A general class of coupled nonlinear differential equations arising in self-similar solutions of convective heat transfer problems

作者：Van Gorder Robert A^*; Vajravelu K

来源：Applied Mathematics and Computation, 2010, 217(2): 460-465.

DOI：10.1016/j.amc.2010.05.077

• Boundary layer flow
• Nonlinear ordinary differential equations
• Coupled equations
• Similarity solution
• Viscous flow
• Stretching surface
• Existence theorem
• Uniqueness theorem

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.

• 出版日期2010-9-15