Mixed convection boundary-layer flow over a vertical surface embedded in a porous medium. (English) Zbl 1033.76055
Summary: We investigate existence and uniqueness of a vertically flowing fluid passed a thin vertical fin in a saturated porous medium. We assume the two-dimensional mixed convection from the fin, which is modelled as a fixed semi-infinite vertical surface embedded in the fluid-saturated porous medium. The temperature, in excess of the constant temperature in the ambient fluid on the fin, varies as , where is measured from the leading edge of the plate, and is a fixed constant. The Rayleigh number is assumed to be large, so that the boundary-layer approximation may be made, and the fluid velocity at the edge of the boundary layer is assumed to vary as . The problem then depends on two parameters, namely and , the ratio of the Rayleigh to Péclet numbers. It is found that when () there are (is) dual (unique) solution(s) when is greater than some negative values of (which depends on ). When , there is a range of negative value of (which depends on ) for which dual solutions exist, and for both and there is a negative value of (which depends on ) for which there is no solution. Finally, solutions for and have been obtained.
|76R05||Forced convection (fluid mechanics)|
|76R10||Free convection (fluid mechanics)|
|76S05||Flows in porous media; filtration; seepage|
|76D10||Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)|
|76M45||Asymptotic methods, singular perturbations (fluid mechanics)|
|80A20||Heat and mass transfer, heat flow|