1. 2-D Steady Heat Equation x y y=b y=0 x=0 x=a T(x,b)=f(x)

4. Example

6. Temperature Distribution in x at different y stations f(x)=100(3-x)sin(x)

7. Constant temperature contour plot Red: max temperature Purple: min temperature Each line corresponds to a constant temperature, therefore, the denser the line distribution, the steeper the temperature gradient and vice versa. The direction of the local heat transfer is normal to the local constant temperature line; and its magnitude is inversely proportional to the local spacing between the two neighboring constant temperature lines.

8. Superposition of Two Solutions T 1 (x,y) T=T A T=T B T 2 (x,y) 0 0 0 0 0 0 T=T A T=T B T(x,y)=T 1 (x,y)+T 2 (x,y) 0 0