In a clutch we have the friction interface of two materials. Therefore, for a given torque we check the ability of the softer material in normal pressure due to the axial load of the spings. A good book in machine design (Shigley, Deutschman, Norton, Juvinal, etc.) solves the problem. However, due to friction and relative velocity of the faces in the interface, we have the production of heat which has to be dissipated to the environment. In this case you have to solve the heat problem for maximun developed temperature (Rothbart HB).
Basically you need to find the maximum PV=constant (pressure vs sliding velocity) for the materials you are using to design the sliding surfaces of the clutch. Once you know your maximum sliding velocity (worse case scenario) you can specify the maximum contact pressure and from there find the dimensions of the disks (inner and outter radius). Also, the maximum working temperature can be found if you equate the kinetic energy times dynamic friction coefficient with the heat dissipation rate, i.e., PVf=CA(Ts-Ta) where f is the dynamic friction coefficient, C=heat transfer coefficient, A=Heat dissipation area, Ts=average dissipation temperature, Ta=Temperature of the surrounding environment