6. In order to solve one-dimensional steady-state heat transfer problem, one element with thre nodes is used. The shape functions and the conductivity matrix before applying boundary cc ditions are given.

' Ni(x) = 1 — 3x + 2x2 f 1 —2 1 "

< iV2 {x) = 4x — 4x2 , [Kr] = —2 4 —2 _ N3 (x) = —x + 2x2 1 ~2 2

(a) When the temperature at Node 1 is equal to 40oC and the heat flux of 80 W is provided Node 3, calculate the temperature at x = 1 /4 m.

(b) When the temperature at node 1 is equal to 40oC and the convection boundary condition applied at node 3 with /j = 4 W/m2/°C, = 100oC, calculate the temperature x = l/4m.

(c) Instead of the previous boundary conditions, heat fluxes at Nodes 1 and 3 are given as Q\ a

<23, respectively. Can this problem be solved for the nodal temperatures? Explain your answ