Heat transfer in fully developed Couette–Poiseuille flow of power‐law fluids with viscous dissipation

Abstract This study investigates fully developed, steady, laminar forced convective heat transfer in Couette–Poiseuille flow of power‐law fluids between heated parallel plates, relevant to dynamic wall heat exchangers, microfluidic devices, and polymer processing. The analysis examines the influence of the flow rate ratio between the shear‐driven (Couette) and total imposed flow on heat transfer for Newtonian and power‐law fluids, with variations in power‐law index , upper plate velocity , and Brinkman number ( or ) including viscous dissipation. A semi‐analytical velocity profile is derived, while the temperature distribution and Nusselt number are obtained analytically. These solutions provide insights into flow and heat transfer mechanisms, allow quick evaluation without extensive computations, and serve as reliable references for validating numerical simulations. Results are validated against ANSYS Fluent simulations and literature data. Findings reveal an optimal shear‐driven component opposing the pressure‐driven flow that maximizes heat transfer for a moving insulated plate. For negligible viscous dissipation , shear‐thinning fluids enhance heat transfer under purely pressure‐driven flow, while shear‐thickening fluids reach a maximum Nusselt number comparable to Newtonian fluids but at lower shear‐driven motion, reducing energy demand. The novelty lies in identifying the optimal flow rate ratio between Couette and Poiseuille components in non‐Newtonian fluids, offering a framework to maximize heat transfer while minimizing energy input. The findings aid thermal management in systems with combined flow‐driving mechanisms, for example, dynamic wall heat exchangers.