Application of copper oxide–thermal oil (CuO-HTO) nanofluid on convective heat transfer enhancement in inclined circular tube

Abstract

The influence of using copper oxide–thermal oil on convective heat transfer and pressure drop in an upward flow in an inclined smooth tube is studied experimentally in this paper. The flow regime and wall temperature are laminar and constant, respectively. The effects of nanofluid, Graetz number, Prandtl number, negative inclination angle on convective heat transfer rate rise moderately with the augmentation of nanoparticles mass concentration. Both correlations are recommended to evaluate Nusselt number and Darcy friction factor in an upward flow under constant wall temperature and laminar flow in smooth pipe. The maximum deviations are 19% and 21%, respectively, which are acceptable for scientific research to be used in industrial applications. Accompaniment of heat transfer ratio with pumping power ratio is presented in this paper. If the increment of pressure drop is more than heat transfer enhancement, it will not be appropriate to use CuO–thermal oil, negative inclination angles and smooth tube. The figure of merit increases up to 1.58% which is calculated with 1.5% nanoparticle mass concentration and inclination angle of 30° at Prandtl number of 387. The results show that most of the values are more than unity, so the heat transfer enhancement is more than increment of pressure drop.

Appendix

Based on the literature [28, 29], if the parameter of R depends on V₁ to V_n variables which can be gauged with an uncertainty of U_V1 to U_Vn, the overall uncertainty of R is:

$$U_{R} = \left[ {\mathop \sum \limits_{i = 1}^{n} \left( {\frac{\partial R}{{\partial V_{\text{i}} }} U_{{V_{\text{i}} }} } \right)^{2} } \right]^{1/2}$$

(18)

Based on the definition of the Darcy friction factor, Eq. (1):

$$U_{f} = \left[ { \left( {\frac{{\pi^{2} D^{5} }}{{L\rho \dot{Q}^{3} }}\Delta pU_{{{\dot{\text{Q}}}}} } \right)^{2} + \left( {\frac{{\pi^{2} D^{5} }}{{L\rho \dot{Q}^{2} }}U_{{\Delta {\text{p}}}} } \right)^{2} + \left( {\frac{{\pi^{2} D^{5} }}{{L\rho^{2} \dot{Q}^{2} }}\Delta pU_{\uprho} } \right)^{2} } \right]^{1/2}$$

(19)

Moreover, for the Nusselt number, Eq. (2):

$$ \begin{aligned} U_{\text{Nu}} & = \left\{ {\left[ {\frac{{\rho c_{\text{p}} }}{\pi Lk}\ln \left( {\frac{{T_{w} - T_{\text{b,i}} }}{{T_{w} - T_{\text{b,o}} }}} \right)U_{{{\dot{\text{Q}}}}} } \right]^{2} + \left[ {\frac{{\rho c_{p} \dot{Q}}}{\pi Lk}\frac{{T_{\text{b,o}} - T_{\text{b,i}} }}{{\left( {T_{\text{w}} - T_{\text{b,i}} } \right)\left( {T_{\text{w}} - T_{\text{b,o}} } \right)}}U_{{{\text{T}}_{\text{w}} }} } \right]^{2} + \left[ {\frac{{\rho c_{\text{p}} \dot{Q}}}{\pi Lk}\frac{1}{{T_{\text{w}} - T_{\text{b,i}} }}U_{{{\text{T}}_{\text{b,i}} }} } \right]^{2} } \right. \\ & \quad \left. { + \,\left[ {\frac{{\rho c_{\text{p}} \dot{Q}}}{\pi Lk}\frac{1}{{T_{\text{w}} - T_{\text{b,o}} }}U_{{{\text{T}}_{{{\text{b}} . {\text{o}}}} }} } \right]^{2} + \left[ {\frac{{c_{\text{p}} \dot{Q}}}{\pi Lk}\ln \left( {\frac{{T_{\text{w}} - T_{\text{b,i}} }}{{T_{\text{w}} - T_{\text{b,o}} }}} \right)U_{\rho } } \right]^{2} + \left[ {\frac{{\rho \dot{Q}}}{\pi Lk}\ln \left( {\frac{{T_{w} - T_{\text{b,i}} }}{{T_{\text{w}} - T_{\text{b,o}} }}} \right)U_{{{\text{c}}_{\text{p}} }} } \right]^{2} } \right\}^{1/2} \\ \end{aligned} $$

(20)

From the definition of the performance index, Eq. (8), it can be concluded that:

$$U_{\eta } = \left[ { \left( {\frac{{1/h_{{{\text{b}}_{\text{f}} }} }}{{\varOmega_{{{\text{n}}_{\text{f}} }} /\varOmega_{{{\text{b}}_{\text{f}} }} }}U_{{{\text{h}}_{{{\text{n}}_{\text{f}} }} }} } \right)^{2} + \left( {\frac{{h_{{{\text{n}}_{\text{f}} }} /h_{{{\text{b}}_{\text{f}} }}^{2} }}{{\varOmega_{{{\text{n}}_{\text{f}} }} /\Delta p_{{{\text{b}}_{\text{f}} }} }}U_{{{\text{h}}_{{{\text{b}}_{\text{f}} }} }} } \right)^{2} + \left( {\frac{{h_{{{\text{n}}_{\text{f}} }} /h_{{{\text{b}}_{\text{f}} }} }}{{\varOmega_{{{\text{n}}_{\text{f}} }}^{2} /\varOmega_{{{\text{b}}_{\text{f}} }} }}U_{{\Delta {\text{p}}_{{{\text{n}}_{\text{f}} }} }} } \right)^{2} + \left( {\frac{{h_{{{\text{n}}_{\text{f}} }} /h_{{{\text{b}}_{\text{f}} }} }}{{\varOmega_{{{\text{n}}_{\text{f}} }} }}U_{{\Delta {\text{p}}_{{{\text{n}}_{\text{f}} }} }} } \right)^{2} } \right]^{1/2}$$

(21)