Authors: S C Ling R Nazar I Pop J H Merkin
Publish Date: 2008/05/29
Volume: 76, Issue: 1, Pages: 139-151
Abstract
The steady mixed convection boundarylayer 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 solutionsWe gratefully acknowledge the financial support received in the form of a research grant IPRA project code 09020210038EAR from the Ministry of Science Technology and Innovation MOSTI Malaysia We also wish to thank the Royal Society London for a Joint Project Grant enabling us to collaborate on this research
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