Transient Temperature Distribution in Partially Filled Rotating Horizontal Cylinders

The transient temperature distribution in an infinitely long horizontal rotating cylinder which is partially filled by a viscous fluid is calculated. Thermal boundary and initial conditions are such that the fluid starts from a uniform temperature, and that the outer boundary (cylinder surface) is isothermal at a different temperature. Nondimensional analysis shows that the problem can be fully described by a properly defined Fourier modulus and a normalized bubble eccentricity.