TY - JOUR
T1 - Effect of viscous dissipation on the Darcy free convection boundary-layer flow over a vertical plate with exponential temperature distribution in a porous medium
AU - Magyari, E
AU - Rees, D A S
N1 - ID number: ISI:000237987200003
PY - 2006
Y1 - 2006
N2 - The title problem is investigated for an upward projecting hot plate ("upflow") and for its downward projecting cold counterpart ("downflow"). When viscous dissipation is negligible, these two cases are physically equivalent, but the heat released by viscous friction breaks the equivalence between the upflow and downflow cases, and substantial differences occur. In particular, we find that, for self-similar flows, downflow is possible for all nonnegative values of the temperature exponent, but upflow only exists above a critical value of this parameter, which equals the half of the Gebhart number of the fluid. Each two upflow and downflow solution branches were found, respectively. All the corresponding solutions decay exponentially with increasing distance from the plate. It could be shown that these up and downflow solution branches do not represent in fact two isolated solutions but, they are the limiting cases of respective families of intermediate solutions which are bounded between the branches, and which decay algebraically in the transversal far field. This paper investigates in detail the heat transfer characteristics of all these self-similar free convection flows analytically and numerically. (C) 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.
AB - The title problem is investigated for an upward projecting hot plate ("upflow") and for its downward projecting cold counterpart ("downflow"). When viscous dissipation is negligible, these two cases are physically equivalent, but the heat released by viscous friction breaks the equivalence between the upflow and downflow cases, and substantial differences occur. In particular, we find that, for self-similar flows, downflow is possible for all nonnegative values of the temperature exponent, but upflow only exists above a critical value of this parameter, which equals the half of the Gebhart number of the fluid. Each two upflow and downflow solution branches were found, respectively. All the corresponding solutions decay exponentially with increasing distance from the plate. It could be shown that these up and downflow solution branches do not represent in fact two isolated solutions but, they are the limiting cases of respective families of intermediate solutions which are bounded between the branches, and which decay algebraically in the transversal far field. This paper investigates in detail the heat transfer characteristics of all these self-similar free convection flows analytically and numerically. (C) 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.
U2 - 10.1016/j.fluiddyn.2006.02.005
DO - 10.1016/j.fluiddyn.2006.02.005
M3 - Article
SN - 0169-5983
VL - 38
SP - 405
EP - 429
JO - Fluid Dynamics Research
JF - Fluid Dynamics Research
IS - 6
ER -