Answer Happy

Please solve D and E.
And Also please solve C.
Q.5 (25-points) A circular thin metal disc of radius unity has the boundary temperature specified by: sin (O) for 0<<27, that is: u(1,0)=sin(e), 0<e<27 A) Write down the heat-equation of the above problem; so that the temperature is u= u(r, 0,t). B) Find the steady-state temperature by using the method of separation of variables and therefore assume that the temperature u=u(,0): C) Does your solution in part (B) satisfy the DE and the boundary condition? Check? D) If the above problem becomes a solid cylinder of length 3 m, rewrite the corresponding heat-equation and boundary conditions assuming that the temperature is initially kept zero on the faces of the cylinder and sin”(@) applied on the upper surface while the lower surface is assumed to be subjected to sin (0). E) If in the above problem becomes a solid sphere of radius 2 m, rewrite the corresponding heat-equation and boundary conditions assuming that initially the boundary temperature is specified by: sin() for all e on the upper surface of the sphere while the temperature is kept (100 °C) on the lower surface where 6 is measured from the positive z-axis and e is measured from the positive x-axis. O Hints: Assume that the solution is bounded, the temperature at r=0 has a finite value, 3 1 for m=n sin (0) sin(0) --sin(30), and sin(ne) sin(m2) = 4 4. 0 for men TE | () (=