Second Law Analysis for Third-Grade Fluid with Variable Properties

This paper investigates the entropy generation in a third-grade fluid flow with variable properties through a channel. Approximate solutions to the nonlinear boundary-value problem are obtained using Adomian decomposition method (ADM). Variation of important parameters on the fluid velocity, temperature distribution, entropy generation and irreversibility ratio are presented graphically and discussed. 1. Introduction Over the past few decades, there has been a tremendous increase in the study of heat transfer to viscous fluids due to its numerous applications in many industrial and engineering processes. As postulated in the second law of thermodynamics, the study could give insight into the thermal performance of the system by improving energy that is available for work [1, 2]. In the class of third-grade fluid, quite a lot has been done in recent times on entropy generation by assuming a constant thermal conductivity. For instance, Pakdemirli and Yilbas investigated the entropy generation in the flow of third-grade fluid through a pipe with constant viscosity in [3] while the temperature dependent viscosity has been investigated in [4] by using Vogel model. We refer interested readers to [5–14] for more interesting results on third-grade fluid flow. Moreover, Makinde and Aziz [15] presented the second law analysis of a pressure-driven temperature dependent fluid flow with asymmetry at the walls. Kahraman and Yürüsoy [16] examined the entropy generation due to non-Newtonian fluid flow in an annular pipe with relative rotation using a third-grade fluid model while Chauhan and Kumar [17] presented a non-Newtonian third-grade fluid flow in an annulus partially filled by a porous medium of very small permeability and many more results on entropy generation in literature. Surprisingly, in spite of the enormous amount of work done on the entropy generation, it is observed that not much has been done on the exergy analysis of third-grade fluid flow with variable thermal conductivity and internal heat generation. As shown by Hayat et al. [18], these variations can significantly affect the flow field. Hence a more accurate result could be obtained by taking these variations into consideration. Therefore, the specific objective of this paper is to investigate the entropy generation in the flow of third-grade fluid channel flow with temperature dependent properties. The problem under discussion is strongly nonlinear boundary valued problem. Approximate solution will be obtained using Adomian decomposition method as presented by Siddiqui et al. [19] for the