Heat Transfer

The simplest and very imprecise approach is to make a balance between the generated thermal power and the accumulating capacity of the cylinder:

P[W]*t [s] = Cp[J/(kg*K)]*(θfinal [K]- θinitial [K])*M[kg]

You may use any kind of units not only metric but the system has to be coherent.

The true time depends on the difusibility of the heated cylinder which depends on the heat conductibility, Cp and ρ. This measures the "speed" of heat ingression in the cylinder. Heat transfer from jacket to cylinder depends on the contact surface between the 2. In a 1st approximation you could consider that the cylinder has at its outside the jacket temperature.

The cylinder core will be always colder than the surface.

Thank you 'nick name' for your quick reply.

However I dont think I was clear enough in my initial explanation. What I am trying to accomplish here is cure a coated fabric with a heating jacket. This material is on a roll with a certain diameter core. I think the following would work

q=(k*Am*deltaT)/delta r

Am=log mean area

I don't know how much heat this jacket generates. Can I just assume a constant temperature of (ie. 230F) on the jacket aka outer wall of the cylinder and figure out how long will it take it to travel the distance? I'm assuming the void space inside the core would heat up if I insulate it from the environment. Thanks in advance.