References for implementation of time dependent Robin BC
 

For a scalar T, the standard robin BC can be written as

alpha * (partial T/ partial Y) + beta * T = gamma

where alpha, beta and gamma are either constants or functions of space/time. In the above equation 'Y' is the independent space variable.

I am looking for a reference which discusses the implementation of slightly different condition, hope I am not wrong in calling it Robin BC. The BC of my interest is as follows

alpha * (partial T/ partial Y) + beta * (partial T/ partial t) = gamma

where 't' is time.

I appreciate your response.

Thank you

but your (partial T/ partial t) depends on your governing equation ... therefore you can substitute the the term evaluating on the boundary