Module 1. Conduction heat transfer

Lesson 6

ASSIGNMENTS

6.1  Assignments

1. The wall of a cold store is laid from (chamotte) brick, and wall thickness = 250 mm. The temperatures of wall surface t_w1 = 1350°C and t_w2 = 50°C. The thermal conductive of brick is a function of temperature, λ = 0.838(1+0.0007t) W/m-°C. Calculate and represent graphically the distribution of temperature through the wall.

ANSWER

x, mm...	0	50	100	125	150	200	225	250
t, °C…..	1350	1145	920	800	670	390	230	50

2. The brickwork of a furnace is built up of layers laid of fireclay and red brick and the space between the two layers of brickwork is filled with crushed diatomite brick. The fireclay is 120 mm thick (δ₁); the thickness of the diatomite filling δ₂ = 50 mm, and the thickness of the red brick layer δ₃ = 250 mm. The thermal conductivity of the three materials are equal respectively λ₁ = 0.93, λ₂ =0.13 and λ₃ = 0.7 W/m-°C. What should be the thickness of the red brick layer d₃, if the brickwork is to be laid without the diatomite filling between the two layers, so that the heat flux through the brickwork remains constant?

ANSWER

The layer of red brick must be 500 mm thick.

3. A steam pipeline, 150/160 mm in diameter, is covered with a layer of heat-insulating materials of thickness t_ins = 100 mm; the thermal conductivity of tube λ₁ = 50 W/m-°C and that of the insulating material λ₂ = 0.08 W/m-°C. The temperature of the pipeline inside surface t_w1 = 400°C and the temperature of the outside surface of the insulating layer t_w3 = 50°C.

Find the loss of heat from length of 1m of the pipeline and the temperature at the interface between the tube and insulation.

ANSWER

The loss of heat from length of 1m of the steam pipeline q_l = 216 W/m. The temperature at the interface between the wall of the pipeline and the insulation t_w2 = 400°C.

4. A steel pipeline of a diameter d₁/d₂ = 100/110 mm with a thermal conductivity λ₁ = 50 W/m-°C is covered with two layers of insulation of equal thickness δ₂ = δ₃ = 50 mm. The temperature of the tube inside surface t_w1 = 250°C and the temperature of the outside surface of insulation t_w4 = 50°C. Determine the loss of heat through the insulation from length of 1 m of the pipeline and the temperature at the interface between the two layers of insulation, if the first layer of insulation, applied on the surface of the tube is made from a material with a thermal conductivity λ₂ = 0.06 W/m-°C and the second layer from an insulating material with a thermal conductivity λ₃ = 0.12 W/m-°C.

ANSWER

The loss of heat from length of 1 m of the pipeline q_l = 89.5 W/m. The temperature at the interface between the two layers of insulation t_w3 = 97°C.

5. A steam pipeline d₁/d₂ = 160/170 mm in diameter is covered with a layer of insulation of thickness = 100 mm with a thermal conductivity depending on the temperature is {0.062 (1 + 0.363×10^-2t)} W/m-°C. Determine the amount of heat loss from length of 1m of pipeline and the temperature of its inner surface, if the temperature of the outer pipeline surface t_w2 = 300°C and the temperature of the outer surface of the insulation  should not exceed 50°C.

ANSWER

The loss of heat from length of 1m of the steam pipeline q_t = 250 W/m. The inner pipeline surface temperature t_w1 = 300°C