Figure 3 shows an infinite plane wall of thickness 2L with uniform internal heat source of q 0 in [0, L] and cooling source of -q 0 in [-L, 0] under...

Figure 3 shows an infinite plane wall of thickness 2L with uniform internal heat source of q0 in [0, L] and cooling source of -q0 in [-L, 0] under steady heat conduction, i.e

{(d2t/dx2)+(q/k)} = 0 where q= q0 when 0<x<L and q= -q0 when -L<x<0

The boundary conditions are T=T1 at x=-L and T=T2 at x=L. We can solve the problem piece wisely by finding solutions in [-L,0] and [0,L]

(a) By requiring the temperature at x=0 to be T0 and heat flux at x=0 to be continuous, show that solutions are

T= [-(q0/2k)* x(x-L)]+ (T2/L)*x + (T0/L)*(L-x) when 0<x<L

T= [(q0/2k)* x(x+L)] - (T1/L)*x + (T0/L)*(L+x) when -L<x<0

where T0= (T1+T2)/2

(b) Find the locations of local maximum and minimum temperature.

(c) Calculate maximum and minimum temperatures.