Question: Consider the electrical space heater of Example

> Determine the steady-state temperatures of two radiation shields placed in the evacuated space between two infinite planes at temperatures of 555 K and 278 K. The emissivity of all surfaces is 0.8.

> For saturated pool boiling of water on a horizontal plate, calculate the peak heat flux at pressures of 10, 20, 40, 60, and 80% of the critical pressure pc. Plot your Where ( is in newtons per meter and T in degrees Centigrade. The critical pressure of w

> Two concentric spheres 0.2 m and 0.3 m in diameter are to be used to store liquid air (133 K). The space between the spheres is evacuated. If the surfaces of the spheres have been flashed with aluminum and the liquid air has a latent heat of vaporization

> (a) Show that / only. (b) For T = 5000 m K, calculate /

> In order to conserve energy, the inner surface of double-glazed windows are treated with a low emissivity coating that reduces the emissivity of the uncoated surface from 0.95 to 0.5 for the coated surface. If the temperatures of the two glass panes are

> Two 1.5-m-square, parallel flat plates are 30 cm apart. Plate A1 is maintained at a temperature of 1100 K and A2 at 500 K. The emissivities of the plates are 0.5 and 0.8, respectively. Considering the surroundings that are black at 0 K and including mult

> Derive an equation for the net rate of radiant heat transfer from surface 1 in the system shown in the accompanying sketch. Assume that each surface is at a uniform temperature and that the geometrical shape factor F1–2 is 0.1.

> The wedge-shaped cavity shown in the accompanying sketch consists of two long strips joined along one edge. Surface 1 is 1 m wide, has an emissivity of 0.4, and has a temperature of 1000 K. The other wall has a temperature of 600 K. Assuming gray diffuse

> A black sphere (2.5 cm in diameter) is placed in a large infrared heating oven whose walls are maintained at 370°C. The temperature of the air in the oven is 90°C, and the heat transfer coefficient for convection between the surface of the sphere and the

> In Problem 1.60, instead of diffusive heating (or by conduction), consider that the water is heated by natural convection from the surface of the heaters. The heat transfer coefficient, /, in W/m2 K, is expressed in the form / where Ts is the s

> Calculate the net radiant-heat-transfer rate if the two surfaces in Problem 11.18 are black and are connected by a refractory surface with an area of 500 m2. A1 is at 555 K, and A2 is at 278 K. What is the refractory surface temperature?

> Show that the effective conductance, / for two black, parallel plates of equal area connected by reradiating walls at a constant temperature is

> Compare the critical heat flux for a flat horizontal surface with that for a submerged horizontal wire of 3-mm diameter in water at saturation temperature and pressure.

> Show that the dimensionless equation for ice formation on the outside of a tube of radius r0 is Assume that the water is originally at the freezing temperature Tf, that the cooling medium inside the tube surface is just below the freezing temperature at

> Compare the axial heat flux achievable by a heat pipe using water as the working fluid with that of a solid silver rod. Assume that both are 20 cm long, that the temperature difference for the rod from end to end is 100oC, and that the heat pipe operates

> Design a heat pipe cooling system for a spherical satellite that dissipates 5000 W/m3, has a surface area of 5 m2, and cannot exceed a temperature of 120oC. All the heat must be dissipated by radiation into space. State all your assumptions.

> Estimate the cross-sectional area required for a 30-cm-long methanol-nickel heat pipe to transport 30 W at atmospheric pressure.

> The one-pass condenser, heat exchanger shown in the sketch has 64 tubes arranged in a square array with 8 tubes per line. The tubes are 1.22 m long and are made of copper with an outside diameter of 1.27 cm. They are contained in a shell at atmospheric p

> The 1-m-long, tube-within-a-tube, heat exchanger shown in the sketch is used to condense steam at 2 atm in the annulus. Water flows in the inner tube, entering at 90oC. The inner tube is made of copper with a 1.27-cm-OD and 1.0-cm-ID. (a) Estimate the w

> A vertical, rectangular water duct 1 m high and 0.10 m deep shown in the sketch is placed in an environment of saturated steam at atmospheric pressure. If the outer surface of the duct is about 50oC, estimate the rate of steam condensation per unit lengt

> Estimate the maximum heat flux obtainable with nucleate pool boiling on a clean surface for (a) water at 100 kPa on brass, (b) water at 1 MPa on brass.

> Saturated methyl chloride at 430 kPa (abs) condenses on a horizontal 10 * 10 bank of tubes. The 5-cm- OD tubes are equally spaced and are 10 cm apart center-to-center on rows and columns. If the surface temperature of the tubes is maintained at 7oC by p

> Problem 9.11 indicated that the Nusselt number for condensation depends on the Prandtl number and four other dimensionless groups including the Jakob number (Ja), the Bond number (Bo), and a nameless group resembling the Grashof number / Give

> The inner wall of a rocket motor combustion chamber receives 160 kW/m2 by radiation from a gas at 2760°C. The convection heat transfer coefficient between the gas and the wall is 110 W/ ( m2 K ) . If the inner wall of the combustion chamber is

> Repeat Problem 9.26 (b) and (c) but assume that condensation occurs on a 5-cm-OD, horizontal tube.

> At a pressure of 490 kPa, the saturation temperature of sulfur dioxide ( SO2) is 32oC, the density is 1350 kg/m3, the latent heat of vaporization is 343 kJ/kg, the absolute viscosity is 3.2 * 10-4 kg/m s, the spe-ific heat is 1445 J/kg K and the thermal

> Saturated steam at 34 kPa condenses on a 1-m-tall vertical plate whose surface temperature is uniform at 608C. Compare the average heat transfer coefficient and the value of the coefficient 1/3 m, 2/3 m, and 1 m from the top. Also, find the maximum heigh

> Repeat Problem 9.23 for a tier of six horizontal 2.5-cm-OD tubes under similar thermal conditions.

> A horizontal, 2.5-cm-OD tube is maintained at a temperature of 27oC on its outer surface. Calculate the average heat transfer coefficient if saturated steam at 12 kPa is condensing on this tube.

> The inside surface of a 1-m-long, vertical, 5-cm-ID tube is maintained at 1208C. For saturated steam at 350 kPa condensing inside, estimate the average heat transfer coefficient and the condensation rate, assuming the steam velocity is small.

> Calculate the average heat transfer coefficient for film-type condensation of water at pressures of 10 kPa and 101 kPa for (a) a vertical surface 1.5 m high, (b) the outside surface of a 1.5-cm-OD vertical tube 1.5 m long, (c) the outside surface of a

> In space-based systems, such as the International Space Station, for example, highly efficient cooling systems are deployed that involve force convection boiling. In a laboratory experiment to develop one such system, a test liquid, which has the physica

> Predict the nucleate-boiling heat transfer coefficient for water boiling at atmospheric pressure on the out- side surface of a 1.5-cm-OD vertical-copper tube, 1.5 m long. Assume the tube surface temperature is constant at 10 K above the saturation temper

> During the 1980s, solar thermal electric technology was commercialized with the installation of 350 MW electrical power-plant capacity in the California desert. The technology involved heating a heat transfer oil in receiver tubes placed at the focus of

> A steam pipe 200 mm in diameter passes through a large basement room. The temperature of the pipe wall is 500°C, while that of the ambient air in the room is 20°C. Determine the heat transfer rate by convection and radiation per unit length of steam pipe

> To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the material is subjected to a uniform heat flux of 2500 W/m2 while thermocouples embedded in the wall at 2.5 cm. intervals are read over a period of time. After

> Calculate the maximum safe heat flux in the nucleate- boiling regime for water flowing at a velocity of 15 m/s through a 0.31-m-long, 1.2-cm-ID tube if the water enters at 100 kPa and 100oC.

> A metal-clad electrical heating element of cylindrical shape, as shown in the sketch below, is immersed in water at atmospheric pressure. The element is 5-cm OD, and heat generation produces a surface temperature of 3008C. Estimate the heat flux under st

> Calculate the heat transfer coefficient for film boiling of water on a 1.3-cm horizontal tube if the tube temperature is 550oC and the system is placed under a pressure of 50 kPa.

> In a metal alloy manufacturing and heat treatment plant and in its immersion quenching process, steel plates are first heated in a furnace and then quenched (or cooled) in a coolant bath to obtain the desired steel properties and surface hardness. In on

> Calculate the peak heat flux for nucleate pool boiling of water at 300 kPa pressure and 110oC on clean copper.

> It has recently been proposed by Andraka et al. of Sandia National Laboratories Albuquerque, in Sodium Reflux Pool-Boiler Solar Receiver On-Sun Test Results (SAND89-2773, June 1992) that the heat flux from a parabolic dish solar concentrator coul

> Environmental concerns have recently motivated the search for replacements for chlorofluorocarbon refrigerants. An experiment has been devised to deter- mine the applicability of one such replacement. A silicon chip is bonded to the bottom of a thin copp

> In boiling (and condensation) heat transfer, the convection heat transfer coefficient, hc, is expected to depend on the difference between the surface and saturation temperatures, /, the body force arising from the density difference between liquid a

> A thin-walled, horizontal copper tube of 0.5-cm OD is placed in a pool of water at atmospheric pressure and 100oC. Inside the tube an organic vapor is condensing, and the outside surface temperature of the tube is uniform at 232oC. Calculate the average

> Water at atmospheric pressure is boiling in a pot with a flat-copper bottom on an electric range that maintains the surface temperature at 115oC. Calculate the boiling heat transfer coefficient.

> A small oven with a surface area of 0.28 m2 is located in a room in which the walls and the air are at a temperature of 27°C. The exterior surface of the oven is at 150°C, and the next heat transfer by radiation between the oven’s surface and the surroun

> Overhead electric transmission lines get heated (due to the electric resistivity of the cable material) and lose heat to the ambient air; this transmission energy loss due to heat transfer is referred to as the Joule effect in the conduction material. Co

> The heat loss from uninsulated hot water pipes installed in homes can be considerable and hence increases the overall energy cost of the home. Consider a 5-m-long section of such a pipe that has an outer diameter of 1.7 cm and a surface temperature of 75

> A 0.15-m-square circuit board is to be cooled in a vertical position, as shown in the sketch. The board is insulated on one side, while on the other, 100 closely spaced square chips are mounted. Each chip dissipates 0.06 W of heat. The board is exposed t

> The following equation has been proposed for the heat transfer coefficient in natural convection from long vertical cylinders to air at atmospheric pressure: where Tf = the film temperature / is in the range 0 to 200°C. The corresponding equat

> A gas-fired industrial furnace is used to generate steam. The furnace is a 3-m cubic structure, and the interior surfaces are completely covered with boiler tubes transporting pressurized wet steam at 150°C. It is desired to keep the furnace losses to 1%

> A horizontal disk 1 m in diameter rotates in air at 25°C. If the disk is at 100°C, estimate the number of revolutions per minute at which natural convection for a stationary disk becomes less than 10% of the heat transfer for a rotating disk.

> A vertical, isothermal plate 30 cm high is suspended in an atmospheric airstream flowing at 2 m/s in a vertical direction. If the air is at 16°C, estimate the plate temperature for which the natural-convection effect on the heat transfer coefficient will

> Suppose a thin, vertical, flat plate 60 cm high and 40 cm wide is immersed in a fluid flowing parallel to its surface. If the plate is at 40°C and the fluid at 10°C, estimate the Reynolds number at which buoyancy effects are essentially negligible for he

> Consider a vertical, 20-cm-tall, flat plate at 120°C, suspended in a fluid at 100°C. If the fluid is being forced past the plate from above, estimate the fluid velocity for which natural convection becomes negligible (less than 10%) in (a) mercury, (b)

> A horizontal, 3-mm-thick flat-copper plate, 1-m long and 0.5-m wide, is exposed in air at 27°C to radiation from the sun. If the total rate of solar radiation absorbed is 300 W and the combined radiation and convection heat transfer coefficients on the u

> Reconsider the problem of cooling of a rotating rod (shaft) by natural convection described in Example 8.6. Determine the shaft rotation at which the heat transfer contribution due to the rotation convection is about the same as that due to natural conve

> A mild steel (1% carbon), 2-cm-OD shaft rotating in 20°C air at 20,000 rev/min is attached to two bearings 0.7 m apart, as shown below. If the temperature at the bearings is 90°C, determine the temperature distribution along the sh

> A sphere 0.1 m in diameter is rotating at 20 rpm in a large container of CO2 at atmospheric pressure. If the sphere is at 60°C and the CO2 at 20°C, estimate the rate of heat transfer.

> Estimate the rate of heat transfer from one side of a 2-m-diameter disk with a surface temperature of 50°C rotating at 600 rev/min in 20°C air.

> The electronic controls of a medical imaging device are housed in a compartment such that it heat dissipates heat to the ambient from a flat vertical plate surface, 15 cm wide and 20 cm high, to which fins are attached so as to enhance the heat transfer

> 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