Summary
The problem considered is that of the cooling of an impermeable horizontal surface embedded in a saturated porous medium, the temperature of which is instantaneously reduced to that of the ambient fluid. Solutions valid for small and large times are obtained. It is found that it is not possible to join these two solutions by a numerical integration of the equations either by using direct integration or by using any of the indirect methods that have been suggested for impulsive heating problems.
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Abbreviations
- f :
-
reduced stream function
- g :
-
acceleration due to gravity
- K :
-
permeability of the porous medium
- L :
-
characteristic length
- Ra:
-
modified Rayleigh number
- t :
-
(non-dimensional) time
- T w :
-
wall temperature (fort<0)
- T 0 :
-
ambient temperature
- x :
-
(non-dimensional) horizontal coordinate
- y :
-
(non-dimensional) vertical coordinate
- α:
-
equivalent thermal diffusivity
- η, τ:
-
transformed coordinates
- θ:
-
(non-dimensional) temperature
- ψ:
-
(non-dimensional) stream function
- ξ:
-
similarity variable
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Ingham, D.B., Merkin, J.H. & Pop, I. Flow past a suddenly cooled horizontal flat surface in a saturated porous medium. Acta Mechanica 56, 205–217 (1985). https://doi.org/10.1007/BF01177118
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DOI: https://doi.org/10.1007/BF01177118