Ratio between heat tranfer coefficient and thermal conductivity 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.
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.