A New Insight into the Convective Boundary Condition

• Published in: Transport in porous media Vol. 99; no. 1; pp. 55 - 71
• Main Author: Magyari, Eugen
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2013; Springer
• Subjects: Boundary conditions; Civil Engineering; Classical and Continuum Physics; Convection; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Exact sciences and technology; Geotechnical Engineering & Applied Earth Sciences; Heat flux; Heat transfer; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Mathematical analysis; Pollution, environment geology; Sedimentary rocks; Transport; Wall temperature; Walls; Convective boundary conditions; Mixed convection; Self-similar solutions; Darcy porous media; Vertical surface; boundary layer; transport; velocity; convection; shear stress; temperature; heat flux; boundary conditions; porous media; heat transfer
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-013-0173-7

The steady mixed convection boundary layer flows over a vertical surface adjacent to a Darcy porous medium and subject respectively to (i) a prescribed constant wall temperature, (ii) a prescribed variable heat flux, q w = q 0 x − 1 / 2 , and (iii) a convective boundary condition are compared to each other in this article. It is shown that, in the characteristic plane spanned by the dimensionless flow velocity at the wall f ′ ( 0 ) ≡ λ and the dimensionless wall shear stress f ′ ′ ( 0 ) ≡ S , every solution ( λ , S ) of one of these three flow problems at the same time is also a solution of the other two ones. There also turns out that with respect to the governing mixed convection and surface heat transfer parameters ε and γ , every solution ( λ , S ) of the flow problem (iii) is infinitely degenerate. Specifically, to the very same flow solution ( λ , S ) there corresponds a whole continuous set of values of ε and γ which satisfy the equation S = − γ ( 1 + ε − λ ) . For the temperature solutions, however, the infinite degeneracy of the velocity solutions becomes lifted. These and further outstanding features of the convective problem (iii) are discussed in the article in some detail.