A plane wall with thickness 10cm and thermal conductivity 10

A plane wall with thickness 10cm and thermal conductivity 10W/mK has internal heat generation of q=400W/m3 . One side of the wall (i.e., at x = -0.05m) is kept at 40C and the other (x = 0.05m) at 20C. (a) Find the temperature distribution in C as a function of x. Assume the midpoint of the wall as your origin. (b) Find the location of maximum temperature in the wall. (c) Find the maximum wall temperature in C.

Solution

a)

T= T₁+(T₂-T₁)x/l +qx\\2k (l-x)

T= 40+20x/1 +400x/20 (1-x)

T= 40 +20x +20x(1-x)

T= -20x^₂+40x+40

b) Tmax will be at dt/dx=0 and d²t/dx²=-ve

at x=1 T is max.

c) Tmax= 60C