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This work investigates the Ohmic heating, nonuniform heat generation, and Hall effects with Cattaneo-Christov model (CCM) on flow and heat transfer of power-low non-Newtonian fluids (NNFs) past stretching surface embedded in a porous medium. Runge-Kutta method is used to solve non-linear ODEs numerically using a shooting procedure. We study non-Newtonian fluids for power law values of 0.7 and 1.2, respectively. Innovation of this work lies in studying the effect of Hall currents in presence of buoyancy force and an irregular heat source on slip flow of NNFs moving through Darcy porous medium. Varying velocities, surface frictional forces, and Nusselt numbers are examined. Resulting entropy is also examined using computational flow problem investigation. Model-simulated results suggested that various factors play critical role in constructing thermal systems. It is asserted that Hall parameter, mixed convection parameter, Biot numbers, and thermal relaxation time improve heat transference rates by directly affecting fluid molecules temperature. [ABSTRACT FROM AUTHOR]