Calculate the temperature and heat fluxes in the x and y

Question

Repeat Exercise 5.8.2 using

(a) one rectangle

(b) four rectangles.

Exercise 5.8.2:

If in Exercise 5.8.1, there is a uniform heat generation of 2 W/cm³, and a line source of 5 W/cm at a location of (x = 30 cm and y = 30 cm) then, calculate the new temperature distribution using

(a) two triangles and

(b) eight triangles. Calculate the temperature at the location (x = 40 cm, y = 40 cm) and the heat fluxes in both the x and y directions.

Exercise 5.8.1:

A square plate of size 100 cm by 100 cm is subjected to an isothermal boundary condition of 500 °C on the top and to a convection environment on all the remaining three sides of 100 ?C with a heat transfer coefficient of 10 W/m²K. The thermal conductivity of the plate is 10 W/m²K. Assume the thickness of the plate is 1 cm. Determine the temperature distribution in the plate using

(a) two triangles and

(b) eight triangles. Calculate the temperature and heat fluxes in the x and y directions at a location (x = 30 cm, y = 30 cm).