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This book explains the hydrodynamic and thermal behavior of laminar Newtonian fluid flow in channels partially filled with porous material, symmetrically distributed at the walls. Using the Successive Accelerated Replacement (SAR) numerical scheme, the analysis explores the influence of porous fraction (Gamma ), Darcy number (Da), Peclet number (Pe), and Brinkman number (Br) on flow and heat transfer. Results show that axial conduction significantly affects temperature profiles at low Pe (<100), while viscous dissipation (Br) alters thermal gradients, elevating bulk temperatures under constant heat flux. A minimum local Nusselt number occurs at intermediate Gamma , independent of axial location, suggesting optimal porous thickness for heat transfer. The interplay of parameters highlights design considerations for systems balancing flow resistance and thermal efficiency, particularly in applications requiring precise thermal management.