7. The one-dimensional heat chamber in the figure is modeled using one element with three nodes.

There is a uniform heat source inside the wall generating Q = 300 W/m3. The thermal conduc¬

tivity of the wall is k = 3 W/m0C. Assume that A = 1 m2 and / = 1 m. The left end has a fixed temperature of T = 20°C, while the right end has zero heat flux.

(a) Calculate the shape function [N] = [/V], A^, iVs] as a function of x.

(b) Solve for nodal temperature {T} = { T\, 7*2, T^ }T using boundary conditions. Plot the temperature distribution in x-T graph.

(c) Calculate the heat fluxes atx = 0 andx = 1 when the solution is {T} = { 20, 58.25, 71 }.

No heat flow 7*1 7*2 7*3