A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. The initial temperature (at time $t=0$ ) of the hot plate and cold plate are $T_{h}$ and $T_{c}$, respectively. Assume perfect contact between the plates.
Which one of the following is an appropriate boundary condition at the surface $S$ for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for $t>0$ ?
- Temperature at $S$ is same for both the plates
- Gradient of temperature at $S$ is same for both the plates
- Gradient of temperature vanishes at S
- Temperature at S is the average of $T_{h}$ and $T_{c}$
