Numerical Methods, Transient & 2D Conduction

3. Shape factors & Numerical Methods: transient

A channel passing hot gases has a square cross section, 300 mm to a side. The walls are

constructed of refractory brick 150 mm thick with a thermal conductivity of 0.85W/mK.

a) Calculate the heat loss from the

flue per unit length when the

interior and exterior surfaces

are maintained at 350°C and

25°C, respectively. Use a grid

spacing of 75 mm.

b) Calculate the heat loss per unit

length using Shape factors, and

compare the result

c) The interior surface is exposed

to hot gases at 350°C with a

convection coefficient of 100

W/m² K, while the exterior

surface experiences convection

with air at 25°C and a

convection coefficient of 5 W/m²

K.

d) Using a grid spacing of 75 mm,

calculate the temperature field

within the system and

determine the heat loss per unit

length by convection from the

outer surface of the flue to the air. Compare this result with the heat gained by

convection from the hot gases to the air.

e) Initially with no flue gases flowing, the walls (a = 5.5x107 m²/s) are at a uniform

temperature of 25C. Using the implicit, finite-difference method with a time increment of

1 h, find the temperature distribution in the wall 5, 10, 50, and 100 h after introduction of

the flue gases.

300 mm

150 mm

350°C

25°C