Buoyancy Effects on Thermal Boundary Layer Over a Vertical Plate With a Convective Surface Boundary Condition

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
O. D. Makinde ◽  
P. O. Olanrewaju
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Vertical Plate ◽  
Nonlinear Partial Differential Equations ◽  
Integration Scheme ◽  
Surface Boundary ◽  
Thermal Buoyancy ◽  
Interface Characteristics ◽  
Surface Boundary Condition

This study aims to analyze the effects of thermal buoyancy on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth-order Runge–Kutta integration scheme. The variations in dimensionless surface temperature and fluid-solid interface characteristics for different values of Prandtl number (Pr), local Grashof number Grx, and local convective heat transfer parameter Bix are graphed and tabulated. A comparison with previously published results on special case of the problem shows excellent agreement.

scholarly journals Mixed Convection Boundary Layer Flow towards a Vertical Plate with a Convective Surface Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Fazlina Aman ◽  
Anuar Ishak
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Mixed Convection ◽  
Vertical Plate ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Surface Boundary ◽  
Convective Parameter ◽  
Surface Boundary Condition

The steady mixed convection flow towards an impermeable vertical plate with a convective surface boundary condition is investigated. The governing partial differential equations are first reduced to ordinary differential equations using a similarity transformation, before being solved numerically. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that dual solutions exist for the opposing flow, whereas for the assisting flow, the solution is unique. Moreover, increasing the convective parameter is to increase the skin friction coefficient and the heat transfer rate at the surface.

scholarly journals Analytical Analysis of Effects of Buoyancy, Internal Heat Generation, Magnetic Field, and Thermal Radiation on a Boundary Layer over a Vertical Plate with a Convective Surface Boundary Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Solomon Bati Kejela ◽  
Mitiku Daba Firdi
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Boundary Condition ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Vertical Plate ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Surface Boundary ◽  
Surface Boundary Condition

In this paper, the effects of magnetic field, thermal radiation, buoyancy force, and internal heat generation on the laminar boundary layer flow about a vertical plate in the presence of a convective surface boundary condition have been investigated. In the analysis, it is assumed that the left surface of the plate is in contact with a hot fluid, whereas a stream of cold fluid flows steadily over the right surface, and the heat source decays exponentially outwards from the surface of the plate. The governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations with the help of similarity transformation which were solved analytically by applying the optimal homotopy asymptotic method. The variations of fluid velocity and surface temperature for different values of the Grashof number, magnetic parameter, Prandtl number, internal heat generation parameter, Biot number, and radiation absorption parameter are tabulated, graphed, and interpreted in physical terms. A comparison with previously published results on similar special cases of the problem shows an excellent agreement.

scholarly journals The role of thermal radiation on the boundary layer past a stationary flat plate with constant surface boundary condition

2021 ◽  
Vol 1 (2) ◽  
pp. 7-11
Author(s):  
Gabriel Samaila
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Prandtl Number ◽  
Thermal Radiation ◽  
Flat Plate ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Surface Boundary ◽  
Surface Boundary Condition

This study is devoted to investigating the importance of thermal radiation on the boundary layer over a horizontal surface considering classical constant surface boundary condition. The mathematical model consists of coupled two-dimensional partial differential equations which are transformed to the set of ordinary differential equations via the similarity transformation. The final set of dimensionless equations is solved numerically using Runge Kutta Fehlberg (RKF45) method in Maple software. The significant effect of the thermal radiation is examined using four fluids namely; water, Sulphur oxide, air and mercury whose respective Prandtl numbers are 7, 2, 0.72 and 0.044. The influence of other prominent parameters affecting the flow formation and temperature profile is demonstrated using tables and graphs. The results indicated that the thermal boundary layer thickness could be increase by reducing the Prandtl number. The results also showed that increasing the thermal radiation parameter has a positive impact on the boundary layer thickness. The heat transfer rate could be improved by increasing thermal radiation or decreased by increasing the values of the Prandtl number. Regarding the temperature gradient, an observable increasing is seen far from the flat plate with the growing of thermal radiation whereas the opposite trend is true near the plate surface.

scholarly journals Similarity solution for natural convection from a moving vertical plate with internal heat generation and a convective boundary condition

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 137-143 ◽  
Author(s):  
Oluwole Makinde
Keyword(s):  
Boundary Condition ◽  
Natural Convection ◽  
Differential Equations ◽  
Heat Generation ◽  
Vertical Plate ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Integration Scheme ◽  
Surface Boundary ◽  
Local Skin

Steady laminar natural convection flow over a semi-infinite moving vertical plate in the presence of internal heat generation and a convective surface boundary condition is examined in this paper. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface of the plate contains a heat source that decays exponentially with the classical similarity variable. The governing non-linear partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth order Runge-Kutta integration scheme. The effects of physical parameters on the dimensionless velocity and temperature profiles are depicted graphically and analyzed in detail. Finally, numerical values of physical quantities, such as the local skin-friction coefficient and the local Nusselt number are presented in tabular form.

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