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Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this article, the similarity form of a non-Boussinesq gaseous plume was developed by obtaining the equation for the conservation of enthalpy flux, and using it and the continuity equation to demonstrate that the flux of density deficiency is conserved, and not the flux flux of buoyancy as is the case for Boussineq plumes.
Abstract: We develop herein the similarity form of a non-Boussinesq gaseous plume. This is done by obtaining the equation for the conservation of enthalpy flux, and using it and the continuity equation to demonstrate that the flux of density deficiency is conserved, and not the flux of buoyancy as is the case for Boussinesq plumes. We then use this conservation relation to describe the form of the similarity solution in the non-Boussinesq case. The similarity solution is then used to derive the theoretical form of the entrainment velocity across the plume edge, which is seen to be in agreement with the ‘modified entrainment assumption’ suggested empirically from experiments by Ricou & Spalding (1961).
110 citations
TL;DR: In this work, a similarity equation of the momentum boundary layer is studied for a moving flat plate with mass transfer in a stationary fluid and the solution is applicable to the practical problem of a shrinking sheet with a constant sheet velocity.
Abstract: In this work, a similarity equation of the momentum boundary layer is studied for a moving flat plate with mass transfer in a stationary fluid. The solution is applicable to the practical problem of a shrinking sheet with a constant sheet velocity. Theoretical estimation of the solution domain is obtained. It is shown that the solution only exists with mass suction at the wall surface. The equation with the associated boundary conditions is solved using numerical techniques. Greatly different from the continuously stretching surface problem and the Blasius problem with a free stream, quite complicated behavior is observed in the results. It is seen that there are three different solution zones divided by two critical mass transfer parameters, f"0"1~1.7028 and f"0"2~1.7324. When f"0f"0"2). There is a terminating point for the solution domain and the terminating point corresponds to a special algebraically decaying solution for the current problem. The current results provide a new solution branch of the Blasius equation, which is greatly different from the previous study and provide more insight into the understanding of the Blasius equation.
108 citations
TL;DR: In this paper, the effect of magnetic field on the visco-elastic liquid flow and heat transfer over a stretching sheet with non-uniform heat source was investigated. But the authors focused on the non-linear boundary layer equation for momentum and the heat transfer differential equation.
107 citations
TL;DR: In this article, the Darcy-Forchheimer flow of non-Newtonian inelastic power-law fluid through porous media has been derived from first principles, using this equation, the problem of natural, forced, and mixed convection within the porous media saturated with a power law fluid has been solved using the approximate integral method.
Abstract: The governing equation for Darcy-Forchheimer flow of non-Newtonian inelastic power-law fluid through porous media has been derived from first principles. Using this equation, the problem of Darcy-Forchheimer natural, forced, and mixed convection within the porous media saturated with a power-law fluid has been solved using the approximate integral method. It is observed that a similarity solution exists specifically for only the case of an isothermal vertical flat plate embedded in the porous media. The results based on the approximate method, when compared with existing exact solutions show an agreement of within a maximum error bound of 2.5%.
107 citations
TL;DR: In this paper, the problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined, and the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter are derived.
Abstract: The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.
106 citations