Steady mixed convection boundary layer flow over a vertical flat plate in a porous medium filled with water at 4°C: case of variable wall temperature |
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Authors: | S C Ling R Nazar I Pop |
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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, 3400 Cluj, CP 253, Romania |
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Abstract: | The problem of steady mixed convection boundary layer flow over a vertical impermeable flat plate in a porous medium saturated
with water at 4°C (maximum density) when the temperature of the plate varies as x
m
and the velocity outside boundary layer varies as x
2 m
, where x measures the distance from the leading edge of the plate and m is a constant is studied. Both cases of the assisting and the opposing flows are considered. The plate is aligned parallel
to a free stream velocity U
∞ oriented in the upward or downward direction, while the ambient temperature is T
∞ = T
m (temperature at maximum density). The mathematical models for this problem are formulated, analyzed and simplified, and further
transformed into non-dimensional form using non-dimensional variables. Next, the system of governing partial differential
equations is transformed into a system of ordinary differential equations using the similarity variables. The resulting system
of ordinary differential equations is solved numerically using a finite-difference method known as the Keller-box scheme.
Numerical results for the non-dimensional skin friction or shear stress, wall heat transfer, as well as the temperature profiles
are obtained and discussed for different values of the mixed convection parameter λ and the power index m. All the numerical solutions are presented in the form of tables and figures. The results show that solutions are possible
for large values of λ and m for the case of assisting flow. Dual solutions occurred for the case of opposing flow with limited admissible values of λ
and m. In addition, separation of boundary layers occurred for opposing flow, and separation is delayed for the case of water at
4°C (maximum density) compared to water at normal temperature. |
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Keywords: | Maximum density Dual solutions Mixed convection Boundary layer Porous medium Vertical plate Variable wall temperature |
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