Analyses of exergy efficiency for forced convection heat transfer in a tube with CNT nanofluid under laminar flow conditions

Abstract

In the present study, the theoretical and experimental results of the second law analysis on the performance of a uniform heat flux tube using are presented in the laminar flow regime. For this purpose, carbon nanotube/water nanofluids is considered as the base fluid. The experimental investigations were undertaken in the Reynolds number range from 800 to 2600, volume concentrations of 0.1–1 %. Results are verified with well-known correlations. The focus will be on the entrance region under the laminar flow conditions for SWCNT nanofluid. The results showed that the Nu number increased about 90–270 % with the enhancement of nanoparticles volume concentration compared to water. The enhancement was particularly significant in the entrance region. Based on the exergy analysis, the results show that exergetic heat transfer effectiveness is increased by 22–67 % employing nanofluids. The exergetic efficiency is increase with increase in nanoparticles concentration. On the other hand, exergy loss was reduced by 23–43 % employing nanofluids as a heat transfer medium with comparing to conventional fluid. In addition, the empirical correlation for exergetic efficiency has also been developed. The consequential results obtained from the correlation are found to be in good agreement with the experimental results within ±5 % variation.

Appendix: Uncertainty analysis

To examine the accuracy of the results, an uncertainty analysis was carried out using the theory of the propagation of error; the uncertainty UF on a quantity F which is function of x₁,…x_n, measured variables with an associated uncertainty U_xi can be expressed as follows:

$$UF = \pm \sqrt {\sum\limits_{i = 1}^{n} {\left( {\frac{\partial F}{{\partial x_{i} }}U_{{x_{i} }} } \right)^{2} } }$$

And the relative uncertainty δF is:

$$\delta F = \frac{{U_{F} }}{F}$$

The uncertainty table for different instruments used in experiment is given in Table 2. The maximum possible error for the parameters involved in the analysis are estimated and summarized in Table 3.

Table 2 Uncertainties of instruments and properties

Table 3 Uncertainties of parameters and variables

Reynolds number, Re:

$$\text{Re} = \frac{{4\dot{m}}}{\pi D\mu },\frac{{U_{\text{Re}} }}{\text{Re}} = \left( {\left( {\frac{{U_{{\dot{m}}} }}{{\dot{m}}}} \right)^{2} + \left( {\frac{{U_{\mu } }}{\mu }} \right)^{2} } \right)^{1/2} = 0.14\,\%$$

Heat Flux:

$$q = \frac{{V^{2} /R}}{\pi dL}\frac{{U_{q} }}{q} = \sqrt {\left( {\frac{{2U_{V} }}{V}} \right)^{2} + \left( {\frac{{U_{R} }}{R}} \right)^{2} } = 0.2\,\%$$

Heat transfer coefficient, h:

$$h = \frac{q}{{T_{w} - T_{b} }},\quad\frac{{U_{h} }}{h} = \left( {\left( {\frac{{U_{q} }}{q}} \right)^{2} + \left( {\frac{{U_{{T_{w} - T_{b} }} }}{{T_{w} - T_{b} }}} \right)^{2} } \right) = 1.14\,\%$$

Nusselt number, Nu:

$$Nu = \frac{hD}{K},\quad\frac{{U_{Nu} }}{Nu} = \left( {\left( {\frac{{U_{h} }}{h}} \right)^{2} + \left( {\frac{{U_{K} }}{K}} \right)^{2} } \right)^{1/2} = 1.15\,\%$$

Friction factor, f:

$$f = \frac{\Delta P}{{\left( {\frac{l}{D}} \right)\left( {\frac{{\rho V^{2} }}{2}} \right)}},\quad U_{f} = \left( {\left( {\frac{{U_{\Delta P} }}{\Delta P}} \right)^{2} + \left( {\frac{{U_{\rho } }}{\rho }} \right)^{2} + \left( {\frac{{2U_{V} }}{V}} \right)^{2} } \right)^{1/2} = 0.15\,\%$$