Q-5) A solid composite sphere has an inner core (material 1) of radius r, and an outer shell (material 2) of outer radius r2.The thermal conductivities of the materials are ki and k2, respectively. If the corresponding rates of heat generations are yy and yv2, and the surface temperature of the sphere is Ts , determine the steady state temperature profile in the composite sphere. [Hint:Two separate equations for the shell and the core have to be solved. Write down these equations based on Eq.(2.53).Satisfy the symmetry condition at r = 0,the surface condition at r = r2, and the continuity of both temperature and heat flux at r=r.] [Check: if the materials are identical ,i.e. Wvi = Wv2, and ki = k2, both T, and T2 reduce to the form of Eq. (2.56).]