Mixed Convection Boundary-Layer Flow in a Porous Medium Filled with Water Close to its Maximum Density |
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Authors: | S C Ling R Nazar I Pop J H Merkin |
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Institution: | (1) School of Mathematical Sciences, National University of Malaysia, 43600 UKM Bangi, Selangor, Malaysia;(2) Faculty of Mathematics, University of Cluj, P.O. Box CP 253, Cluj, 3400, Romania;(3) Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK |
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Abstract: | The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water
close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity
form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures
the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing
flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus
putting a finite limit on the range of existence of solutions. |
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Keywords: | Mixed convection Porous medium Boundary-layer flow Dual solutions |
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