A bar of length x = L has its two edges insulated and an applied initial...

  

Transcribed Image Text:

A bar of length x = L has its two edges insulated and an applied initial tempera- ture profile of u(x, t = 0) = 10x. a) State the diffusion equation and the general solutions. b) Define boundary conditions for the two edges. Hence explain which gen- eral solutions are ruled out. c) Express the remaining solution as a series and hence find the coefficients to the series. d) Suppose that the r = 0 end was kept at a fixed temperature To and the x = L end was kept insulated. Write down the boundary conditions in this case and determine the general form of the solution giving a conditon on k. A bar of length x = L has its two edges insulated and an applied initial tempera- ture profile of u(x, t = 0) = 10x. a) State the diffusion equation and the general solutions. b) Define boundary conditions for the two edges. Hence explain which gen- eral solutions are ruled out. c) Express the remaining solution as a series and hence find the coefficients to the series. d) Suppose that the r = 0 end was kept at a fixed temperature To and the x = L end was kept insulated. Write down the boundary conditions in this case and determine the general form of the solution giving a conditon on k.