Is it possible to use the PDE Toolbox to simulate heating an object with radiation from multiple sources in an environment that includes passive reflectors?

Is it possible to use the PDE Toolbox to simulate heating an object with radiation from multiple sources in an environment that includes passive reflectors?

I would like to use the PDE Toolbox for heat transfer problems where radiation is the dominant mode. Is it possible to use this tool to simulate heating an object with radiation from multiple sources in an environment that includes passive reflectors?

Answer 1

[MathWorks Support Team]

You can introduce radiation sinks and sources for stationary problems in the generic scalar

application using the elliptic PDE. The parabolic PDE (time dependent models) can not be used for

this type of problem because it is nonlinear.

Radiation sinks or sources can be defined in the 'g' coefficient in the boundary condition as an appropriate expression in 'u' and ambient temperature:

g=-5.7e-8*(u.^4-273^4)

and in the 'f' coefficient in the PDE:

f=-5.7e-8*(u.^4-273^4)

In these examples the ambient temperature was set to 273 K.

You must use the nonlinear solver and supply a reasonable initial solution. Problems with purely radiative boundary conditions will most likely not converge so you must add some convection (q>0) on the boundaries.

Thus, you can model blackbody radiation. The radiative coupling to other objects is through the ambient temperature. There is no easy way to couple several domains via radiation.

Additionally, if you change the Jacobian setting in the nonlinear solver parameter dialog to 'full'

rather than 'fixed' you will get convergence without adding any convective losses.