Develop an expression for the heat flux passing radically through a long composite cylinder of length L made up of three concentric layers of different materials and thicknesses in terms of r1, the inside radius of the inner cylinder; r2, r3 and r4, the outside radii of the inner, middle and the outer cylinders respectively; their corresponding thermal conductivities k1, k2 and k3 the temperature T1 at the inner surface of the inner cylinder and the temperature T4 at the outer surface of the outer, cylinder, T1 being greater than T4. If the inside heat transfer coefficient of a fluid at temperature T1 flowing through this cylinder is hi and the outside heat transfer coefficient of another fluid at temperature T2 Following on the outside is h0, determine the overall heat transfer coefficient referred to the inside surface.