Ramification of Hall effects in a non-Newtonian model past an inclined microchannel with slip and convective boundary conditions

Many applications, including micro air vehicles, automotive, aerospace, refrigeration, mechanical–electromechanical systems, electronic device cooling, and micro heat exchanger systems, can be used to determine the heat flow in microchannels. Regarding engineering applications, heat flow optimization discusses the role of entropy production minimization. Therefore, this work explores new facets of entropy production in fully developed Carreau fluid heat transport in an inclined microchannel considering exponential space/temperature dependence, radiative heat flux, and Joule heating. The Carreau fluid model’s rheological properties are taken into account. Additionally, the influence of Hall slip velocity and convective boundary conditions is considered. Using appropriate transformation constraints, the governing equations are transformed into a system of ordinary differential equations, which are then numerically solved using the fourth- and fifth-order Runge–Kutta–Fehlberg method. Graphs illustrate a significant discussion of physical parameters on production of entropy, Bejan number, thermal field, and velocity. Our findings established that there is a dual impact of entropy generation for the exponential space/temperature-dependent, radiation parameter, Hall parameter, Weissenberg number, and velocity slip parameter. The Bejan number decreased with the Hall current and the Weissenberg number, and it enhanced with exponential space/temperature dependent. The convection constraint maximizes the entropy at the channel walls. The results are compared with exact solutions, which show excellent agreement.