Consider heat conduction through a wall of thickness L and area A. Under what conditions will the temperature distributions in the wall be a straight line?
The local atmospheric pressure in Denver, Colorado (elevation 1610 m) is 83.4 kPa. Air at this pressure and at 25C flows with a velocity of 9 m/s over a 2.5-m 5-m flat plate. Determine the drag...
Hot exhaust gases leaving a stationary diesel engine at 450C enter a l5-cm-diameter pipe at an average velocity of 4.5 m/s. The surface temperature of the pipe is 180C. Determine the pipe length if...
A 10-cm thick aluminum plate (Ï = 2702 kg/m 3 , c p = 903 J/kg·K, k = 237 W/m·K, and α = 97.1 à 10 6 m 2 /s) is being heated in liquid with temperature of...
Steam in a heating system flows through tubes whose outer diameter is 5 cm and whose walls are maintained at a temperature of 180°C. Circular aluminum alloy 2024-T6 fins (k = 186 W/m·K) of...
A long aluminum wire of diameter 3 mm is extruded at a temperature of 280°C. The wire is subjected to cross air flow at 20°C at a velocity of 6 m/s. Determine the rate of heat transfer from...
Consider a 2-m-high electric hot-water heater that has a diameter of 40 cm and maintains the hot water at 55°C. The tank is located in a small room whose average temperature is 27°C, and the...
Parallel plates form a solar collector that covers a roof, as shown in the figure. The plates are maintained at 15°C, while ambient air at 10°C flows over the roof with V = 2 m/s. Determine...
A 10-in-thick, 30-ft-long, and 10-ft-high wall is to be constructed using 9-in-long solid bricks (k = 0.40 Btu/h·ft·°F) of cross section 7 in à 7 in, or identical size bricks...
Light oil at 75F flows over a 22-ft-long flat plate with a free-stream velocity of 6 ft/s. Determine the total drag force per unit width of the plate.
Air at 25C and 1 atm is flowing over a long flat plate with a velocity of 8 m/s. Determine the distance from the leading edge of the plate where the flow becomes turbulent, and the thickness of the...
Dust particles of diameter 0.06 mm and density 1.6 g/cm 3 are unsettled during high winds and rise to a height of 200 m by the time things calm down. Estimate how long it takes for the dust particles...
The roof of a house consists of a 15-cm-thick concrete slab (k = 2 W/m·K) that is 15 m wide and 20 m long. The convection heat transfer coefficients on the inner and outer surfaces of the roof...
Consider an airplane whose takeoff speed is 220 km/h and that takes 15 s to take off at sea level. For an airport at an elevation of 1600 m (such as Denver), determine (a) The takeoff speed, (b) The...
A 50-m-long section of a steam pipe whose outer diameter is 10 cm passes through an open space at 15°C. The average temperature of the outer surface of the pipe is measured to be 150°C. If...
A thin metal plate is insulated on the back and exposed to solar radiation on the front surface. The exposed surface of the plate has an absorptivity of 0.7 for solar radiation. If solar radiation is...
The cylindrical chimney of a factory has an external diameter of 1.1 m and is 20 m high. Determine the bending moment at the base of the chimney when winds at 110 km/h are blowing across it. Take the...
Define thermal conductivity and explain its significance in heat transfer.
Consider heat loss through the two walls of a house on a winter night. The walls are identical, except that one of them has a tightly fit glass window. Through which wall will the house lose more...
Air at 20°C with a convection heat transfer coefficient of 25 W/m 2 ·K blows over a horizontal steel hot plate (k = 43 W/m·K). The surface area of the plate is 0.38 m 2 with a...
The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm) is - 196°C. Therefore, nitrogen is commonly used in low-temperature scientific studies since the temperature of...
Consider laminar flow of air across a hot circular cylinder. At what point on the cylinder will the heat transfer be highest? What would your answer be if the flow were turbulent?
Consider a hot boiled egg in a spacecraft that is filled with air at atmospheric pressure and temperature at all times. Will the egg cool faster or slower when the spacecraft is in space instead of...
In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
A 0.5-m-long thin vertical plate is subjected to uniform heat flux on one side, while the other side is exposed to cool air at 5°C. The plate surface has an emissivity of 0.73, and its midpoint...
The top surface of the passenger car of a train moving at a velocity of 70 km/h is 2.8 m wide and 8 m long. The top surface is absorbing solar radiation at a rate of 200 W/m 2 , and the temperature...
Warm air is blown over the inner surface of an automobile windshield to defrost ice accumulated on the outer surface of the windshield. Consider an automobile windshield (k w = 0.8 Btu/hftR) with an...
An array of power transistors, dissipating 6 W of power each, are to be cooled by mounting them on a 25-cm à 25-cm-square aluminum plate and blowing air at 35°C over the plate with a fan...
What is a reradiating surface? What simplifications does a reradiating surface offer in the radiation analysis?
During a winter day, wind at 55 km/h, 5°C, and 1 atm is blowing parallel to a 4-m-high and 10-m-long wall of a house. Approximating the wall surfaces as smooth, determine the friction drag acting...
The weight of a thin flat plate 50 cm à 50 cm in size is balanced by a counterweight that has a mass of 2 kg, as shown in Fig. P1554. Now a fan is turned on, and air at 1 atm and 25°C...
Two concentric spheres with diameters of 5 cm and 10 cm are having the surface temperatures maintained at 200°C and 100°C, respectively. The enclosure between the two concentric spherical...
A solar collector consists of a horizontal copper tube of outer diameter 5 cm enclosed in a concentric thin glass tube of 9 cm diameter. Water is heated as it flows through the tube, and the annular...
How can you determine the view factor F 12 when the view factor F 21 and the surface areas are available?
A furnace that has a 40-cm 40-cm glass window can be considered to be a blackbody at 1200 K. If the transmissivity of the glass is 0.7 for radiation at wavelengths less than 3 m and zero for...
A vertical 4-ft-high and 6-ft-wide double-pane window consists of two sheets of glass separated by a 1-in air gap at atmospheric pressure. If the glass surface temperatures across the air gap are...
In a plant that manufactures canned aerosol paints, the cans are temperature-tested in water baths at 55°C before they are shipped to ensure that they withstand temperatures up to 55°C during...
A 2-m-internal-diameter double-walled spherical tank is used to store iced water at 0°C. Each wall is 0.5 cm thick, and the 1.5-cm-thick air space between the two walls of the tank is evacuated...
Consider the two parallel coaxial disks of diameters a and b, shown in Fig. P21132. For this geometry, the view factor from the smaller disk to the larger disk can be calculated from where, A = a/2L,...
Under what conditions can the overall heat transfer coefficient of a heat exchanger be determined from U = (1/h i + 1/h o ) -1 ?
A long thin-walled double-pipe heat exchanger with tube and shell diameters of 1.0 cm and 2.5 cm, respectively, is used to condense refrigerant-134a by water at 20C. The refrigerant flows through the...
Water at an average temperature of 180F and an average velocity of 4 ft/s flows through a thin-walled 3/4-indiameter tube. The water is cooled by air that flows across the tube with a velocity of 12...
A large number of long tubes, each of diameter D, are placed parallel to each other and at a center-to-center distance of s. Since all of the tubes are geometrically similar and at the same...
Solar radiation is incident on the front surface of a thin plate with direct and diffuse components of 300 and 250 W/m 2 , respectively. The direct radiation makes a 30° angle with the normal of...
Water at an average temperature of 110C and an average velocity of 3.5 m/s flows through a 5-m-long stainless steel tube (k = 14.2 W/mK) in a boiler. The inner and outer diameters of the tube are D i...
What is the heat capacity rate? What can you say about the temperature changes of the hot and cold fluids in a heat exchanger if both fluids have the same capacity rate? What does a heat capacity of...
Under what conditions will the temperature rise of the cold fluid in a heat exchanger be equal to the temperature drop of the hot fluid?
In the heat transfer relation Q = UA s T lm for a heat exchanger, what is T lm called? How is it calculated for a parallel-flow and counter-flow heat exchanger?
Can the outlet temperature of the cold fluid in a heat exchanger be higher than the outlet temperature of the hot fluid in a parallel-flow heat exchanger? How about in a counter-flow heat exchanger?...
Explain how the LMTD method can be used to determine the heat transfer surface area of a multipass shelland-tube heat exchanger when all the necessary information, including the outlet temperatures,...
In the heat transfer relation Q = UA s FT lm for a heat exchanger, what is the quantity F called? What does it represent? Can F be greater than one?
When the outlet temperatures of the fluids in a heat exchanger are not known, is it still practical to use the LMTD method? Explain.
For specified inlet and outlet temperatures, for what kind of heat exchanger will the T lm be greatest: double-pipe parallel-flow, double-pipe counter-flow, cross-flow, or multipass shell-and-tube...
A stream of hydrocarbon (c p = 2.2 kJ/kgK) is cooled at a rate of 720 kg/h from 150C to 40C in the tube side of a double-pipe counter-flow heat exchanger. Water (c p = 4.18 kJ/ kgK) enters the heat...
Reconsider Prob. 2240. Using an appropriate software, investigate the effects of temperature and mass flow rate of geothermal water on the length of the tube. Let the temperature vary from 100C to...
Glycerin (c p = 2400 J/kgK) at 20C and 0.5 kg/s is to be heated by ethylene glycol (c p = 2500 J/kgK) at 60C in a thin-walled double-pipe parallel-flow heat exchanger. The temperature difference...
A heat exchanger contains 400 tubes with inner diameter of 23 mm and outer diameter of 25 mm. The length of each tube is 3.7 m. The corrected log mean temperature difference is 23C, while the inner...
A thin-walled double-pipe counter-flow heat exchanger is to be used to cool oil (c p = 2200 J/kgK) from 150C to 40C at a rate of 2 kg/s by water (c p = 4180 J/kgK) that enters at 22C at a rate of 1.5...
Cold water (c p = 4180 J/kgK) leading to a shower enters a thin-walled double-pipe counter-flow heat exchanger at 15C at a rate of 1.25 kg/s and is heated to 45C by hot water (c p = 4190 J/kgK) that...
Consider the flow of engine oil (c p = 2048 J/kg·K) through a thin-walled copper tube at a rate of 0.3 kg/s. The engine oil that enters the copper tube at an inlet temperature of 80°C is...
In a parallel flow heat exchanger, hot fluid enters the heat exchanger at a temperature of 150C and a mass flow rate of 3 kg/s. The cooling medium enters the heat exchanger at a temperature of 30C...
A counter-flow heat exchanger is stated to have an overall heat transfer coefficient of 284 W/m 2 ·K when operating at design and clean conditions. Hot fluid enters the tube side at 93°C...
Reconsider Prob. 2249. Using an appropriate software, investigate the effects of oil exit temperature and water inlet temperature on the overall heat transfer coefficient of the heat exchanger. Let...
Hot exhaust gases of a stationary diesel engine are to be used to generate steam in an evaporator. Exhaust gases (c p = 1051 J/kgK) enter the heat exchanger at 550C at a rate of 0.25 kg/s while water...
Steam is to be condensed on the shell side of a 1-shell-pass and 8-tube-passes condenser, with 50 tubes in each pass at 90°F (h fg = 1043 Btu/lbm). Cooling water (c p = 1.0 Btu/lbm·°F)...
Reconsider Prob. 2252E. Using an appropriate software, investigate the effect of the condensing steam temperature on the rate of heat transfer, the rate of condensation of steam, and the mass flow...
Reconsider Prob. 2254. Using an appropriate software, investigate the effect of the exhaust gas inlet temperature on the rate of heat transfer, the exit temperature of exhaust gases, and the rate of...
In a textile manufacturing plant, the waste dyeing water (c p = 4295 J/kg·K) at 75°C is to be used to preheat fresh water (c p = 4180 J/kg·K) at 15°C at the same flow rate in a...
A shell-and-tube heat exchanger with 2-shell passes and 12-tube passes is used to heat water (c p = 4180 J/kgK) in the tubes from 20C to 70C at a rate of 4.5 kg/s. Heat is supplied by hot oil (c p =...
Repeat Prob. 2264 for a mass flow rate of 3 kg/s for water. Repeat Prob. A shell-and-tube heat exchanger with 2-shell passes and 12-tube passes is used to heat water (c p = 4180 J/kgK) in the tubes...
What does the effectiveness of a heat exchanger represent? Can effectiveness be greater than one? On what factors does the effectiveness of a heat exchanger depend?
For a specified fluid pair, inlet temperatures, and mass flow rates, what kind of heat exchanger will have the highest effectiveness: double-pipe parallel-flow, double-pipe counterflow, cross-flow,...
Explain how you can evaluate the outlet temperatures of the cold and hot fluids in a heat exchanger after its effectiveness is determined.
A performance test is being conducted on a doublepipe counter-flow heat exchanger that carries engine oil and water at a flow rate of 2.5 kg/s and 1.75 kg/s, respectively. Since the heat exchanger...
In an industrial facility a counter-flow double-pipe heat exchanger uses superheated steam at a temperature of 250°C to heat feed water at 30°C. The superheated steam experiences a...
Reconsider Prob. 2262. Using an appropriate software, investigate the effect of the mass flow rate of water on the rate of heat transfer and the tubeside surface area. Let the mass flow rate vary...
A single-pass cross-flow heat exchanger is used to cool jacket water (c p = 1.0 Btu/lbm·°F) of a diesel engine from 190°F to 140°F, using air (c p = 0.245 Btu/lbm·°F)...
Can the temperature of the cold fluid rise above the inlet temperature of the hot fluid at any location in a heat exchanger? Explain.
Consider a heat exchanger in which both fluids have the same specific heats but different mass flow rates. Which fluid will experience a larger temperature change: the one with the lower or higher...
Explain how the maximum possible heat transfer rate Q max in a heat exchanger can be determined when the mass flow rates, specific heats, and the inlet temperatures of the two fluids are specified....
Under what conditions can a counter-flow heat exchanger have an effectiveness of one? What would your answer be for a parallel-flow heat exchanger?
Consider a double-pipe counter-flow heat exchanger. In order to enhance heat transfer, the length of the heat exchanger is now doubled. Do you think its effectiveness will also double?
Consider a shell-and-tube water-to-water heat exchanger with identical mass flow rates for both the hot- and cold-water streams. Now the mass flow rate of the cold water is reduced by half. Will the...
Consider two double-pipe counter-flow heat exchangers that are identical except that one is twice as long as the other one. Which heat exchanger is more likely to have a higher effectiveness?
How is the NTU of a heat exchanger defined? What does it represent? Is a heat exchanger with a very large NTU (say, 10) necessarily a good one to buy?
The radiator in an automobile is a cross-flow heat exchanger (UA s = 10 kW/K) that uses air (c p = 1.00 kJ/kgK) to cool the engine-coolant fluid (c p = 4.00 kJ/kgK). The engine fan draws 30C air...
Consider an oil-to-oil double-pipe heat exchanger whose flow arrangement is not known. The temperature measurements indicate that the cold oil enters at 20C and leaves at 55C, while the hot oil...
Water (c p = 4180 J/kgK) is to be heated by solarheated hot air (c p = 1010 J/kgK) in a double-pipe counter-flow heat exchanger. Air enters the heat exchanger at 90C at a rate of 0.3 kg/s, while...
A thin-walled double-pipe, counter-flow heat exchanger is to be used to cool oil (c p = 0.525 Btu/lbmF) from 300F to 105F at a rate of 5 lbm/s by water (c p = 1.0 Btu/lbmF) that enters at 70F at a...
A one-shell and two-tube type heat exchanger has an overall heat transfer coefficient of 300 Btu/hft 2 F. The shell side fluid has a heat capacity rate of 20,000 Btu/hF, while the tube side fluid has...
In a one-shell and two-tube heat exchanger, cold water with inlet temperature of 20C is heated by hot water supplied at the inlet at 80C. The cold and hot water flow rates are 5000 kg/h and 10,000...
Reconsider Prob. 2285. Using an appropriate software, investigate the effects of the mass flow rate of water and the tube length on the outlet temperatures of water and air. Let the mass flow rate...
Cold water (c p = 4180 J/kg·K) leading to a shower enters a thin-walled double-pipe counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (c p =...
A double-pipe parallel-flow heat exchanger is to heat water (c p = 4180 J/kgK) from 25C to 60C at a rate of 0.2 kg/s. The heating is to be accomplished by geothermal water (c p = 4310 J/kgK)...
Ethylene glycol is heated from 25C to 40C at a rate of 2.5 kg/s in a horizontal copper tube (k = 386 W/mK) with an inner diameter of 2.0 cm and an outer diameter of 2.5 cm. A saturated vapor (T g =...
A shell-and-tube heat exchanger with 2-shell passes and 12-tube passes is used to heat water (c p = 4180 J/kgK) with ethylene glycol (c p = 2680 J/kgK). Water enters the tubes at 22C at a rate of 0.8...
A shell-and-tube heat exchanger with 2-shell passes and 8-tube passes is used to heat ethyl alcohol (c p = 2670 J/kgK) in the tubes from 25C to 70C at a rate of 2.1 kg/s. The heating is to be done by...
In a one-shell and eight-tube pass heat exchanger, the temperature of water flowing at rate of 50,000 lbm/h is raised from 70F to 150F. Hot air (c p = 0.25 Btu/lbmF) that flows on the tube side...
Oil is being cooled from 180°F to 120°F in a 1-shell and 2-tube heat exchanger with an overall heat transfer coefficient of 40 Btu/h·ft 2 ·°F. Water (c pc = 1.0...
Air (c p = 1005 J/kgK) enters a cross-flow heat exchanger at 20C at a rate of 3 kg/s, where it is heated by a hot water stream (c p = 4190 J/kgK) that enters the heat exchanger at 70C at a rate of 1...