Coupled conductive-convective heat transfer using FDM

AI Thread Summary
The discussion focuses on solving a transient heat transfer problem involving both conduction and convection for a thin plate heated by two constant-temperature sources. The user has successfully implemented a finite difference method (FDM) for pure conduction using Matlab but is struggling to incorporate convection due to air velocity. They seek guidance on the appropriate equations that combine conduction and convection and how to express these in FDM form. Clarification on the problem statement is also requested. The user aims to effectively model the coupled heat transfer phenomena.
angsu119
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Now I need to solve a transient problem involving both conduction and convection.

Homework Statement


In this problem there's a thin plate being heated by two constant-temperature sources. One small source is in contact with part of the plate. Another one is separated with the plate by air.

Homework Equations


The Attempt at a Solution


I'm using Matlab, and able to solve pure conduction problem. I use the heat equation a*dT/dt=delta2dT and five point scheme. But now significant convection is coupled into the problem when air velocity is given. I'm not sure what is the corresponding equation combining both conduction and convection, and how to write the FDM form. Can anyone help me? Thanks!
 
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Is my question not stated clearly?
 
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