Making special cases less special

Four special cases are taken from the fields of thermodynamics and heat transfer, where the general solution appears not to be applicable and a separate analysis is invariably employed to produce a satisfactory result. This article shows that a separate analysis is unnecessary, and two mathematical techniques are presented which allow the general result to be reduced to a suitable expression for each special case. This alternative approach raises the interesting question as to whether or not these cases should be described as ‘special’ because they have now been dealt with by the general treatment using purely mathematical manipulation.