. 6
figure 6

Variation of Nusselt number enhancement ratio with volume fraction of all nanofluids

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Fig. 7
figure 7

Variation of heat transfer coefficient enhancement ratio with volume fraction of all nanofluids

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Fig. 8
figure 8

Variation of FOM with volume fraction of all nanofluids

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To analyze the performance of all used nanofluids, a comparison Table 1 has been introduced below. In this table, for all the nanofluids at a uniform heat transfer coefficient of 700 W/m2-k for the optimum 3% volume concentration, the pumping power benefit, reduction in volumetric flow rate, pressure difference and mass flow rate have been analyzed for channel. For optimum 3% volume fraction of channel, pumping power benefit of Al2O3 is more than other nanofluids, and it is examined that SiC shows less pumping power benefit among them. Similarly, the mass flow rate reduction for TiO2 is less than other nanofluids, and Al2O3 gives more reduction in mass flow rate.

Table 1 Differentiation of performance of all the used nanofluids (∅ = 3%) with base fluid water
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9 Conclusion

In the present work, four different nanofluids Al2O3–water, CuO–water, SiC–water and TiO2–water have been studied through typical parallel plates to observe the performance comparison between them on the basis of heat transfer enhancement and the pumping power benefits. Among the four nanofluids, Al2O3–water shows more heat transfer enhancement ratio compared to others, and also to get this more heat transfer, Al2O3–water required lower pumping power compared to others which is cleared from the graph of FOM. Beside this, Al2O3–water also needs lower volumetric/mass flow rate for getting higher heat transfer compared to water and other nanofluids which is also cleared from comparison table. However, TiO2–water provides lowest performance between all, and CuO–water and SiC–water show almost same performance in heat transfer application on the basis of FOM and pumping power benefit.