Abstract
The fully developed free convection flow in a vertical slot with open to capped ends discussed by Weidman [5] and Magyari [6] is scrutinized in this present work. Exact solution of momentum and energy equations under relevant boundary conditions as discussed in [5, 6] is obtained using the D’Alembert’s method. Numerical comparison of this present work is made with previous result of [6] and the results were justified using the well-known implicit finite difference method (IFDM); this gives an excellent comparison. During the course of numerical investigation, it is found that D’Alembert’s approach is a simpler, reliable and accurate tool for solving coupled equations.
Highlights
IntroductionLaminar flow between two differentially-heated vertical plates is a classical problem in free convection flow due to its applications in industrial and technological world
Laminar flow between two differentially-heated vertical plates is a classical problem in free convection flow due to its applications in industrial and technological world.A lot of researchers have worked on fluid flow when both ends are capped as well as when both ends are opened
In order to verify the accuracy of the present method, we obtained numerical values of equations (14) and (15), compare it with the solutions of Magyari [6] and use the well-known implicit finite difference method (IFDM) to justify the results
Summary
Laminar flow between two differentially-heated vertical plates is a classical problem in free convection flow due to its applications in industrial and technological world. A lot of researchers have worked on fluid flow when both ends are capped as well as when both ends are opened. Batchelor [1] gives a detailed analysis of the conduction and convection regime flow whereas the analytical studies and experimental values of τ were carried out by Elder [2]. Daniel [3] discussed a transition from the conductive to convective regime for closed cavities for flow with large Prandtl numbers. Buhler [4] reported a significant result of stable laminar convection in a tall slender cavity. He proposed a generalized case by assuming the ends of the channel to be porous
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