Coupled conductive-convective heat transfer using FDM

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SUMMARY

This discussion focuses on solving a transient heat transfer problem involving both conduction and convection using the finite difference method (FDM) in MATLAB. The scenario involves a thin plate heated by two constant-temperature sources, one in direct contact and another separated by air. The user successfully addresses pure conduction using the heat equation but seeks guidance on incorporating convection due to air velocity into the FDM formulation. The key challenge is to derive the appropriate equation that combines conduction and convection for accurate modeling.

PREREQUISITES
  • Understanding of transient heat transfer principles
  • Familiarity with the heat equation and its applications
  • Proficiency in MATLAB programming for numerical simulations
  • Knowledge of finite difference methods (FDM) for solving differential equations
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  • Research the combined heat transfer equation for conduction and convection
  • Learn how to implement the finite difference method for transient heat conduction problems
  • Explore MATLAB functions for simulating fluid dynamics and heat transfer
  • Study the effects of boundary conditions on heat transfer in coupled systems
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Students and professionals in mechanical engineering, thermal analysis, and computational fluid dynamics who are working on heat transfer problems involving both conduction and convection.

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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