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  Chapter 1: Chapter 1 Heat Transfer 1. Past ME board Problem Calculate the energy transfer rate across 6 in. Wall of firebrick with a temperature diffrence across the firewall of 50°C. The thermal conductivity of the firebrick is 0.65 Btu/hr -ft°F at the temperature interest. : 1. Past ME board Problem Calculate the energy transfer rate across 6 in. Wall of firebrick with a temperature diffrence across the firewall of 50°C. The thermal conductivity of the firebrick is 0.65 Btu/hr -ft°F at the temperature interest. A. 285 W/m² B. 369W/m² C. 112W/m² D. 429W/m² Slide 3: 2. Past ME board Problem At an average temperature of 100°C, hot air flows through a 2.5 m long tube with an inside diameter of 50 mm. The temperature of the tube is 20°C along its entire length. Convective film coefficient is 20.1 W/m²-K. Determine the convective heat transfer from air to the tube. 900 W 909 W 624 W 632 W Slide 4: 3. Past ME board Problem Stream, initially saturated at 2.05 Mpa, passes through a 10.10 cm standard steel pipe for a total distance of 152 m. The stream line is insulated with 5.08 cm thickness of 85% magnesia. For an ambient tempreature of 22°C , what is the quality of the stream which arises at its destination if the mass flow rate is 0.125 kg stream per second ? Note : k for 85% magnesia is 0.069 W/m- K and h˳ for still air is 9.36 W/m² -K 93% 98% 84% 76% Slide 5: 4. Past ME board Problem The sun generates 1 kW/m² when used as a source for solar collectors. A collector with an area of 1 m² heat water. The flow rate is 3.0 liters per minute. What is the tempera- ture rise in the water ? The specific heat of water is 4,200 J/Kg°C. 4.8°C 0.48°C 0.50°C 0.84°C Slide 6: 5. Past ME board Problem The hot combustion gases of a furnace are separated from the ambient air and its surrounding which are at 25°C, by a brick wall 0.15 m thick. The brick has a thermal conductivity 0f 1.2 W/m-K and a surface emissivity of 0.80. Under steady state conditions and outer surface temperature of 100°C is measured. Free convection heat transfer to the air adjoining this surface is characterized by a convection coefficient of 20 W/m²-K. What is the inner temperature in °C ? 623.7 352 461.4 265.3 Slide 7: 6. Past ME board Problem A 6 in. X 20 ft uninsulated B.I. pipe conveys steam at 385°F with an average ambient temperature of 85°F. If the cost of the fuel is P 250.00 per 10 ⁶  Btu with the net energy conversion efficiency of 75%, what is the annual cost of the heat lost ? P 60,482.00 P 65,482.00 P 70,482.00 P 75,482.00 Slide 8: 7. Past ME board Problem What is the external heating surface area in square feet of a tube with the following dimensions : tube inside diameter = 5 in. Wall thickness = ½ in. Length =18 ft. 26.5 24.25 19.25 28.26 Slide 9: 8. Past ME board Problem Determine the vacuum efficiency of a surface condenser which operates at a vacuum of 635 mm Hg and exhaust steam enters the condenser at 45.81°C . The barometric pressure is 760 mmHg and the saturation pressure at 45.81°C is 0.010 Mpa. 80.4% 85.2% 92.7% 98.3% Slide 10: 9. Past ME board Problem A heat exchanger was installed purposely to cool 0.50 kg of gas per second. Molecular weigth is 28 and k- 1.32. The gas is cooled from 150°C to 80°C . Water is available at the rate of 0.30 kg/s and at a temperature of 12°C. Calculate the exit temperature of the water. 48 42 46 44 Slide 11: 10. Past ME board Problem An uninsulated steam pipe passes through a room in which the air and walls are at 25°C. The outside diameter of the pipe is 70 mm, and its surface temperature and emissivity are 200°C and 0.80 repectively. If the coefficient associated with free convection heat transfer from the surface to the air is 15 w/ m²-K, what is the rate of heat koss from the surface per unit of length of pipe? 997.84 W/m 897.84 W/m 797.84 W/m 697.84 W/m  Slide 12: 11. Past ME board Problem A heat exchanger is used to be designed for the following specifications : Hot gas temperature 1145°C Cold gas temperature 45°C Unit surface conductance on the hot side 230W/m²-K Unit surface conductance on the cold side 290W/m²-K Thermal thickness of the metal wall 115W/ m²-K Find the maximum thickness of the metal wall between the hot gas and cold gas so that the maximum temperatureof the wall does not exceed 545°C. 10.115 mm 13.115 mm 17.115 mm 20.115 mm Slide 13: 12. Past ME board Problem Calculate the heat transfer per hour through a solid brick wall 6 m long, 2.9 m high, and 225 mm thick, when the outer surface is at 5°C and the inner surface 17°C , the coefficient of the thremal conductivity of the brick being 0.6 W/m-K 2,004.48 Kj 3,004.48 kJ 2,400.48 kJ 3,400,48 kJ Slide 14: 13. Past ME board Problem A vertical furnace wall is made up of an inner wall firebrick20 cm thick followed by insulating brick 15 cm thick and an outer wall of steel 1 cm thick, The surface temperature of the wall adjacent to the combustion chamber is 1200° C while that of the outer surface of steel is 50°C. The thermal conductivities of the wall material in W/m-K are : firebrick 10 ; insulating brick,0.26 ; and steel, 45. Neglecting the film resistance and contact resistance of joints , determine the heat loss per sq.m. Of wall area. 1.93 W/m² 2.93 W/m² 1.55 W/m² 2.55 W/m² Slide 15: 14. Past ME board Problem A composite wall is made up of an external thickness of brickwork 110 mm thick inside which is a layer of fiberglass is faced internally by an insulating board 25 mm thick. The coefficient of thermal conductivity for the three as follows : Brickwork 1.5 W/m-K Fiberglass 0.04 W/m-K Insulating board 0.06 w/m-K The surface transfer coefficient of the inside wall is 3.1 W/m²-K while that of the outside wall is 2.5 W/m²-K. Take the internal ambient temperature as 10°C and the external temperature is 27°C. Determine the heat loss through such wall 6 m high and 10 m long . 330.10 W 230.10 W 430.10 W 530. 10 W Slide 16: Supplementary Problem One insulated wall of a cold storage compartment is 8 m long 2.5 m high and con- sist of an outer steel plate 18 mm thick. An inner wood wall 22.5 mm and thick, the steel and wood are 90 mm apart to form a cavity ahich filled with cork. If the tempearture drop across extreme faces of the composite wall is 15°C. Calculate the heat transfer per hour through the wall and the temperature drop across the the thickness of the cork. Take the coefficient of thermal conductivity for steel cork, and wood as 45, 0,045, and 0.18 W/m-K repectively. 408.24 kJ, 12,12°C 708.24 kJ 11.12°C 608.24 kJ 13. 12°C 508.24 kJ 14. 12°C Slide 17: 16. Supplementary Problem A cubical tank of 2 sides is constructed of metal plate 12 mm and contains water at 75°C. The surrounding air temperature is 16°C. Calculate the overall heat transfer from water to air. Take the coeefficient of thermal condcutivity of the metal as 48 W/m-K , the coefficient of thermal conductivity of the metal as 48 W/m-K, the coefficient of thermal conductivity of metal as 48W/m-K, the coefficient of heat trasfer of water is 2.5 kW/m²-K and the coefficient of heat transfer of the air is 16 W/m²-K. 15. 84 W/m²°C 14.84 W/m²°C 16.84 W/m²°C 13.84 W/m²°C Slide 18: 17. Supplementary Problem Calculate the quatity of heat conducted per minute through a duralumin circular disc 127 mm diameter and 19 mm thick when the temprature drop across the thickness of the plate is 5°C. Take the coefficient of thermal conductivity of duralumin as 150 W/m-K. 30 kJ 40 kJ 35 kJ 45kJ Slide 19: 18. Supplementary Problem A cold storage compartment is 4.5 m long by 4 m wide by 2.5 m high. The four walls , ceiling and floor are covered to a thickness of 150 mm with insulating material which has coefficient of thermal conductivity of 5.8 x 10²W/m-K. Calculate the quantity of heating leaking through the insulation per hour when the outside and inside face temperatures of the material is 15°C and -5°C respctively. 2185.44 kJ 118 5. 44 kJ 3185. 44 kJ 4185. 44 kJ Slide 20: 19. Supplementary Problem A thin square steel plate , 10 cm on a side is heated in a blacksmiths forge to a temperature of 800°C. If the emissivity is 0.60, what is the total rate of radiation energy ? 900 Watts 400 Watts 300 Watts 700 Watts    Slide 21: 20. Supplementary Problem A furnace wall consist of 35 cm firebrick ( k= 1.55 7 W/m-K ) , 12 cm insulating refractory ( k= 0.346 ) and 20 cm common brick ( k= 0.692 ) covered with 7 cm steel plate ( k= 45 ) . The temperature at hte inner surface of the firebrick is 1,230°C and at the outer face of the steel plate is 60°C. Atmosphere 27°C. What is the value of the combined coefficient for convention and radiation from the outside wall ? 31. 13 W/m²-K 30.13 W/m-K 41.3 W/m²-K 40.13 W/m²-K Slide 22: 21. Supplementary Problem A dry ice storage chest is a wooden box lined with glass fiber insulation 5 cm thick. The wooden box ( k = 0.069 ) is 2 cm thick and cubical 60 cm on an edge. The inside surface temperature is -76°C and the outside temperature is 18°C. Use l = 0.035 glass fiber insulation. Determine the heat gain per day 10,211 kJ 11,195 kj 12,211 kJ 9,185 kJ Slide 23: 22. Supplementary Problem One side of refrigerated cold chamber is 6 cm long by 3.7 m high and consists 0f 168 mm thickness of cork between outer and inner walls of wood. The outer woll wall is 30 cm thick and its outside face temperature is 20°C, the inner wood wall is 35 mm thick and its inside face temperature is -3°C. Taking the coefficient of thermal conductivity of cork and wood as 0.42 and 0.20 W/m-K respectively , calculate the heat transfer per second per sq. M of surface area. 5.138 J 4.138 J 6.318 3.318 J Slide 24: 23. Supplementary Problem Hot gases at 280°C flow on one side of a metal plate of 10mm thickness and air at 35°C flows on the other side. The heat ransfer coefficient of the gases is 31.5 W/m²-K and that of the air is 32 W/m²-K. Calculate the over-all transfer coefficient A. 15.82 W/m²-K B. 16.82 W/m²-K C. 14.82 W/m²-k D. 17.82 W/m²-K Slide 25: 24. Supplementary Problem The surface temperature of the hot side of the furnace wall is 1200°C. It is desired to mainttain the outside of the wall at 38°C. A 152 mm of refractory silica is used adjacent to the combustion chamber and 10 mm of steel covers the outside. What thickness of insulating bricks is necessary between refractory and steel , if the heat loss should be kept at 788 W/m² ? Use k = 13.84 W/m-K for refractory silica ; 0.15 for insulating brick, and 45 for steel. 220 mm 240 mm 260 mm 280 mm Slide 26: 25. Supplementary Problem How much heat will flow has an outside flow in 24 hours through a palster wall that is 0.51 in thick 8 ft x 14 ft ina area if the temperature is 80°F on one side and 40°F on the other. Use k = 3.25 Btu  –  in/ hr - ft² -°F 5.99 x 10 ⁵  Btu 6.99 x 10 ⁵  Btu 7.99 x 10 ⁵  Btu 4.99 x 10 ⁵  Btu Slide 27: 26. Supplementary Problem A hollow sphere has an outside radius of 1 m and is made of polystyrene foam with a thickness of 1 cm. A heat source inside keeps the inner surface 5.20°C hotter than the outside surface. How much power is produced by the heat source The thermal conductivity of polytrene foam os 0.033 W/m°C 200 W 216 W 300 W 316 W Slide 28: 27. Supplementary Problem A glass window has an area of 1.60m² and a thickness of 4 mm. If one side is at a temperature of 6.80°C and the other is at -5°C, how much thermal energy flows through the window in a time of 24 hours ? The thermal conductivity of glass is 1.89 x 10ˉ ⁴  kCal/m-s-°C. 26,200 kCal 58,000 kCal 40,700 kCal 77,100 kCal Slide 29: 28. Supplementary Problem The wall of a cold room consist of a layer of cork sandwiched between outer and inner walls of wood , the wood walls being each 30 mm thicj. The inside atmosphere of the room is maintained at -20°C when the external atmospheric temperature is 25°C, and the heat loss through the wall is 42 W/m². Taking the thermal conductibity of wood and cork as 0.20 W.m-K and 0.05 W/m-K respectively , and the rate of heat transfer between each exposed wood surface and their respective atmospheres as 15W/m²-K , calculate the thickness of the cork. 31.90 mm 21.90 mm 41.90 mm 51.90 mm Slide 30:  29. Supplementary Problem A slab of material has an area of 2m² and is 1 mm thick. Ine side is maintained at a temperature of 0°C while the other is at 12°C. It is determined that 6820 J of heat flows through the material in a time of 10 minutes. What is the thermal conductivity of the material ? A. 4.74 x 10ˉ ⁴   W/m°C B. 5.74 x 10ˉ ⁴  W/m°C C. 2.66 x 10ˉ ⁴   W/m°C D. 9.79 x 10ˉ² W/m°C   Slide 31: 30. Supplementary Problem An insulated steam piece located where the ambient temperature is 32°C, has an inside diameter of 50 mm with 10 mm thick wall. The outside diameter of the corrugated asbestos insulation is 125 mm and the surface coeffiecient of still air, h˳ = 12 W/m² -K. Inside the pipe is steam having a temperature of 150 °C with film coefficient h ₁  = 6000 W/m²-K. Thermal conductivity of pipe and asbestos insulation are 45 and 0.12 W/m-K respectively. Determine the heat loss per unit length of pipe. 110 W 120 W 130 W 140 W Slide 32: 31. Supplementary Problem A pipe 200 mm outside diameter and 20 m length is covered with a later, 70 mm thick of insulation having a thermal conductivity of 0.05 W/m-K and a thermal conductance of 10 W/m² at the outer surface. If the temperature of the pipe is 350 °C and the ambient temperature 15 °C, calculate the external surface temperature of the lagging. A. 32.6 °C B. 22.6 °C C. 42.6 °C D. 53.5 °C Slide 33: 32. Supplementary Problem Dry and saturated steam at 6 Mpa abs. Enters a 40 m length of 11.5 cm O.D. Steel pipe at a flow rate of 0.12 kg/s. The pipe is covered with a 5 cm thick asbestos imsulation ( k = 0.022 W/m-K ). The pipe is located in a tunnel with stagnant air temperature of 27 °C. The unit outside convective coefficient is 10 W/m²-K. Neglecting steam film and pipe wall resistances, determine the mass of steam. 4.86 kg/hr 3.86 kg/hr 5.86 kg/hr 6.86 kg/hr Slide 34: 33. Supplementary Problem Calculate the heat loss per linear ft. From 2 in. Nominal pipe ( 2.375 in. Outside diameter ) covered with 1 in. of an insulating material having an average thermal conductivity of 0.0375 Btu/hr-ft °F. Assume that the inner and outer surface temperatures of the insulation are 380 °F and 80 °F respectively. 110 Btu/hr-ft 116 Btu/hr-ft 120 Btu/hr-ft 126 Btu/hr-ft Slide 35: 34. Supplementary Problem Calculate the heat loss per linear foot from a 10 in. Nominal pipe ( outside diameter = 10.75 in. ) covered with a composite pipe insulation consisting of 1½ in. Of insulation I placed next to the pipe and 2 in. Of insulation II placed upon insulation I. Assume that the inner and outer surface temperatures of the composite insulation aree 700 °F and 100 °F respectively, and that the thermal conductivity of material I is 0.05 Btu/hr-ft- °F and for material II is 0.039 Btu/hr-ft- °F. 3 23.13 Btu/hr-ft 123.13 Btu/hr-ft 120 Btu/hr-ft 126 Btu/hr-ft Slide 36: 35. Supplementary Problem A steam pipe carrying steam at 380 kPa pressure for a pressure for a distance of 120 m in a chemical plan is not insulated. Estimate the saving in steam cost that would be made per year if this 8 cm steam line were covered with 85% magnesia pipe covering 5 cm thick. Take room temperature to be 25 °C, the cost of steam is 65 cents per 1000 kg. Thermal conductivity of magnesia k = 0.0745 W/m-k\K, unit convective coefficient of room air, h˳ = 12 W/m²-K. $ 305 $ 405 $ 505 $ 605 Slide 37: 36. Supplementary Problem A liquid to liquid counterflow heat exchanger is used to heat a cold fluid from 120 °F to 310 °F. Assuming that the hot fluid enters at 500 °F and leaves at 400 °F, calculate the log mean temperature difference fot the heat exchanger. 132 °F 232 °F 332 °F 432 °F Slide 38: 37. Supplementary Problem A turbo-generator, 16 cylinder, Vee type diesel engine has an air consumption of 3000 kg/hr per cylinder at rated load and speed. This air is drawn in thru a filter by a centrifugal compressor direct connected to the exhaust gas turbine. The temperature Of the aircon from the compressor is 145°C and a counterflow air cooler reduces the air temperature to 45°C before it goes to the engine suction header. Cooling water aur cooler at 30°C and leaves at 38°C. Calculates the arithmetic mean temprature difference. 41°C 51°C 61°C 71°C Slide 39:
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