Cairo University Heat Transfer

Faculty of Engineering Year Comm. & Elec.

Mechanical Power Dept.

SHEET (1)Steady State Conduction Without Heat Generation

1. A plane wall has a thickness of 30 mm with surfaces maintained at 320 K and400 K. Determine the heat flux through the wall if it is constructed from:

a) Plane Carbon Steal b) Pure copper c) Lead d) Brass e) Concrete.

2. A solid cylindrical rod of length 0.2 m and diameter of 25.4 mm is insulated along its cylindrical surface while its end faces are maintained at temperature of 100 ºC and 0 ºC. What is the rate of heat transfer through the rod if it is constructed from:a) Pure copper b) Aluminium alloy 2024-T6 c) AISI stainless steel d) Wood (oak)

3. A spherical shell made of brass (k =110 W/m.K) and of 0.15/0.18 m diameter has its inner and outer surfaces maintained at 400 °C and 100 °C respectively. Obtain the rate of heat transfer through the shell in Watts.

4. A house has a composite wall of concrete 100 mm, with two finishing cement layer of 10 mm on its both faces. In summer, the inside air temperature is maintained by an air conditioning system at 22 ºC while the outside temperature has a maximum value of 45 ºC. The inner and outer heat transfer coefficients are 15 W/m2K and 70 W/m2K. The total wall surface area is 300 m2. Determine:a) The thermal resistance of the wall (with inner and outer convective steams)b) The total heat gain through the wall. .If the wind velocity increases and results in raising the outer convective coefficient to 140 W/m2K, find the percentage increase in the heat gained.

5. A composite wall of height H and of unit length normal to the page is insulated at its ends and is composed of four different materials arranged as shown below.a) Sketch the thermal network of the system.b) Consider a wall for which H = 3 m, Hb = Hc = 1.5 m, L1 = L3 = 0.05 m, L2 = 0.1 m, kA = kD = 50 W/m.K, kB= 10 W/m.K and kc= 1W/m.K. Under conditions for which T∞1 = 200 ºC, h1 = 50 W/m2.K, T∞2 = 25 ºC, h2 = 10 W/m2.K, what is the rate of heat transfer through the wall? What are the interface temperatures, Tl and T2?

6. A steam pipe of 0.12 m outside diameter and 3 mm thickness is made of carbon steel (k=15 W/m.K). The steam has a temperature of 800 K, with convection heat

transfer coefficient of 1000 W/m2K. The pipe is surrounded by air at 30oC with convective heat transfer coefficient of 40 W/m2K.a) Find the inner and outer temperatures of the pipe.b) If it is required to insulate the pipe with calcium silicate to maintain the insulation outer surface at 70oC, find the required insulation thickness. (Keeping heat transfer coefficient the same).c) Find the heat loss per unit pipe length in both cases.

7. A steam pipe of 25/20 mm diameter and of 35 W/m.K thermal conductivity carrying steam at 400 ºC, with convection heat transfer coefficient of 500 W/m2K. Two insulation layers of thickness 2 cm and 3 cm, with thermal conductivities equal to 0.03 and 0.08 W/m.K, respectively, cover the pipe. The outside air temperature is 30 ºC with estimated convection heat transfer coefficient of 20 W/m2.K. Find:a) The heat flux per unit length of pipe in W/mb) The temperatures of inner and outer pipe surfaces.c) The temperatures at interface of insulating materials and of the outside of the external insulating material.

8. A 1.0 mm diameter wire is insulated at temperature of 400°C' and exposed to a convection environment at 40°C and heat transfer coefficient of 120 W/m2K. Calculate the thermal conductivity which will just cause an insulation thickness of 0.2 mm to produce a critical radius. How much of this insulation must be added to reduce the heat transfer by 75% from which would be experienced by bare wire?

9. A Copper cable 5 cm in diameter is to be covered by an electrical insulation material whose thermal conductivity is 0.16 W/m.K. The heat transfer coefficient between the outer surface of insulation and surrounding air is 5 W/m2K and the air temperature is 20oC. Find the thickness of insulation that gives the maximum rate of

heat dissipation. If the electrical resistivity of the wire is 1.72 x 10 -8 .m, find the

maximum allowable current in the cable in order that the temperature of insulation does not exceed 280 ºC.

10. A spherical shell made of brass (k =110 W/m.K) and has 15cm and 18 cm inner and outer diameters, respectively. Liquid ammonia at -20°C having a heat transfer coefficient of 40 W/m.K is stored inside the shell. If the surrounding air is at 35 ºC and having a heat transfer coefficient of 10 W/m.K, obtain the overall heat transfer coefficient and the rate of heat transfer through the shell.

11. A stainless steel pipe of inner and outer diameters 6 cm and 8 cm respectively and thermal conductivity of 13.5 W/m.K is covered with an insulation layer of magnesia of thickness 2 cm and thermal conductivity of 0.071. There is a fluid flows inside the pipe with a temperature of 112 ºC and heat transfer coefficient of 346 W/m2K. If the surrounding has a temperature of 20 ºC and heat transfer coefficient of 6 W/m2K, calculate the heat transfer rate and the overall heat transfer coefficient.

12. Hollow spheres may be used to measure the thermal conductivity of some insulating materials. A hollow aluminium sphere of 0.15/0.18 m diameter with an electric heater installed in the sphere core results in establishing a temperature of 250 ºC at the sphere inner surface under steady state conditions. A spherical shell of

Cairo University Heat Transfer

Faculty of Engineering Year Comm. & Elec.

Mechanical Power Dept.

insulation is cast on the outer surface of the sphere to a thickness of 0.12 m. The surrounding air is at 20 °C and the outside convection heat transfer coefficient is 30 W/m2.K. The measured heater input power is 80 W. Under the above conditions, obtain the thermal conductivity of the insulating material.