NONE 20251219115855046 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER 1790-5044 2224-3461 M. H. Hamdan Department of Mathematics and Statistics University of New Brunswick 100 Tucker Park Road, Saint John, New Brunswick CANADA Fima Fima Department of Mathematics and Statistics University of New Brunswick 100 Tucker Park Road, Saint John, New Brunswick CANADA D. C. Roach Department of Engineering, University of New Brunswick, 100 Tucker Park Road, Saint John, New Brunswick, E2L 4L5, CANADA Equations governing the flow of a polar fluid, with pressure-dependent Newtonian viscosity, through a variable-porosity medium are developed. Averaged equations are obtained using intrinsic volume averaging. A drag function is introduced to account for the interactions of the fluid with the porous matrix. Darcy and Forchheimer generalized terms, which utilize friction factor description, are included in the model equations for both granular and consolidated media to account for the effects of the porous microstructure. The developed model equations are important in the study of blood and nutrient flows in body tissues and organs, and in modelling and control of flow through synthetic porous materials that replace human tissues in burn victims. Potential other applications include flow simulation of oil products in ground layers and industrial porous domains. 12 19 2025 12 19 2025 103 10 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/232012.2025.20.10 https://wseas.com/journals/hmt/2025/a205112-010(2025).pdf S.C. Cowin, The Theory of Polar Fluids, Advances in Applied Mechanics, Vol. 14, pp. 279–347, 1974. https://doi.org/10.1016/S0065-2156(08)70034-6. E.L. Aero, A.N. Bulygin and E.V. 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