Effect of the Source Term on Steady Free Convection Boundary Layer Flows over an Vertical Plate in a Porous Medium. Part I |
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Authors: | E Magyari I Pop A Postelnicu |
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Institution: | (1) Institute of Building Technology, Swiss Federal Institute of Technology (ETH Zürich), CH-8093 Zürich, Switzerland;(2) Faculty of Mathematics, University of Cluj, R-3400, Cluj, CP 253, Romania;(3) Department of Thermal Engineering and Fluid Mechanics, Transilvania University, 500036 Brasov, Romania |
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Abstract: | The Darcy free convection boundary layer flow over a vertical flat plate is considered in the presence of volumetric heat
generation/absorption. In the present first part of the paper it is assumed that the heat generation/absorption takes place
in a self-consistent way, the source term q
′′′≡ S of the energy equation being an analytical function of the local temperature difference T − T
∞. In a forthcoming second part, the case of the externally controlled source terms S = S(x,y ) will be considered. It is shown that due to the presence of S, the physical equivalence of the up- and downflows gets in general broken, in the sense that the free convection flow over
the upward projecting hot plate (“upflow”) and over its downward projecting cold counterpart (“downflow”) in general become
physically distinct. The consequences of this circumstance are examined for different forms of S. Several analytical solutions are given. Some of them describe algebraically decaying boundary layers which can also be recovered as limiting cases of exponentially decayingones. This asymptotic phenomenon is discussed in some detail. |
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Keywords: | volumetric heat generation parallel flows exact solutions algebraic decay exponential decay Similar flows Porous media |
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