Question

Bricks 0.15 m thick separate the inside of the furnace from the room surrounding it. The temperature of the air and the walls of the room are both 25°C. The thermal conductivity of the bricks is 1.2 W/(m - K). The thermal conductivity of the brick is 1.2 W/(m - K), and the insolation coefficient of the outer surface is 0.8. The temperature of the outer surface of the brick under steady state conditions was 100°C, and the heat transfer coefficient of natural convection of air at the outer surface was 20 W/(m2 - K). Find the temperature of the inside surface of the brick.

Answer 1

Step-by-step explanation:

To find the temperature of the inside surface of the brick, we can use the one-dimensional steady-state heat conduction equation:

Q/A = (k * ΔT) / L

Where:

Q/A is the heat flux (W/m^2)

k is the thermal conductivity of the brick (1.2 W/(m - K))

ΔT is the temperature difference across the brick (K)

L is the thickness of the brick (0.15 m)

The heat transfer rate can also be expressed as:

Q/A = h * (T_out - T_in)

Where:

h is the heat transfer coefficient of natural convection of air at the outer surface (20 W/(m^2 - K))

T_out is the temperature of the outer surface of the brick (100°C)

T_in is the temperature of the inside surface of the brick (unknown)

Since the brick is in steady state, the heat flux through it is the same as the heat flux from the outside to the inside.

We can set up the following equation:

(20 W/(m^2 - K)) * (100°C - T_in) = (1.2 W/(m - K)) * (100°C - 25°C) / (0.15 m)

Simplifying:

20(100 - T_in) = (1.2 * 75) / 0.15

2000 - 20T_in = 9 * 75

2000 - 20T_in = 675

-20T_in = -1325

T_in = 66.25°C

Therefore, the temperature of the inside surface of the brick is 66.25°C.