Abstract
A finite element method is used to study the heat-transfer response of an incompressible, laminar, transient free convection flow over a semi-infinite vertical plate. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved using the Newton–Raphson iteration. The resulting first-order ordinary differential equations with respect to time are solved using the implicit Euler scheme. Numerical results for the details of the velocity and temperature contours and profiles as well as heat transfer rate in terms of Nusselt number which are shown on graphs have been presented.
Zusammenfassung
Eine Finite Elemente Methode wird für die Untersuchung der Wärmeübertragung bei der laminaren, instationären freikonvektiven Strömung eines inkompressiblen Fluids über eine halb-unendliche, vertikale Platte eingesetzt. Die das Problem beschreibenden nichtlinearen und dimensionsfreien Gleichungen werden linearisiert und unter Einsatz des Newton–Raphson Iterationsverfahrens gelöst. Die erhaltenen, zeitabhängigen Differentialgleichungen 1. Ordnung werden unter Verwendung des impliziten Eulerverfahrens numerisch ausgewertet. Ergebnisse für Geschwindigkeit- und Temperaturprofile und auch für die Nusseltzahl werden dargestellt und diskutiert.
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Abbas, I. Finite element analysis of transient free convection flow over vertical plate . Forsch Ingenieurwes 70, 263–268 (2005). https://doi.org/10.1007/s10010-006-0039-z
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DOI: https://doi.org/10.1007/s10010-006-0039-z