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Consider the Robin boundary condition for the diffusion/heat equation $u_t=a(t)u_{xx}+f(x,t)$:

$$-k(t)u_x(0,t)=h(t)u(0,t)$$

or

$$u_x(0,t)+\frac{h(t)}{k(t)}u(0,t)=0$$

where $k(t)$ thermal conductivity and $h(t)$ heat tranfer coefficient.

My Question: Is it possible that the ratio $h(t)/k(t)$ to be constant? Could anyone please help me? I have really no idea.

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  • $\begingroup$ İ want to solve the equation and if this ratio is constant i can continue. I just want to know that whether it has a physical meaning or not $\endgroup$
    – math
    Commented Apr 9, 2015 at 3:03
  • $\begingroup$ From dimensional analysis it should be clear that the ratio is time independent... $\endgroup$
    – J. LS
    Commented Apr 9, 2015 at 14:57
  • $\begingroup$ @J.LS thanks for answering. Can you give a specific reference so that I can look at it. $\endgroup$
    – math
    Commented Apr 9, 2015 at 20:03

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The heat transfer coefficient and the thermal conductivity can often be treated as constants in practical heat transfer problems. However, the heat transfer coefficient can change if the exterior convective flow conditions change.

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  • $\begingroup$ Thanks for answering. Do you know a physical/ chemical process in which such boundary condition occurs and the ratio in problem can be taken as constant. $\endgroup$
    – math
    Commented Apr 13, 2015 at 10:33

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