Analytical solution for coupled heat equations with convective term

Asked Dec 21 '21 at 13:51

Active Feb 17 '22 at 13:39

Viewed 33 times

The equations for (non-equilibrium) convective heat transfer between a fluid and a solid are

$$\frac{\partial T_f}{\partial t}=-v\frac{\partial T_f}{\partial x}+g(T_s-T_f)$$ $$\frac{\partial T_s}{\partial t}=h(T_f-T_s)$$

Evaluated on the spatial doman $[0,L]$. With initial and BCs $$T_f(x,0)=T_s(x,0)=T_0$$ $$T_f(0,t)=T_{in}$$

To solve these coupled equations, would one need to take a Fourier transform of both equations? If yes, what would be the next step?

Edit: deleted last BC

edited Feb 17 '22 at 13:39

asked Dec 21 '21 at 13:51

DozerD

You have four boundary conditions to impose, and a problem which admits only three conditions. Something was left over. – Cesareo Dec 24 '21 at 10:30
Yes, my bad. The last condition should not be there. – DozerD Jan 12 '22 at 17:58

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