Second law analysis of forced convection in a circular duct for non-Newtonian fluids

The second law characteristics of fluid flow and heat transfer inside a circular duct under fully developed forced convection for non-Newtonian fluids are presented. Heat flux is kept constant at the duct wall. Analytical expressions for dimensionless entropy generation number (_NS$N_{\mathrm{S}}$), irreversibility distribution ratio (Φ  ), and Bejan number (Be$\mathit{Be}$) are obtained as functions of dimensionless radius (R$R$), Peclet number (Pe$\mathit{Pe}$), modified Eckert number (Ec$\mathit{Ec}$), Prandtl number (Pr), dimensionless temperature difference (Ω  ), and fluid index (m$m$ or n$n$). Spatial distributions of local and average entropy generation number, irreversibility ratio, and Bejan number are presented graphically. For a particular value of fluid index, n=1$n=1$ (or m=2$m=2$), the general entropy generation number expression for a non-Newtonian power-law fluid reduces to the expression for Newtonian fluid as expected. Furthermore, entropy generation minimization is applied to calculate an optimum fluid index (_nEGM$n_{\mathrm{EGM}}$). A correlation is proposed that calculates _nEGM$n_{\mathrm{EGM}}$as a function of group parameter (Ec×Pr/Ω$\mathit{Ec}\times \mathit{Pr}/\Omega$) and Peclet number (Pe$\mathit{Pe}$) within ±5% accuracy. Finally, for some selected fluid indices, the governing equations are solved numerically in order to obtain Nusselt number. It is observed that the numerically obtained asymptotic Nusselt number shows excellent agreement with the analytically obtained Nusselt number.