Topic
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 paper, the authors apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD) heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate.
Abstract: We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD) heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to where is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.
14 citations
TL;DR: In this paper, a new class of similarity transformation was implemented in analyzing the three-dimensional boundary layer flow of hybrid nanofluid, which reduced skin frictions and the velocity profiles for different values of the physical parameters.
Abstract:
Purpose
The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties.
Design/methodology/approach
The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed.
Findings
The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only.
Originality/value
The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.
14 citations
TL;DR: In this paper, a perturbation theory for the vorticity generation is developed that employs, as a zero order solution, a novel two-dimensional similarity solution, and full gas-dynamic simulations of this CF demonstrate the V2G generation and support the theory.
Abstract: We show that any generic non-adiabatic slow flow of ideal compressible fluid develops a significant vorticity. As an example, an initially irrotational conductive cooling flow is considered. A perturbation theory for the vorticity generation is developed that employs, as a zero order solution, a novel two-dimensional similarity solution. Full gasdynamic simulations of this CF demonstrate the vorticity generation and support the theory. The relevance of this problem to the experiments with the "hot channels" is discussed.
14 citations
TL;DR: In this paper, the authors describe similarity solution to a general scheme for the wall jet flow of nanofluids, accounting both the similarity branches (say upper and lower), allowed with respect to the suction and moving wall conditions in the context of Glauert type e-jets.
14 citations
TL;DR: In this article, it was shown that the standard analytic similarity solution is positively stable with respect to symmetric (one-dimensional) perturbations, and all other similarity solutions are positively unstable.
Abstract: A necessary condition for the asymptotic approach of symmetric converging flows to a self‐ similar form is the stability of the one‐dimensional partial differential equations when linearized about the appropriate similarity solutions. For the converging shock problem, and (for sufficiently large adiabatic exponent γ) also for the collapsing free‐surface problem, it is found that (1) the standard, analytic similarity solution is positively stable with respect to symmetric (one‐ dimensional) perturbations, and (2) that all other similarity solutions are positively unstable. For the free‐surface problem when γ is small, there seem to be three regimes: neutral stability, instability of all solutions, and stability of a degenerate solution.
14 citations