Analytic solution for heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects

• Published in: Communications in nonlinear science & numerical simulation Vol. 14; no. 11; pp. 3867 - 3878
• Main Authors: Khani, F., Farmany, A., Ahmadzadeh Raji, M., Aziz, Abdul, Samadi, F.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2009
• Subjects: Heat transfer; Homotopy analysis method; Non-Darcy porous media; Non-Newtonian; Viscoelastic fluid; 47.65+a; 47.15.Cb; Viscoelastic fluid; Non-Darcy porous media; 47.27.Te; Homotopy analysis method; Non-Newtonian; 47.55; Heat transfer
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2009.01.031

An analytic approximate solution is presented for the natural convective dissipative heat transfer of an incompressible, third grade, non-Newtonian fluid flowing past an infinite porous plate embedded in a Darcy–Forchheimer porous medium. The mathematical model is developed in an (x,y) coordinate system. Using a set of transformations, the momentum equation is rendered one-dimensional and a partly linearized heat conservation equation is derived. The viscoelastic formulation presented by Akyildiz [Akyildiz FT. A note on the flow of a third grade between heated parallel plates. Int J Non-Linear Mech 2001;36:349–52] is adopted, which generates lateral mass and viscoelastic terms in the heat conservation equation, as well as in the momentum equation. A number of special cases of the general transformed model are discussed. A homotopy analysis method (HAM) is implemented to solve, with appropriate boundary conditions, the coupled third-order, second degree ordinary differential equation for momentum and the second-order, fourth degree heat conservation equation.