Semi-analytical solution of Graetz–Brinkman problem combined with non-Newtonian Ellis fluid flow in a passive channel

Heat transfer analysis of non-Newtonian fluids has numerous applications in the industrial and chemical engineering fields. Inspired by the prevalence of non-Newtonian liquids in chemical industries, this article aims to elaborate on the Graetz–Brinkman problem for an Ellis fluid inside the horizontal channel. The developed heat equation is first solved employing an analytical approach, i.e., the separation of variables, and then, the numerical solution of the eigenvalue problem is obtained by employing the MATLAB function bvp4c. The simulation is carried out for the situation of the isothermal walls. The temperature distribution under the impact of Brinkman number and model parameters is analyzed through various graphs. A comparison between the Ellis fluid and Newtonian fluid is also expounded. The results reveal that while using Ellis fluid, a higher heat transfer rate is achieved as compared to Newtonian fluid. The results may improve our comprehension of how non-Newtonian fluids transmit heat in a variety of situations. Furthermore, it is thought that this approach has made a significant contribution to the chemical sector in terms of developing and enhancing various types of thermal equipment.