Alexandria University Faculty of Engineering Chemical Engineering Dept. nd 2 year Heat Transfer Sheet # 2
1. The forced convective heat transfer coefficient for a hot fluid flowing over a cool surface is 225 W/m2. C for a particular problem. The fluid temperature upstream of the cool surface is 120 C, and the surface is held at 25 C. Determine: a. The heat transfer rate per unit surface area from the fluid to the surface. b. The temperature at the lower surface of the metal if the thermal conductivity is 379 W/m.k and the metal thickness is 5 cm. ◦
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2. A 1 inch outside diameter steel pipe with its outside surface at 400°F is located in air 90°F with the convective heat-transfer coefficient between the surface of the pipe and the air equal to 1.5 Btu/hr ft2 °F. It is proposed to add insulation having a thermal conductivity of 0.06 Btu/hr ft °F to the pipe to reduce the heat loss to one-half that for the bare pipe. What thickness of insulation is necessary if the surface temperature of the steel pipe and ho remain constant? 3. A composite wall is to be constructed of ¼ -in. stainless steel (k =10 =10 Btu/h ft °F), 3-in. of corkboard (k =0.025 =0.025 Btu/h ft °F) and ½ in. of plastic (k =1.5 =1.5 Btu/h ft °F), a. Draw the thermal circuit for the steady state conduction through this wall. b. E v a l u a t e the individua individuall therm thermal al resista resistance nce of each mater material ial layer layer.. c. Determine the heat flux if the steel surface is maintained at 250°F and the plastic surface held at 80°F. d. What are the temperatures on each surface of the corkboard under these conditions? e. If the convective heat-transfer coefficients coef ficients at the inner (steel) and outer surfaces are 40 and 5 Btu/h ft °F, Determine i. The heat flux if the gases are at 250 and 70°F, adjacent to the inner and outer surfaces ii. Th T h e maximum maximum temperature temperature reached reached within the plastic plastic iii. Which of the individual resistance is controlling?
4. A 12 in thick brick outer wall is used in an office building in a southern city with no insulation or added internal finish. On a winter day the following temperatures were measured: inside air temperature, Ti = 70 ° F; outside air temperature, To = 15°F; inside surface temperature, T1=56°F; outside surface temperature, T2= 19.5° F. Using k = 0.76 Btu/h-ft.°F, a. Estimate the average values of the inner and outer heat transfer coefficients, hi and ho. b. Determine U for the situation previously described. From U and the overall temperature difference, determine q/A. Compare this with the result of (a). 5. Fluid at 250 °F is stored in an insulated spherical container. The shell is 1%carbon steel and has an inside radius of 2.0 in and an outside radius of 2.25 in. The shell is covered with a one-inch layer of 85% magnesia. The inside heat transfer coefficient, hi, is 15 Btu/h.ft2.°F, and the outside coefficient, ho, is 2.2 Btu/h.ft2.°F. Determine the overall heat transfer coefficient Uo, and the heat transfer rate from the Fluid, if the surrounding air temperature is 65 °F. ksteel= 25 Btu/h-ft.°F, kmag= 0.041 Btu/h-ft.°F. 6. Liquid nitrogen at 77 K is stored in a cylindrical container having an inside diameter of 25 cm. the cylinder is made of stainless steel and has a wall thickness of 1.2 cm. Insulation is to be added to the outside surface of the cylinder to reduce the nitrogen boil-off rate to 25% of its value without insulation. The insulation to be used has a thermal conductivity of 0.12 W/m.K. Energy loss through the top ends of the cylinder may be presumed neglected. Neglecting radiation effects, determine the thickness of insulation when the inner surface of the cylinder is at 77 K, the convective heat transfer coefficient at the insulation surface has a value of 12 W/m2. K and the surrounding air is at 25°C. 7. Liquid oxygen, which has a boiling point of 90 K and a latent heat of vaporization of 214 kJ/kg, is stored in a spherical container whose outer surface is of 500-mm diameter and at a temperature of -10 oC. The container is housed in a laboratory whose air and walls are at 25 oC. If the heat transfer coefficient associated with free convection at the outer surface of the container is 10 W / m 2 .K, what is the rate, in kg/s, at which oxygen vapor must be vented from the system?
8. Steam at a temperature of 250°C flows through a steel pipe (AISI 1010) of 60-mm inside diameter and 75-mm outside diameter. The convection coefficient between the steam and the inner surface of the pipe is 500 W/m2 .K, while that between the outer surface of the pipe and the surroundings is 25 W/m2 .K. The temperature of the air and the surroundings is 20°C. What is the heat loss per unit length of pipe? And what is the overall heat transfer coefficient based on inner area? 9. The concrete slab of a basement is 11 m long, 8 m wide and 0.20 m thick. During the winter, temperatures are nominally 17 °C and 10 °C at the top and bottom surfaces, respectively. If the concrete has a thermal conductivity of 1.4 W/m. K, what is the rate of heat loss through the slab? If the basement is heated by a gas furnace operating at an efficiency of ᵑf 0.90 and natural gas is priced at Cg $0.01/MJ, what is the daily cost of the heat loss? 10. A 0.20-m-diameter, thin-walled steel pipe is used to transport saturated steam at a pressure of 20 bars in a room for which the air temperature is 25°C and the convection heat transfer coefficient at the outer surface of the pipe is 20 W/m2 .K. a) What is the heat loss per unit length from the bare pipe (no insulation)? Estimate the heat loss per unit length if a 50-mm-thick layer of insulation (magnesia, 85%) is added. The steam-side convection resistance may be neglected. b) What is the hourly rate of steam transported? Hin t: (latent
heat of vaporization of steam at 20 bars is 1900 kJ/kg and the saturation temperature is 485 K) 11. A spherical tank of 3-m diameter contains a liquefied petroleum gas at 60°C. Insulation with a thermal conductivity of 0.06 W/m.K and thickness 250 mm is applied to the tank to reduce the heat gain. Determine the radial position in the insulation layer at which the temperature is 0°C when the ambient air temperature is 20°C and the convection coefficient on the outer surface is 6 W/m2.K.
Prof. Dr. Hassan Farag Eng. Mohamed Abbas Eng. Moataz Okazy
