Entropy analysis in the Rabinowitsch fluid model through inclined Wavy Channel: Constant and variable properties

Entropy production in a system affects the efficiency of the system because it minimizes the output of the system. For the better performance of the system, it is very important to minimize the entropy production. Entropy generation is always observed in any irreversible process while it remains constant in any reversible process. Second law of thermodynamics play an important in the optimization of entropy generation rate. The main objective of this investigation is to minimize the entropy production through an inclined channel filled with Rabinowitsch fluid. For the better results, we will visually show the entropy generation under the account of two different cases. In the first case, we will choose the viscosity and thermal conductivity of the fluid as a constant and for the second case, viscosity and thermal conductivity will be treated as a variable. Further, the comparison of both the cases will be given under the effects of fluidic parameters. The Exact solutions of velocity and energy equations are obtained for the constant properties model with the help of MATHEMATICA software, while for the second model, the solution of the velocity profile is obtained in terms of analytic form with the help of MATHEMATICA version 11.0. The regular perturbation method is selected to solve the energy equation due to its complexity and presented the temperature profile in the form of an approximate analytical solution. In the end, the analytical solutions for total entropy and Bejan number for both cases are obtained with the help of Mathematica version 11.0. A small amount of entropy is observed at the bottom of the channel and maximum entropy is noted at the ciliated walls under the effect of Brinkman number. Maximum value of the entropy number is observed for the case of variable properties as compared to the uniform properties, which showed that the variable liquid properties are the best choice to minimize the entropy of the system and to increase the efficiency of the system.