An infinite plate of thickness 2L is suddenly exposed to a constant-temperature radiation heat source or sink of temperature Ts. The plate has a uniform initial temperature of Ti. The radiation heat loss from each side of the plate is given by q = σεA(T4 − T4s), where σ and ε are constants and A is the surface area. Assuming that the plate behaves as a lumped capacity, that is, k → ∞, derive an expression for the temperature of the plate as a function of time.