Unified treatment of free convection adjacent to a vertical plate with three thermal boundary conditions

1992 ◽  
Vol 27 (6) ◽  
pp. 393-396 ◽  
Author(s):  
G. Ramanaiah ◽  
G. Malarvizhi
Keyword(s):  
Free Convection ◽  
Boundary Conditions ◽  
Vertical Plate ◽  
Thermal Boundary Conditions

scholarly journals Numerical Studies for Solving a Free Convection Boundary–Layer Flow Over a Vertical Plate

2020 ◽  
Vol 22 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Mohamed I. A. Othman ◽  
A. M. S. Mahdy
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Boundary Conditions ◽  
Vertical Plate ◽  
Body Force ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Legendre Collocation Method ◽  
Layer Flow ◽  
Free Convection Boundary Layer

AbstractIn this paper, The aim of this study is to present a reliable combination of the shifted Legendre collocation method to approximate of the problem of free convection boundary-layer flow over a vertical plate as produced by a body force about a flat plate in the direction of the generating body force. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shift Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The obtained results are in good agreement with those provided previously by the iterative numerical method. As a result, without taking or estimating missing boundary conditions, the shifted Legendre collocation method provides a simple, non-iterative and effective way for determining the solutions of nonlinear free convection boundary layer problems possessing the boundary conditions at infinity.

Natural Convection to Power-Law Fluids From a Heated Vertical Plate Under Mixed Thermal Boundary Conditions

1999 ◽  
Author(s):  
Elif Büyük ◽  
Mehmet C. Ece
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Power Law ◽  
Vertical Plate ◽  
Flow Behavior ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Thermal Boundary Conditions ◽  
Power Law Fluids ◽  
Mixed Thermal Boundary Conditions

Abstract Steady free convection laminar boundary-layer flow subject to mixed thermal boundary conditions along a heated vertical plate immersed in a quiescent power-law fluid is investigated. Similarity solutions are obtained numerically for the boundary-layer velocity and temperature profiles. The effects of flow behavior index and the generalized Prandtl number on the surface shear stress and heat flux are determined.

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