Translate the following into a PDE with boundary conditions

The ends of a homogeneous rod of length L are insulated, but heat leaks from the lateral surface of the rod into the surrounding medium, which is at temperature . Heat travels through the rod's surface much more slowly than within the rod so, at any particular time, on any cross section of the rod, the temperature difference between the center and the edge of the cross section is negligible. The initial temperature is throughout the rod. How to enter the answers.

The PDE is
The boundary values / initial conditions are:
Left end is insulated :
Right end is insulated :
Initial temperature is :

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