<p>The primary motivation behind this study is to conduct an analysis of entropy generation (within the broader context of the pursuit of entropy generation minimization, EGM) in the unsteady, pressure-driven flow of a third-grade fluid subjected to various fluid flow and heat transfer conditions. The specific fluid flow and heat transfer conditions are the following; the flow domain is permeated with porous media which will be modelled via a modified Darcy law; the fluid is chemically reactive leading to exothermic reactions which are modelled via Arrhenius kinetics; the flow is subjected to thermal radiation which is modelled via the Rosseland approximation; the flow field is subjected to a transverse magnetic field; and finally, transverse injection/suction flow is applied to the flow field at constant velocity. The fluid velocity will be considered temperature dependent as modelled via a Nahme law. The resultant system of governing equations is a set of coupled partial differential equations (PDEs) whose coupled and complex nature requires the application of robust numerical solution methodologies. We solve the governing PDEs via an efficient and robust direct numerical solution methodology which utilizes semi-implicit finite difference techniques as derived from the finite difference methods. The primary flow field variables (namely the velocity and temperature) as well as the corresponding derivative variables, such as the wall shear stress (skin friction), wall heat transfer rate, irreversibility ratio, and entropy generation, are presented graphically and hence analysed qualitatively. Key insights obtained from the study include the following. The sensitivity of the primary flow field variables to changes in the values of the embedded flow parameters leads to similar qualitative behaviour, specifically parameters that increase/decrease the flow velocity and in turn also increase/decrease the fluid temperature, respectively, and vice versa. We also notice that the behaviour of the primary flow field variables also mirrors the behaviour of both the wall shear stress (skin friction) and the wall heat transfer rate. Specifically, parameters that increase/decrease the primary flow field variables qualitatively also increase/decrease the skin friction as well as the wall heat transfer rate. We additionally also notice that exothermic reactions as well as thermal radiation may lead to the thermal runaway phenomena. The study subsequently demonstrates conditions under which the thermal runaway phenomena may be mitigated. The concept of EGM is a fundamental engineering design-related issue, specifically with regard to heat transfer processes in which irreversibility concepts are a major concern. The results demonstrate the effects of the various important parameters on entropy generation and hence also give insights into how EGM may be achieved. This study therefore connects in a natural way, the concept of EGM to the various important fluid flow and heat transfer mechanisms such as the drag-inducing properties (such as injection/suction, magnetic field strength, porous media strength, and viscosity) and the thermal runaway inducing properties (such as exothermic reactions and thermal radiation). The results, findings, and observations of the present study are therefore of fundamental importance to optimal engineering designs that are focused on EGM.</p>