scholarly journals Dual Solutions for Boundary Layer Flow of Moving Fluid over a Moving Surface with Power-Law Surface Temperature

2013 ◽  
Vol 18 (1) ◽  
pp. 113-124 ◽  
Author(s):  
S. Mukhopadhyay ◽  
R.S.R. Gorla
Keyword(s):  
Boundary Layer ◽  
Surface Temperature ◽  
Power Law ◽  
Flat Surface ◽  
Similarity Solutions ◽  
Dual Solutions ◽  
Power Law Exponent ◽  
Layer Flow ◽  
Forced Convective Flow ◽  
Moving Fluid

An analysis of heat transfer for boundary layer forced convective flow past a moving flat surface parallel to a moving stream is presented. The power-law surface temperature at the boundary is prescribed. The surface temperature varying directly (or inversely) with power-law exponent is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with known results from the open literature for some particular cases of the present study. When the surface and the fluid move in the opposite directions, dual solutions exist.

Influence of Space-Varying Surface Heat Flux on the Heat Transfer Due to a Moving Fluid Over a Moving Surface

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Swati Mukhopadhyay ◽  
Iswar Chandra Mondal ◽  
Kuppalapalle Vajravelu ◽  
Robert A. Van Gorder
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Power Law ◽  
Surface Heat Flux ◽  
Flat Surface ◽  
Similarity Solutions ◽  
Surface Heat ◽  
Forced Convective Heat Transfer ◽  
Moving Fluid

Boundary-layer forced convective heat transfer at a moving flat surface parallel to a moving stream is presented for the case where the plate is subjected to a variable heat flux. In particular, we assume that the surface heat flux varies with spatial variable x according to a power-law rule. The similarity solutions for the problem are obtained by solving the reduced ordinary differential equations numerically, while exact solutions are provided for certain parametric values. It is noted that even in the case of prescribed surface heat flux, dual solutions exist when the surface and the fluid move in opposite directions.

SIMILARITY SOLUTIONS OF THE MIXED CONVECTION BOUNDARY-LAYER FLOW IN A POROUS MEDIUM

2007 ◽  
Vol 04 (04) ◽  
pp. 621-631 ◽  
Author(s):  
S. A. KHURI
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Mixed Convection ◽  
Power Law ◽  
Boundary Layer Flow ◽  
Vertical Surface ◽  
Similarity Solutions ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Layer Flow

This paper deals with the asymptotic analysis of similarity solutions of the two-dimensional mixed convection boundary-layer flow over a vertical surface with a power law temperature. It is shown that the extended governing equations can be reduced, using a coordinate transform, to the case of the boundary-layer development of large time solutions for the unsteady mixed convection near the stagnation point on a vertical surface in a porous medium. The perturbation solutions for small and large values of the mixed convection parameter are obtained. The asymptotic behavior of the solution was examined for different values of the power law exponent parameter.

Additional results for the problem of MHD boundary-layer flow past a stretching/shrinking surface

2016 ◽  
Vol 26 (7) ◽  
pp. 2283-2294 ◽  
Author(s):  
Ioan Pop ◽  
Natalia C. Roşca ◽  
Alin V. Roşca
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Layer Flow ◽  
Similarity Solutions ◽  
Lower Solution ◽  
Dual Solutions ◽  
Suction Parameter ◽  
Content Type ◽  
Layer Flow ◽  
The Stability

Purpose The purpose of this paper is to reinvestigate the problem of multiple similarity solutions of the two-dimensional magnetohydrodynamic boundary-layer flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking permeable surface studied by Aly et al. (2007). Design/methodology/approach The transformed ordinary (similarity) differential equation was solved numerically using the function bvp4c from MATLAB. The relative tolerance was set to 10^(−10). Findings Dual solutions were found and a stability analysis was performed to show which solutions are stable and which are not stable. On the other hand, Aly et al. (2007) have shown that for each value of the power index and magnetic parameter in the range and for any specific values of the stretching/shrinking parameter and suction parameter the problem has only a solution. Originality/value The paper describes how multiple (dual) solutions for the flow reversals were obtained. The stability analysis has shown that the lower solution branches are unstable, while the upper solution branches are stable.

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