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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 paper, numerical solutions for the similarity formulation of the equations, closed with an eddy viscosity model, governing the flow in a buoyant plume in a stratified environment are found.
Abstract: Numerical solutions are found for the similarity formulation of the equations, closed with an eddy viscosity model, governing the flow in a buoyant plume in a stratified environment The effects of the stratification on the velocity and temperature profiles are studied Comparisons between computed results and experimental data are made
TL;DR: Wei et al. as discussed by the authors derived generalized analytical solutions for the mean transverse velocity and Reynolds shear stress for the far field of planar turbulent wakes under arbitrary pressure gradients by using a combination of integral and self-similarity analyses.
Abstract: By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. The findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.
16 Jun 2022
TL;DR: In this article , an analytic solution is found for the temperature and velocity profiles at the leading edge of a heated flat plate under forced uniform flow, by defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytical solution at the edge.
Abstract: The heated flat plate under uniform flow has been vastly studied, with the Blasius and Pohlhausen solutions developed over 100 years ago. These solutions are numerical in nature. Here, an analytic solution is found for the temperature and velocity profiles at the leading edge of a heated flat plate under forced uniform flow. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution at the leading edge. This report gives justification for the similarity variable via scaling analysis, details the process of converting to similarity form, and presents a similarity solution. The analytic fluid and thermal solutions are then checked against a numerical solution obtained via computational dynamics.
01 Jan 2023
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TL;DR: In this article, the problem of magnetohydrodynamic (MHD) free convection over a non-isothermal axisymmetric body under the action of transverse magnetic field was investigated.
Abstract: The study investigates the problem of magnetohydrodynamic (MHD) free convection over a non-isothermal axisymmetric body under the action of transverse magnetic field. The body is embedded in a porous medium saturated with electrically conducting non-Newtonian power law fluid. In order to obtain similarity solution, it is assumed that the viscosity of the fluid decays exponentially with temperature. The qualitative results are illustrated for a vertical flat plate, horizontal cylinder and sphere.