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Couple two nonlinear pdes

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Hi everyone,

I am working on a problem in which hot viscous fluid from an inlet spreads on inclined cold surface. The fluid film is thin so vertical variation of temperature is ignored. The problem has two coupled nonlinear pdes, one for the film thickness h(x,y), and one for the temperature T(x,y). I use the pde interface to do the simulation. For current simple treatment, the viscosity is temperature independent, so h(x,y) does not involve T(x,y), and the simulation of h(x,y) works well. But the temperature simulation, which depends on h(x,y), gives nonsensical result. I am not sure if I coupled the two pdes correctly. Can someone help me on this?

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