1. A closed container filled with hot coffee is in a room whose air and walls are at a fixed temperature. Identify all heat transfer processes that contribute to the cooling of the coffee. Comment on features that would contribute to a superior container design.

2. What are the important modes of heat transfer for a person sitting quietly in a room? What if the person is sitting near a roaring fireplace?

3. Consider a person standing in a breezy room at 20°C. Determine the total rate of heat transfer from this person if the exposed surface area and the average outer surface temperature of the person are 1.6 m 2 and 29°C, respectively, and the convection heat transfer coefficient is 6 W/m2 °C

4. A 0.5-m-diameter pipe (€ = 0.9) carrying steam has a surface temperature of 500 K. The pipe is located in a room at 300 K, and the convection heat transfer coefficient between the pipe surface and the air in the room is 20 W/m2 K. Calculate the combined heat transfer coefficient and the rate of heat loss per meter of pipe length.

5. Calculate the rate of heat loss from a furnace wall per unit area. The wall is constructed from an inner layer of 0.5-cm-thick steel (k = 40 W/m K) and an outer layer of 10-cm zirconium brick (k = 2.5 W/m K) as shown in Fig. The inner surface temperature is 900 K and the outside surface temperature is 460 K. What is the temperature at the interface?

6. A section of a composite wall with the dimensions shownbelow has uniform temperatures of 200°C and 50°C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA = 70 W/m K, kB = 60 W/m K, kC = 40 W/m K and kD = 20 W/m K, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces.

7. A flat roof of a house absorbs a solar radiation flux of600 W/m2. The backside of the roof is well insulated, while the outside loses heat by radiation and convection to ambient air at 20°C. If the emittance of the roof is 0.80 and the convection heat transfer coefficient between the roof and the air is 12 W/m2 K, calculate (a) the equilibrium surface temperature of the roof and(b) the ratio of convection to radiation heat loss. Can one or the other of these be neglected? Explain your answer.

8. A hot fluid at an average temperature of 200°C flows through a plastic pipe of 4 cm OD and 3 cm ID. The thermal conductivity of the plastic is 0.5 W/m2 K, and the convection heat transfer coefficient at the inside is 300 W/m2 K. The pipe is located in a room at 30°C, and the heat transfer coefficient at the outer surface is 10 W/m2 K. Calculate the overall heat transfer coefficient and the heat loss per unit length of pipe.

1. A plane wall 15-cm thick has a thermal conductivity given by the relation k = 2.0 + 0.0005T W/m K where T is in kelvin. If one surface of this wall is maintained at 150°C and the other at 50°C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.

2. A long, hollow cylinder is constructed from a material whose thermal conductivity is a function of temperature according to k = 0.15 + 0.0018 T, where T is in °C and k is in W/(m K). The inner and outer radii of the cylinder are 12.5 cm and 25 cm, respectively. Under steady-state conditions, the temperature at the interior surface of the cylinder is 427°C and the temperature at the exterior surface is 93°C. (a) Calculate the rate of heat transfer per metre length, taking into account the variation in thermal conductivity with temperature. (b) If the heat transfer coefficient on the exterior surface of the cylinder is 17 W/(m2 K), calculate the temperature of the air on the outside of the cylinder.

Show that the rate of heat conduction per unit length through a long hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, k = ko (1 + βT) is given by

Ti = temperature at the inner surfaceTo = temperature at the outer surfaceA = 2 π (ro – ri) / ln (ro/ri)km = ko [1 + βk (Ti + To)/2]L = length of cylinder

3.

4.

1.

Draw Flux Plot and find shape factor and compare the answer from table

A 20-m-long and 8-cm-diameter hot water pipe of a district heating system is buried in the soil 80 cm below the ground surface. The outer surface temperature of the pipe is 60°C. Taking the surface temperature of the earth to be 5°C and the thermal conductivity of the soil at that location to be 0.9 W/m · °C, determine the rate of heat loss from the pipe.

Use Conduction shape factor S from table

2. Hot and cold water pipes 8 m long run parallel to each other in a thick concrete layer. The diameters of both pipes are 5 cm, and the distance between the centerlines of the pipes is 40 cm. The surface temperatures of the hot and cold pipes are 60°C and 15°C, respectively. Taking the thermal conductivity of the concrete to be k = 0.75 W/m · °C, determine the rate of heat transfer between the pipes. Answer: 306 WUse Conduction shape factor S from table

A small cubic furnace 50 cm X 50 cm on the inside is constructed of fireclay brick (k =1.04 W/m°C) with a wall thickness of 10 cm as shown in Fig. The inside of the furnace is maintained at 500°C and the outside at 50°C. Calculate the heat lost through the walls.

Use Conduction shape factor S from table3. Derive finite difference equations by energy balance method for the cases shown below

Case I Case II Case III

4. How the result will change if in Case II (a) horizontal boundary is insulated and vertical boundary is subjected to convention at corner (b) if both horizontal and vertical boundary are insulated

5. Consider two-dimensional, steady-state conduction in a square cross section with prescribed surface temperatures. Determine the temperatures at nodes 1, 2, 3, and 4. Estimate the midpoint temperature. Use Liebmann method with over relaxation factor of 1.5.

6. In a fabrication process, steel components are formed hot and then quenched in water. Consider a 2.0-m-long, 0.2-m-diameter steel cylinder (k = 40W/m K, α = 1.0 x 10 –5, m2/s), initially at 400O C, that is suddenly

quenched in water at 50O C. If the heat transfer coefficient is 200W/m2 K, calculate the following 20 minutes after immersion (a)The centre temperature (b) The surface temperature (c) The heat transfer to the water

during the initial 20 minutes