Similarity Solutions for Natural Convection Flow and Heat Transfer of Powell-Eyring Fluids in Porous Media with Heat Source Effects

This study investigates the natural convection flow and heat transfer characteristics of Powell-Eyring non-Newtonian fluids in a porous medium, incorporating the effects of internal heat generation or absorption.The governing equations-continuity, momentum, and energy-are formulated for an incompressible, laminar flow regime and transformed into a dimensionless form using similarity variables derived through group symmetry analysis.The Powell-Eyring constitutive relation introduces non-linear rheological behavior, transitioning smoothly to Newtonian fluid behavior under specific parameter limits.The resulting coupled non-linear ordinary differential equations are solved numerically using established methods such as the Runge-Kutta shooting technique.Parametric analyses are performed to assess the influence of key dimensionless parameters, including the Prandtl number, porous drag coefficient, heat source/sink strength, and Powell-Eyring fluid constants, on velocity and temperature profiles.The findings provide insights into thermal boundary layer behavior in complex rheological fluids and are applicable to engineering systems involving porous media heat transfer, such as geothermal reservoirs, polymer processing, and energy storage devices.