Question: A simple solar heater consists of a

> Use Fig. 8.3 to determine the Nusselt number and the heat transfer coefficient for the conditions given in Problem 8.4.

> An electronic device is to be cooled by natural convection in atmospheric air at 20°C. The device generates 50 W internally, and only one of its external surfaces is suitable for attaching fins. The surface available for attaching cooling fins

> An electronic device is to be cooled in air at 20°C by an array of equally spaced vertical rectangular fins, as shown in the following sketch. The fins are made of aluminum and their average temperature, Ts, is 100°C. Estimate (a)

> Consider the problem described in Example 8.5. Show that the transient heating of the water in the pan, assuming the water to be well-mixed and thermally homogenous at any instant in time, can be expressed by the following: where V is the volume of water

> The refrigeration system for an indoor ice rink is to be sized by an HVAC contractor. The refrigeration system has a COP (coefficient of performance) of 0.5. The ice surface is estimated to be 22°C, and the ambient air is -4°C. Dete

> A flat roof is modeled as a flat plate insulated on the bottom and placed in the sunlight. If the radiant heat that the roof receives from the sun is 600 W/m2, the convection heat transfer coefficient between the roof and the air is 12 W/m2 K, and the ai

> The surfaces of two concentric spheres with radii of 75 and 100 mm are maintained at 325 K and 275 K, respectively. (a) If the space between the spheres is filled with nitrogen at 500 kPa, estimate the convection heat transfer rate. (b) If both sphere

> Liquid oxygen at -183°C is stored in a thin-walled spherical container with an outside diameter of 2 m. This container is surrounded by another sphere of 2.5-m inside diameter to reduce heat loss. The inner spherical surface has an emissivity of 0.05, an

> A solar collector design consists of several parallel tubes, each enclosed concentrically in an outer tube that is transparent to solar radiation. The tubes are thin walled with inner and outer cylinder diameters of 0.10 and 0.15 m, respectively. The ann

> Two long, concentric, horizontal aluminum tubes of 0.2 m and 0.25 m diameter are maintained at 300 K and 400 K, respectively. The space between the tubes is filled with nitrogen. If the surfaces of the tubes are polished to prevent radiation, estimate th

> Calculate the rate of heat transfer between a pair of concentric horizontal cylinders 20 mm and 126 mm in diameter. The inner cylinder is maintained at 37°C, and the outer cylinder is maintained at 17°C.

> Determine the rate of heat loss through a double-paned window shown in the sketch if the inside room temperature is 65°C and the average out- side air is 0°C during December. Neglect the effect of the window frame. If the house is e

> A long cylinder 0.1 m in diameter has a surface temperature of 400 K. If it is immersed in a fluid at 350 K, natural convection will occur as a result of the temperature difference. Calculate the Grashof and Rayleigh numbers that will determine the Nusse

> A flat-plate solar collector of 3 m * 5 m area has an absorber plate that is to operate at a temperature of 70°C. To reduce heat losses, a glass cover is placed 0.05 m from the absorber. Its operating temperature is estimated to be 35Â&d

> An architect is asked to determine the heat loss through a wall of a building constructed as shown in the sketch. The space between the walls is 10 cm and contains air. If the inner surface is at 20°C, and the outer surface is at -8Â&de

> Estimate the rate of convection heat transfer across a 1-m-tall double-pane window assembly in which the outside pane is at 0°C and the inside pane is at 20°C. The panes are spaced 2.5 cm apart. What is the thermal resistance (R-value) of the window if t

> To reduce home heating requirements, modern building codes in many parts of the country require the use of double-glazed or double-pane windows, i.e., windows with two panes of glass. Some of these so-called thermos pane windows have an evacuated space b

> In petroleum processing plants, it is often necessary to pump highly viscous liquids such as asphalt through pipes. To keep pumping costs within reason, the pipelines are electrically heated to reduce the viscosity of the asphalt. Consider a 15-cm-OD un

> A long steel rod (2 cm in diameter, 2 m long) has been heat treated and quenched to a temperature of 100°C in an oil bath. To cool the rod further, it is necessary to remove it from the bath and expose it to room air. Is cool-down faster by cooling the c

> An 20-cm-diameter horizontal steam pipe carries 1.66 kg/min of dry, pressurized, saturated steam at 120°C. If the ambient air temperature is 20°C, deter- mine the rate of condensate flow at the end of 3 m of pipe. Use an emissivity of 0.85 for the pi

> A 2-cm-diameter bare aluminum electric power trans- mission line with an emissivity of 0.07 carries 500 A at 400 kV. The wire has an electrical resistivity of 1.72 / and is suspended horizontally between two towers separated by 1 km. Determine the surfac

> Only 10% of the energy dissipated by the tungsten filament of an incandescent lamp is in the form of useful visible light. Consider a 100-W lamp with a 10-cm spherical glass bulb, as shown in the sketch. Assuming an emissivity of 0.85 for the glass and a

> A sphere 20 cm in diameter containing liquid air (-140°C) is covered with 5-cm-thick glass wool (50 kg/m3 density) with an emissivity of 0.8. Estimate the rate of heat transfer to the liquid air from the surrounding air at 20°C by convection and ra

> A thermocouple (0.8-mm OD) is located horizon- tally in a large enclosure whose walls are at 37°C. The enclosure is filled with a transparent, quiescent gas that has the same properties as air. The electromotive force (emf) of the thermocouple indicates

> Using standard steam tables, calculate the coefficient of thermal expansion, , from its definition for steam at 450°C and pressures of 10 kPa and 1 MPa. Then compare your results with the value obtained by assuming that steam is a perfect gas, and expla

> Compare the rate of condensate flow from the pipe in Problem 8.28 ( air pressure = 200 kPa) with that for a 3.89-cm-OD pipe and 200 kPa air pressure. What is the rate of condensate flow if the 2-cm pipe is submerged in a 20°C constant-temperature water

> A long, 2-cm-diameter horizontal copper pipe carries dry saturated steam at 120 kPa absolute pressure. The pipe is contained within an environmental testing chamber in which the ambient air pressure can be adjusted from 50 kPa to 200 kPa absolute, while

> An electronic device that internally generates 600 mW of heat has a maximum permissible operating temperature of 70°C. It is to be cooled in 25°C air by attaching aluminum fins with a total surface area of 12 cm2. The convection

> A laboratory experiment has been performed to determine the natural-convection heat transfer correlation for a horizontal cylinder of elliptical cross section in air. The cylinder is 1 m long, has a hydraulic diameter of 1 cm, a surface area of 0.0314 m2

> A pot of coffee has been allowed to cool to 17°C. If the electric coffee maker is turned back on, the hot plate on which the pot rests is brought up to 70°C immediately and held at that temperature by a thermostat. Consider the pot

> A thin electronic circuit board, 0.1 m * 0.1 m in size, is to be cooled in air at 25°C, as shown in the sketch. The board is placed in a vertical position, and the back side is well insulated. If the heat dissipation is uniform at 200 W/m2, d

> A 2.5-m * 2.5-m steel sheet 1.5 mm thick is removed from an annealing oven at a uniform temperature of 425°C and placed in a large room at 20°C in a horizontal position. (a) Calculate the rate of heat transfer from the steel sheet immediately after its

> A 1-m-square copper plate is placed horizontally on 2-m-high legs. The plate has been coated with a material that provides a solar absorptivity of 0.9 and an infrared emissivity of 0.25. If the air temperature is 30°C, determine the equilibrium temperatu

> Solar radiation at 600 W/m2 is absorbed by a black roof inclined at 30° as shown. If the underside of the roof is well insulated, estimate the maximum roof temperature in Tinfinity = 20°C air.

> Cooled air is flowing through a long, sheet metal air-conditioning duct 0.2 m high and 0.3 m wide. If the duct temperature is 10°C and passes through a crawl space under a house at 30°C, estimate (a) the heat transfer rate to the cooled air per meter le

> An electronic circuit board the shape of a flat plate is 0.3 m * 0.3 m in planform and dissipates 15 W. It is placed in operation on an insulated surface either in a horizontal position or at an angle of 45° to horizontal; in both cases, it is in still a

> From its definition and from the property values in Appendix 2, Table 13, calculate the coefficient of thermal expansion, , for saturated water at 403 K. Then compare your results with the value in the table.

> A laboratory apparatus is used to maintain a horizontal slab of ice at –2.2°C so that specimens can be prepared on the surface of the ice and kept close to 0°C. If the ice is 10 cm 3 3.8 cm and the laboratory is kept at 16°C, find the cooling rate in wat

> A composite refrigerator wall is composed of 5 cm of corkboard sandwiched between a 1.2-cm-thick layer of oak and a 0.8-mm-thick layer of aluminum lining on the inner surface. The average convection heat transfer coefficients at the interior and exterio

> A 0.1-cm-thick square, flat copper plate, 2.5 m * 2.5 m, is to be cooled in a vertical position. The initial temperature of the plate is 90°C with the ambient fluid at 30°C. The fluid medium is either atmospheric air or water. For both fluids, (a) calcu

> An aluminum sheet 0.4 m tall, 1 m long, and 0.002 m thick is to be cooled from an initial temperature of 150°C to 50°C by immersing it suddenly in water at 20°C. The sheet is suspended from two wires at the upper corners

> An electric heating blanket is subjected to an acceptance test. It is to dissipate 400 W on the high set- ting when hanging in air at 20°C. (a) If the blanket is 1.3 m wide, what is the length required If its average temperature at the high setting is t

> A mercury bath at 60°C is to be heated by immersing cylindrical electric heating rods, each 20 cm tall and 2 cm in diameter. Calculate the maximum electric power rating of a typical rod if its maximum surface temperature is 140°C.

> Consider a design for a nuclear reactor using natural- convection heating of liquid bismuth as shown. The reactor is to be constructed of parallel vertical plates 1.8 m tall and 1.2 m wide in which heat is generated uniformly. Estimate the maximum possib

> A long, heated, cylindrical steel rod is removed from a heat treatment furnace and has to be cooled to complete the process. If the surface temperature of the rod is at 150°C and the cooling fluid temperature is maintained at 25°C, what is the minimum di

> An electric room heater has been designed in the shape of a vertical cylinder 2 m tall and 30 cm in diameter. For safety, the heater surface cannot exceed 35°C. If the room air is at 20°C, find the power rating of the heater in watts.

> Compare the rate of heat loss from a human body with the typical energy intake from consumption of food (4.325 MJ/day). Model the body as a vertical cylinder 30 cm in diameter and 1.8 m high in still air. Assume the skin temperature is 2°C bel

> Solar One, located near Barstow, CA, was the first large-scale (10-MW electric) solar-thermal electric-power-generating plant in the United States. A schematic diagram of the plant is shown below. The receiver can be treated as a cylinder 7 m in dia

> Show that the coefficient of thermal expansion for an ideal gas is 1/T, where T is the absolute temperature.

> Air at an average temperature of 150°C flows through a short, square duct 10 * 10 * 2.25 cm at a rate of 15 kg/h, as shown in the sketch below. The duct wall temperature is 430°C. Determine the average heat transfer coefficient usin

> Air at 30°C enters a rectangular duct 1 m long and 4 mm by 16 mm in cross section at a rate of 0.0004 kg/s. If a uniform heat flux of 500 W/m2 is imposed on both of the long sides of the duct, calculate (a) the air outlet temperature, (b) th

> Nitrogen at 30°C and atmospheric pressure enters a triangular duct 0.02 m on each side at a rate of 4 * 10-4 kg/s. If the duct temperature is uniform at 200°C, estimate the bulk temperature of the nitrogen 2 m and 5 m from the inlet.

> Purified water, flowing at the rate of 45 kg/h is to be heated from 25°C to 75°C in a food processing plant before it is mixed with thickened tomato puree for sauce production. A thin-walled, 1.25 cm diameter, stainless steel tube is used, which is maint

> Reconsider Problem 7.19, where the tube-to-coil effects were ignored. By considering a helical coiled- tube heat exchanger where the tube length (straight length of an unwound coil) is the same as calculated previously, recommend a coil diameter, dc, for

> A nuclear reactor has rectangular flow channels with a large aspect ratio /Heat generation from the upper and lower surfaces is equal and uniform at any value of x. However, the rate varies along the flow path of the sodium coolant according to Assuming

> A 5000 m2 condenser is constructed with 2.5-cm-OD brass tubes that are 2.7 m long and have a 1.2 mm wall thickness. The following thermal resistance data were obtained at various water velocities inside the tubes (Trans. ASME, Vol. 58, p. 672, 1936). Ass

> Water in turbulent flow is to be heated in a single-pass tubular heat exchanger by steam condensing on the outside of the tubes. The flow rate of the water, its inlet and outlet temperatures, and the steam pressure are fixed. Assuming that the tube wall

> A long, 1.2-m-OD pipeline carrying oil is to be installed in Alaska. To prevent the oil from becoming too viscous for pumping, the pipeline is buried 3 m below ground. The oil is also heated periodically at pumping stations, as shown schematically in the

> A 3.05 m vertical cylindrical exhaust duct from a commercial laundry has an ID of 15.2 cm. Exhaust gases having physical properties approximating those of dry air enter at 316°C. The duct is insulated with 10.2 cm of rock wool having a thermal conductivi

> A submarine is to be designed to provide a comfortable temperature of no less than 21°C for the crew. The submarine is idealized by a cylinder 9 m in diameter and 61 m in length, as shown. The combined heat transfer coefficient on the interior

> Exhaust gases having properties similar to dry air enter an exhaust stack at 800 K. The stack is made of steel and is 8 m tall with a 0.5-m-ID. The gas flow rate is 0.5 kg/s, and the ambient temperature is 280 K. The outside of the stack has an emissivit

> A plastic tube of 7.6-cm-ID and 1.27-cm wall thick- ness has a thermal conductivity of 1.7 W/m K, a density of 2400 kg/m3, and a specific heat of 1675 J/kg K. It is cooled from an initial temperature of 77°C by passing air at 20°C inside and outside the

> In a biomedical processing plant, a newly developed liquid drug or medication that leaves a mixing chamber at 20°C needs to be heated to 70°C in a thermal curing process. This is achieved by heating the liquid media at the rate of 10 kg/h in a thin metal

> In a pipe-within-a-pipe heat exchanger, water flows in the annulus and an aniline-alcohol solution having the properties listed in Problem 7.28 flows in the central pipe. The inner pipe has a 1.3-cm-ID and a 1.6-cm-OD, and the ID of the outer pipe is

> Evalute the rate of heat loss per meter from pressurized water flowing at 200°C through a 10-cm-ID pipe at a velocity of 3 m/s. The pipe is covered with a 5-cm-thick layer of 85% magnesia wool with an emissivity of 0.5. Heat is transferred to the surroun

> Assume that the inner cylinder in Problem 7.40 is a heat source consisting of an aluminum-clad rod of uranium with a 5-cm diameter and 2 m long. Estimate the heat flux that raises the temperature of the bismuth 40°C and the maximum center and surface tem

> A double-pipe heat exchanger is used to condense steam at 7370 N/m2. Water at an average bulk temperature of 10°C flows at 3.0 m/s through the inner pipe, which is made of copper and has a 2.54-cm ID and a 3.05-cm OD. Steam at its saturation temperature

> A 2.54-cm-OD, 1.9-cm-ID steel pipe carries dry air at a velocity of 7.6 m/s and a temperature of 27°C. Ambient air is at 21°C and has a dew point of 10°C. How much insulation with a conductivity of 0.18 W/mK is needed to

> For fully turbulent flow in a long tube of diameter D, develop a relation between the ratio /in terms of flow and heat transfer parameters, where /is the tube length required to raise the bulk temperature of the fluid by / Use Eq. (7.61) for fluids with

> Liquid sodium is to be heated from 500 K to 600 K by passing it at a flow rate of 5.0 kg/s through a 5-cm- ID tube whose surface is maintained at 620 K. What length of tube is required?

> A heat exchanger wall consists of a copper plate 2 cm thick. The heat transfer coefficients on the two sides of the plate are 2700 and 7000 W/ ( m2 K ) , corresponding to fluid temperatures of 92 and 32°C, respectively. Assuming that the thermal conducti

> A heat exchanger is to be designed to heat a flow of molten bismuth from 377°C to 477°C. The heat exchanger consists of a 50-mm-ID tube with a sur- face temperature maintained uniformly at 500°C by an electric heater. Find the length of the tube and the

> Mercury flows inside a copper tube 9 m long with a 5.1-cm inside diameter at an average velocity of 7 m/s. The temperature at the inside surface of the tube is 38°C uniformly throughout the tube, and the arithmetic mean bulk temperature of the mercury is

> Determine the heat transfer coefficient for liquid bismuth flowing through an annulus (5-cm-ID, 6.1-cm- OD) at a velocity of 4.5 m/s. The wall temperature of the inner surface is 427°C, and the bismuth is at 316°C. Assume that heat losses from the outer

> Water enters a small copper tube, with an inner diameter of 2.5 cm, at the rate of 0.025 kg/s and a temperature of 15°C. Steam is condensing on the outer surface of the tube at atmospheric pressure so that tube-surface temperature is uniformly at 100°C.

> Atmospheric air at 10°C enters a 2-m-long smooth, rectangular duct with a 7.5-cm * 15-cm cross section. The mass flow rate of the air is 0.1 kg/s. If the sides are at 150°C, estimate (a) the heat transfer coefficient, (b) the air outlet temperature, (

> Atmospheric air at a velocity of 61 m/s and a temperature of 16°C enters a 0.61-m-long square metal duct of 20-cm * 20-cm cross section. If the duct wall is at 149°C, determine the average heat transfer coefficient. Comment briefly on the L/Dh effect.

> If the total resistance between the steam and the air (including the pipe wall and scale on the steam side) in Problem 7.36 is 0.05 m2 K/W, calculate the temperature difference between the outer surface of the inner pipe and the air. Show the thermal cir

> Atmospheric pressure air is heated in a long annulus (25-cm-ID, 38-cm-OD) by steam condensing at 149°C on the inner surface. If the velocity of the air is 6 m/s and its bulk temperature is 38°C, calculate the heat transfer coefficie

> The equation has been proposed by Hausen for the transition range /as well as for higher Reynolds numbers. Compare the values of Nu predicted by Hausen’s equation for Re 5 3000 and Re = 20,000 at D/L = 0.1 and 0.01 with those obtained f

> Air at 16°C and atmospheric pressure enters a 1.25-cm-ID tube at 30 m/s. For an average wall temperature of 100°C, determine the discharge temperature of the air and the pressure drop if the pipe is (a) 10 cm long and (b) 102 cm long.

> As a designer working for a major electric appliance manufacturer, you are required to estimate the amount of fiberglass insulation packing (k = 0.035 W/m K) that is needed for a kitchen oven shown in the figure below. The fiberglass layer is to be sandw

> To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the 6-cm 3 6-cm guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermo

> Suppose an engineer suggests that air instead of water could flow through the tube in Problem 7.32 and that the velocity of the air could be increased until the heat transfer coefficient with the air equals that obtained with water at 1.5 m/s. Determine

> High-pressure water at a bulk inlet temperature of 93°C is flowing with a velocity of 1.5 m/s through a 0.015-m-diameter tube that is 0.3 m long. If the tube wall temperature is 204°C, determine the average heat transfer coefficient and estimate the bulk

> The intake manifold of an automobile engine is approximated in the figure as a 4-cm-ID tube, 30 cm in length. Air at a bulk temperature of 20°C enters the manifold at a flow rate of 0.01 kg/s. The manifold is a heavy aluminum casting and is at a uniform

> Derive an equation of the form hc = f (T, D, U) for the turbulent flow of water through a long tube in the temperature range between 20° and 100°C.

> A miniature heat sink heat exchanger is constructed with circular cross section channels (similar to that in Example 7.4), each of which has a diameter of 3.0 mm, drilled through a rectangular block. Cooling water at 20°C flows at the rate of 0.5 kg/h th

> In an industrial refrigeration system, brine (10% NaCl by weight) having a viscosity of 0.0016 N s/m2 and a thermal conductivity of 0.85 W/m K is flowing through a long, 2.5-cm-ID pipe at 6.1 m/s. Under these conditions, the heat transfer coefficient was

> An aniline-alcohol solution is flowing at a velocity of 3 m/s through a long, 2.5-cm-ID thin-wall tube. Steam is condensing at atmospheric pressure on the outer surface of the tube, and the tube wall temperature is 100°C. The tube is clean, an

> Water at an average temperature of 27°C is flowing through a smooth 5.08-cm-ID pipe at a velocity of 0.91 m/s. If the temperature at the inner surface of the pipe is 49°C, determine (a) the heat transfer coefficient, (b) the rate of heat flow per meter

> Exhaust gases having properties similar to dry air enter a thin-walled cylindrical exhaust stack at 800 K. The stack is made of steel and is 8 m tall with a 0.5-m inside diameter. If the gas flow rate is 0.5 kg/s and the heat transfer coefficient at the

> Mercury at an inlet bulk temperature of 90°C flows through a 1.2-cm-ID tube at a flow rate of 4535 kg/h. This tube is part of a nuclear reactor in which heat can be generated uniformly at any desired rate by adjusting the neutron flux level. Determine th

> On a cold winter day, the outside wall of a home is exposed to an air temperature of 22°C when the inside temperature of the room is at 22°C. As a result of this temperature gradient, there is heat loss through the wall to the outside. Consider the conve

> Water at 80°C is flowing through a thin copper tube (15.2-cm-ID) at a velocity of 7.6 m/s. The duct is located in a room at 15°C, and the heat transfer coefficient at the outer surface of the duct is 14.1 W/m2 K. (a) Determine the heat transfer

> Compute the average heat transfer coefficient hc for 10°C water flowing at 4 m/s in a long, 2.5-cm-ID pipe (surface temperature 40°C) using three different equations. Compare your results. Also determine the pressure drop per meter length of pipe.

> Calculate the Nusselt number and the convection heat transfer coefficient for water at a bulk temperature of 32°C flowing at a velocity of 1.5 m/s through a 2.54-cm-ID duct with a wall temperature of 43°C. Use the Gnielinski correlation, Eq. (7.66), and

> A solar thermal central receiver generates heat by using a field of mirrors to focus sunlight on a bank of tubes through which a coolant flows. Solar energy absorbed by the tubes is transferred to the coolant, which can then deliver useful heat to a loa

> Water at 20°C enters a 1.91-cm-ID, 57-cm-long tube at a flow rate of 3 g/s. The tube wall is maintained at 30°C. Determine the water outlet temperature. What percent error in the water temperature results if natural convection effects are neglected?

> Consider fully developed laminar flow of a fluid inside a wide rectangular duct with both the upper and lower surface at uniform surface temperature, as schematically shown in the figure below. The effect of the two sides of the duct is neglected /and at