A general class of coupled nonlinear differential equations arising in self-similar solutions of convective heat transfer problems |
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Authors: | Robert A Van Gorder K Vajravelu |
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Institution: | Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA |
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Abstract: | We establish existence and uniqueness results for a general class of coupled nonlinear third order differential equations arising in flow and heat transfer problems. We consider solutions over the semi-infinite interval. As special cases, we recover the existence and uniqueness results of solutions for the following physically meaningful scenarios (among others): (i) flow and heat transfer over a stretching sheet, (ii) flow and heat transfer over a nonlinearly stretching porous sheet, (iii) linear convective flow and heat transfer over a porous nonlinearly stretching sheet and (iv) nonlinear convective heat transfer over a porous nonlinearly stretching sheet. In all the cases the effects of viscous dissipation and the internal heat generation/absorption on the flow and heat transfer characteristics are included. Moreover, the obtained results are applicable to several problems dealing with flow and heat transfer phenomena. |
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Keywords: | Boundary layer flow Nonlinear ordinary differential equations Coupled equations Similarity solution Viscous flow Stretching surface Existence theorem Uniqueness theorem |
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