The transient temperature field in a rectangular area with movable heat sources at its edge

The paper provides an exact solution to a nonstationary two-dimensional heat transfer problem where heat sources move along the edge of the area. Finite Fourier transforms are applied to find the solution. It is given as a sum of four parts. The investigations aim at the determination of the temperature distribution in a brake drum while the vehicle rolls down a slope at a constant velocity. Brake linings, brought into frictional contact with the drum in braking, constitute moving heat sources. Due to the nature of the process under examination, it is possible to assume that the heat transfer is two-dimensional. The dimensions of the brake drum (the internal radius to external radius ratio is approx. 0.95) and simplifications allow one to model it as a rectangular area.