On the convection heat transfer and pressure drop of copper oxide-heat transfer oil Nanofluid in inclined microfin pipe

Abstract

In this pioneering work, mixed convection heat transfer and pressure drop of the CuO -HTO nanofluid flow in the inclined Microfin pipe is studied experimentally. The flow regime is laminar and temperature of the pipe wall is stable. The influence of nanoparticle and Richardson number on the mixed convection is studied as Richardson number is from 0.1 to 0.7. The results demonstrate that mixed convection heat transfer rate rise substantially with the promotion of nanoparticle mass concentration. Based on the empirical results, the four equations are recommended to be utilised for appraisal of nanofluid flow Nusselt number and Darcy friction factor in term of Richardson number and nanoparticle mass concentration with the peaked deflection of 16%. Moreover, the four equations put forward to appraise the Nusselt number based on the Rayleigh number in inclined pipe from 2,000,000 to 7,000,000. A new correlation is acquired to anticipate the flow Darcy friction factor in the inclined Microfin pipe. Accordingly, the maximum figure of merit is 1.61% which is achieved with 1.5% nanoparticles mass concentration and an inclined angle of 30° at the Richardson number of 0.7. These results show that using nanoparticles is more in favour of heat transfer enhancement rather than in the increase of the pressure drop.

Appendix

Based on Holman [34], 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:

$$ {U}_R={\left[{\sum}_{i=1}^n{\left(\frac{\partial R}{{\partial V}_i}\ {U}_{V_i}\right)}^2\right]}^{1/2} $$

(10)

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

$$ {U}_f={\left[\ {\left(\frac{\pi^2{D}^5}{L\rho {\dot{Q}}^3}\Delta p{U}_{\dot{Q}}\right)}^2+{\left(\frac{\pi^2{D}^5}{L\rho {\dot{Q}}^2}{U}_{\Delta p}\right)}^2+{\left(\frac{\pi^2{D}^5}{L{\rho}^2{\dot{Q}}^2}\Delta p{U}_{\rho}\right)}^2\right]}^{1/2} $$

(11)

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

$$ {U}_{Nu}=\left\{{\left[\frac{\rho {c}_p}{\pi Lk}\mathit{\ln}\left(\frac{T_w-{T}_{b,i}}{T_w-{T}_{b,o}}\right){U}_{\dot{Q}}\right]}^2+{\left[\frac{\rho {c}_p\dot{Q}}{\pi Lk}\frac{T_{b,o}-{T}_{b,i}}{\left({T}_w-{T}_{b,i}\right)\left({T}_w-{T}_{b,o}\right)}{U}_{T_w}\right]}^2+{\left[\frac{\rho {c}_p\dot{Q}}{\pi Lk}\frac{1}{T_w-{T}_{b,i}}{U}_{T_{b,i}}\right]}^2+{\left[\frac{\rho {c}_p\dot{Q}}{\pi Lk}\frac{1}{T_w-{T}_{b,o}}{U}_{T_{b.o}}\right]}^2+{\left[\frac{c_p\dot{Q}}{\pi Lk}\mathit{\ln}\left(\frac{T_w-{T}_{b,i}}{T_w-{T}_{b,o}}\right){U}_{\rho}\right]}^2+{\left[\frac{\dot{\rho Q}}{\pi Lk}\mathit{\ln}\left(\frac{T_w-{T}_{b,i}}{T_w-{T}_{b,o}}\right){U}_{c_p}\right]}^{21/2}\right\} $$

(12)

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

$$ {U}_{\eta }={\left[\ {\left(\frac{1/{h}_{b_f}}{{\Delta p}_{n_f}/{\Delta p}_{b_f}}{U}_{h_{n_f}}\right)}^2+{\left(\frac{h_{n_f}/{h}_{b_f}^2}{{\Delta p}_{n_f}/{\Delta p}_{b_f}}{U}_{h_{b_f}}\right)}^2+{\left(\frac{h_{n_f}/{h}_{b_f}}{{\Delta p}_{n_f}^2/{\Delta p}_{b_f}}{U}_{{\Delta p}_{n_f}}\right)}^2+{\left(\frac{h_{n_f}/{h}_{b_f}}{{\Delta p}_{n_f}}{U}_{{\Delta p}_{n_f}}\right)}^2\right]}^{1/2} $$

(13)