Analytic solution for heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects
✍ Scribed by F. Khani; A. Farmany; M. Ahmadzadeh Raji; Abdul Aziz; F. Samadi
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 541 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1007-5704
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✦ Synopsis
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 ðx; yÞ 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.