This work presents hybrid numerical-analytical solutions for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the interface fluid-solid wall. This conjugated conduction-convection problem is first simplified through the employment of the Coupled Integral Equations Approach (CIEA) to reformulate the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, a partial differential formulation for the average wall temperature is obtained, while a third kind boundary condition is achieved for the fluid in the heat balance at the solid-fluid interface. From the available velocity distributions, the solution method is then proposed for the coupled partial differential equations, based on the Generalized Integral Transform Technique (GITT) under its partial transformation mode, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve.
Transient Conjugated Conduction: External Convection With Front Face Imposed Wall Heat Flux
Naveira, CP, Cotta, RM, Lachi, M, & Padet, J. "Transient Conjugated Conduction: External Convection With Front Face Imposed Wall Heat Flux." Proceedings of the ASME 2007 International Mechanical Engineering Congress and Exposition. Volume 8: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A and B. Seattle, Washington, USA. November 11–15, 2007. pp. 1371-1380. ASME. https://doi.org/10.1115/IMECE2007-41417
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