Show that the thermal resistance of a rectangular enclosure can be expressed as R = Lc /(AkNu), where k is the thermal conductivity of the fluid in the enclosure.
> Oil at 60°C flows at a velocity of 20 cm/s over a 5.0-m-long and 1.0-m-wide flat plate maintained at a constant temperature of 20°C. Determine the rate of heat transfer from the oil to the plate if the average oil properties are ρ = 880 kg/m3, μ = 0.005
> Consider a circular grill whose diameter is 0.3 m. The bottom of the grill is covered with hot coal bricks at 950 K, while the wire mesh on top of the grill is covered with steaks initially at 5°C. The distance between the coal bricks and the
> A group of 25 power transistors, dissipating 1.5 W each, are to be cooled by attaching them to a black-anodized square aluminum plate and mounting the plate on the wall of a room at 30°C. The emissivity of the transistor and the plate surfaces
> Four power transistors, each dissipating 10 W, are mounted on a thin vertical aluminum plate (k = 237 W/m⋅K) 22 cm × 22 cm in size. The heat generated by the transistors is to be dissipated by both surfaces of the plate to the surrounding air at 20°C, wh
> Consider a 4-m × 4-m × 4-m cubical furnace whose floor and ceiling are black and whose side surfaces are reradiating. The floor and the ceiling of the furnace are maintained at temperatures of 550 K and 1100 K, respectively. Determine the net rate of rad
> A 4-L rigid tank contains 2 kg of saturated liquid–vapor mixture of water at 50°C. The water is now slowly heated until it exists in a single phase. At the final state, will the water be in the liquid phase or the vapor phase
> The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of quantities, obtain a relation for the filling time in terms of the volume V of the tank (in L) and the discharge rate of gasol
> A plate (0.5 m × 0.5 m) is inclined at an angle of 30°. The top surface of the plate is well insulated. Estimate the rate of heat loss from the plate when the bottom surface is maintained at 60°C and the surrounding atmospheric quiescent air is at 0°C.
> A concentric annulus tube has inner and outer diameters of 25 mm and 100 mm, respectively. Liquid water flows at a mass flow rate of 0.05 kg/s through the annulus with the inlet and outlet mean temperatures of 20°C and 80°C, respect
> A 9-ft-high room with a base area of 12 ft × 12 ft is to be heated by electric resistance heaters placed on the ceiling, which is maintained at a uniform temperature of 90°F at all times. The floor of the room is at 65°F and has an emissivity of 0.8. The
> During a plant visit, it was observed that a 1.5-m-high and 1-m-wide section of the vertical front section of a natural gas furnace wall was too hot to touch. The temperature measurements on the surface revealed that the average temperature of the expose
> Reconsider Prob. 19–92. Using appropriate software, investigate the effect of the volume flow rate of air on the exit temperature of air and the rate of heat loss. Let the flow rate vary from 0.05 m3/s to 0.15 m3/s. Plot the exit temper
> The speed of light in a vacuum is given to be 3.0 × 108 m/s. Determine the speed of light in air (n = 1), in water (n = 1.33), and in glass (n = 1.5).
> Show that the volume expansion coefficient of an ideal gas is β = 1/T, where T is the absolute temperature.
> Hot air at atmospheric pressure and 75°C enters a 10-m-long uninsulated square duct of cross section 0.15 m × 0.15 m that passes through the attic of a house at a rate of 0.2 m3/s. The duct is observed to be nearly isothermal at 7
> What is an electromagnetic wave? How does it differ from a sound wave?
> An 8-m-long, uninsulated square duct of cross section 0.2 m × 0.2 m and relative roughness 10−3 passes through the attic space of a house. Hot air enters the duct at 1 atm and 80°C at a volume flow rate of 0.15 m3/s. The duct surface is nearly isothermal
> A 10-kg mass of superheated refrigerant-134a at 1.2 MPa and 70°C is cooled at constant pressure until it exists as a compressed liquid at 20°C. (a) Show the process on a T-v diagram with respect to saturation lines. (b) Determine the change in volume. (c
> An electric resistance space heater is designed such that it resembles a rectangular box 50 cm high, 80 cm long, and 15 cm wide filled with 45 kg of oil. The heater is to be placed against a wall, and thus heat transfer from its back surface is negligibl
> Two concentric spheres of diameters Di = 20 cm and Do = 30 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are Ti = 320 K and To = 280 K, respectively. Determine the rate of heat transfer from the
> Air (1 atm) enters into a 5-cm-diameter circular tube at 20°C with an average velocity of 5 m/s. The tube wall is maintained at a constant surface temperature of 160°C, and the outlet mean temperature is 80°C. Estimate the length of the tube. Is the flow
> Reconsider Prob. 20–76. Using appropriate software, plot the rate of natural convection heat transfer as a function of the hot surface temperature of the sphere as the temperature varies from 250 K to 450 K, and discuss the results. Data from Prob. 20-7
> During air cooling of potatoes, the heat transfer coefficient for combined convection, radiation, and evaporation is determined experimentally to be as shown: Consider an 8-cm-diameter potato initially at 20°C. Potatoes are cooled by refrigera
> Two concentric spheres of diameters 15 cm and 25 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are T1 = 350 K and T2 = 275 K, respectively. Determine the rate of heat transfer from the inner sphe
> The hot water needs of a household are to be met by heating water at 55°F to 180°F with a parabolic solar collector at a rate of 5 lbm/s. Water flows through a 1.25-in-diameter thin aluminum tube whose outer surface is anodized blac
> Two concentric spheres with diameters of 5 cm and 10 cm have their surface temperatures maintained at 100°C and 200°C, respectively. The enclosure between the two concentric spherical surfaces is filled with nitrogen gas at 1 atm. D
> Consider a fluid with a Prandtl number of 7 flowing through a smooth circular tube. Using the Colburn, Petukhov, and Gnielinski equations, determine the Nusselt numbers for Reynolds numbers at 3500,104, and 5 × 105. Compare and discuss the results.
> Consider two concentric horizontal cylinders of diameters 55 cm and 65 cm and length 125 cm. The surfaces of the inner and outer cylinders are maintained at 54°C and 106°C, respectively. Determine the rate of heat transfer between the cylinders by natura
> A 9-m3 tank contains nitrogen at 17°C and 600 kPa. Some nitrogen is allowed to escape until the pressure in the tank drops to 400 kPa. If the temperature at this point is 15°C, determine the amount of nitrogen that has escaped.
> Water is to be heated from 10°C to 80°C as it flows through a 2-cm-internal-diameter, 13-m-long tube. The tube is equipped with an electric resistance heater, which provides uniform heating throughout the surface of the tube. The outer surface of the hea
> Reconsider Prob. 20–72. Using appropriate software, plot the rate of heat loss from the water by natural convection as a function of the ambient air temperature as the temperature varies from 4°C to 40°C, and discu
> Determine the convection heat transfer coefficient for the flow of (a) air and (b) water at a velocity of 5 m/s in an 8-cm-diameter and 10-m-long tube when the tube is subjected to uniform heat flux from all surfaces. Use fluid properties at 25Â&de
> A simple solar collector is built by placing a 5-cm diameter clear plastic tube around a garden hose whose outer diameter is 1.6 cm. The hose is painted black to maximize solar absorption, and some plastic rings are used to keep the spacing between the h
> Air flows with an average velocity of 3 ft/s in a duct that is 1 ft wide and 1 in high and 40 ft long. The aspect ratio of the duct is very small (0.083), and the duct can be treated as a parallel-plate channel. The duct passes through a heated oven, and
> Reconsider Prob. 20–70E. Using appropriate software, investigate the effect of the air gap thickness on the rates of heat transfer by natural convection and radiation and the R-value of insulation. Let the air gap thickness vary from 0.
> Air flows in a pipe under fully developed conditions with an average velocity of 1.25 m/s and a temperature of 20°C. The pipe’s inner diameter is 4 cm, and its length is 4 m. The first half of the pipe is kept at a constant w
> 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 measured to be 65°F and 40°F, determ
> Water flows through a circular pipe. The pipe’s inner diameter is 2 cm, and its length is 6 m. The average velocity of the water is 15 cm/s, and its inlet temperature is 20°C. Assuming that the heating is uniform and the flow is fully developed, what is
> Physically, what does the Grashof number represent? How does the Grashof number differ from the Reynolds number?
> Water initially at 300 kPa and 250°C is contained in a constant-volume tank. The water is allowed to cool until its pressure is 150 kPa. On the P-v and T-v diagrams, sketch, with respect to the saturation lines, the process curve passing through both the
> Air flows in an isothermal tube under fully developed conditions. The inlet temperature is 60°F and the tube surface temperature is 120°F. The tube is 10 ft long, and the inner diameter is 2 in. The air mass flow rate is 18.2 lbm/h. Calculate the exit
> A vertical 1.5-m-high, 2.8-m-wide double-pane window consists of two layers of glass separated by a 2.0-cm air gap at atmospheric pressure. The room temperature is 26°C while the inner glass temperature is 18°C. Disregarding radiation heat transfer, dete
> Reconsider Prob. 19–80. Using appropriate software, evaluate the effect of the glycerin mass flow rate on the surface temperature of the parallel plates and the total rate of heat transfer necessary to keep the outlet mean temperature of the glycerin at
> A vertical 1.5-m-high and 3.0-m-wide enclosure consists of two surfaces separated by a 0.4-m air gap at atmospheric pressure. If the surface temperatures across the air gap are measured to be 280 K and 336 K and the surface emissivities to be 0.15 and 0.
> Glycerin is being heated by flowing between two parallel 1-m-wide and 10-m-long plates with 12.5 mm spacing. The glycerin enters the parallel plates with a temperature of 25°C and a mass flow rate of 0.7 kg/s. The plates have a constant surface temperatu
> Flat-plate solar collectors are often tilted up toward the sun in order to intercept a greater amount of direct solar radiation. The tilt angle from the horizontal also affects the rate of heat loss from the collector. Consider a 1.5-m-high and 3-m-wide
> The convection heat transfer coefficient for a clothed person standing in moving air is expressed as h = 14.8V0.69 for 0.15 < V < 1.5 m/s, where V is the air velocity. For a person with a body surface area of 1.7 m2 and an average surface temperature of
> Consider a 3-m-high rectangular enclosure consisting of two surfaces separated by a 0.1-m air gap at 1 atm. If the surface temperatures across the air gap are 30°C and −10°C, determine the ratio of the heat transfe
> Air at 20°C (1 atm) enters into a 5-mm-diameter and 10-cm-long circular tube at an average velocity of 5 m/s. The tube wall is maintained at a constant surface temperature of 160°C. Determine the convection heat transfer coefficient and the outlet mean t
> A rigid tank with a volume of 0.117 m3 contains 1 kg of refrigerant-134a vapor at 240 kPa. The refrigerant is now allowed to cool. Determine the pressure when the refrigerant first starts condensing. Also, show the process on a P-v diagram with respect t
> Liquid glycerin is flowing through a 25-mm-diameter and 10-m-long tube. The liquid glycerin enters the tube at 20°C with a mass flow rate of 0.5 kg/s. If the outlet mean temperature is 40°C and the tube surface temperature is constant, determine the surf
> What does the effective conductivity of an enclosure represent? How is the ratio of the effective conductivity to thermal conductivity related to the Nusselt number?
> In a manufacturing plant that produces cosmetic products, glycerin is being heated by flowing through a 25-mm diameter and 10-m-long tube. With a mass flow rate of 0.5 kg/s, the flow of glycerin enters the tube at 25°C. The tube surface is maintained at
> Consider a double-pane window consisting of two glass sheets separated by a 1-cm-wide airspace. Someone suggests inserting a thin vinyl sheet between the two glass sheets to form two 0.5-cm wide compartments in the window in order to reduce natural conve
> A computer cooled by a fan contains eight printed circuit boards (PCBs), each dissipating 12 W of power. The height of the PCBs is 12 cm and the length is 15 cm. The clearance between the tips of the components on the PCB and the back surface of the adja
> Someone claims that the airspace in a double-pane window enhances the heat transfer from a house because of the natural convection currents that occur in the airspace and recommends that the double-pane window be replaced by a single sheet of glass whose
> Consider a 10-m-long smooth rectangular tube, with a = 50 mm and b = 25 mm, that is maintained at a constant surface temperature. Liquid water enters the tube at 20°C with a mass flow rate of 0.01 kg/s. Determine the tube surface temperature n
> The upper and lower compartments of a well-insulated container are separated by two parallel sheets of glass with an airspace between them. One of the compartments is to be filled with a hot fluid and the other with a cold fluid. If it is desired that he
> In a thermal system, water enters a 25-mm-diameter and 23-m-long circular tube with a mass flow rate of 0.1 kg/s at 25°C. The heat transfer from the tube surface to the water can be expressed in terms of heat flux as qs(x) = ax. The coefficient a is 400
> A hot liquid is poured into a spherical tank with an inner diameter of 3 m and a wall thickness of 3 cm. The tank wall is made of a material with a thermal conductivity of 0.15 W/m⋅K. The hot liquid in the tank causes the inner surface temperature to be
> One kilogram of R-134a fills a 0.090-m3 rigid container at an initial temperature of –40°C. The container is then heated until the pressure is 280 kPa. Determine the initial pressure and final temperature.
> Consider a 25-mm-diameter and 15-m-long smooth tube that is maintained at a constant surface temperature. Fluids enter the tube at 50°C with a mass flow rate of 0.01 kg/s. Determine the tube surface temperatures necessary to heat water, engine oil, and
> Consider two fluids, one with a large coefficient of volume expansion and the other with a small one. In what fluid will a hot surface initiate stronger natural convection currents? Why? Assume the viscosity of the fluids to be the same.
> Consider a 25-mm-diameter and 15-m-long smooth tube that is used for heating fluids. The wall is heated electrically to provide a constant surface heat flux along the entire tube. Fluids enter the tube at 50°C and exit at 150°C. If the mass flow rate is
> A 2-m-diameter, thin-walled stainless steel spherical tank is filled with chemicals undergoing a reaction. The reaction releases heat through the tank, where the tank outer surface temperature is 50°C and is exposed to air at 20°C. The stainless steel su
> Reconsider Prob. 19–70. Using appropriate software, evaluate the effect of the tube length on the average convection heat transfer coefficient of air. By varying the tube length from 3 to 18 m, plot the average convection heat transfer
> The water in a 40-L tank is to be heated from 15°C to 45°C by a 6-cm-diameter spherical heater whose surface temperature is maintained at 85°C. Determine how long the heater should be kept on.
> In a gas-fired boiler, water is being boiled at 120°C by hot air flowing through a 5-m-long, 5-cm diameter tube submerged in water. Hot air enters the tube at 1 atm and 300°C at a mean velocity of 7 m/s and leaves at 150°
> An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 5 percent of the electrical energy it consumes into light while converting the remaining 95 percent into heat. The gla
> An average man has a body surface area of 1.8 m2 and a skin temperature of 33°C. The convection heat transfer coefficient for a clothed person walking in still air is expressed as h = 8.6V0.53 for 0.5 < V < 2 m/s, where V is the walking velocity in m/s.
> An average person generates heat at a rate of 240 Btu/h while resting in a room at 70°F. Assuming one-quarter of this heat is lost from the head and taking the emissivity of the skin to be 0.9, determine the average surface temperature of the head when i
> A rigid tank contains nitrogen gas at 227°C and 100 kPa gage. The gas is heated until the gage pressure reads 250 kPa. If the atmospheric pressure is 100 kPa, determine the final temperature of the gas, in °C.
> Reconsider Prob. 19–68. Using appropriate software, evaluate the effect of the cooling water mean velocity on the rate of steam condensation in the condenser. By varying the cooling water mean velocity for 0 Data from Prob. 19-68: Insi
> A hot liquid (cp = 1000 J/kg⋅K) flows at a flow rate of 0.05 kg/s inside a copper pipe with an inner diameter of 45 mm and a wall thickness of 5 mm. At the pipe exit, the liquid temperature decreases by 10°C from its temperature at the inlet. The outer s
> Inside a condenser, there is a bank of seven copper tubes with cooling water flowing in them. Steam condenses at a rate of 0.6 kg/s on the outer surfaces of the tubes, which are at a constant temperature of 68°C. Each copper tube is 5 m long a
> A hot fluid (kfluid = 0.72 W/m⋅K) is flowing as a laminar fully developed flow inside a pipe with an inner diameter of 35 mm and a wall thickness of 5 mm. The pipe is 10 m long, and the outer surface is exposed to air at 10°C. The average temperature dif
> Reconsider Prob. 19–65. Using appropriate software, investigate the effect of the cooling water average (mean) velocity on the number of tubes needed to achieve the indicated heat transfer rate in the condenser. By varying the cooling water average veloc
> Reconsider Prob. 20–52. Using appropriate software, evaluate the effect of the insulation layer thickness on the outer surface temperature. By varying the insulation layer thickness from 5 to 15 mm, plot the outer surface temperature as a function of the
> Repeat Prob. 19–65 for steam condensing at a rate of 0.60 kg/s. Data from Prob. 19-65: Cooling water available at 10°C is used to condense steam at 30°C in the condenser of a power plant at a rate of 0.15 kg/s by circulating the cooling water through a
> Hot engine oil is being transported in a horizontal pipe (k = 15 W/m⋅K, Di = 5 cm) with a wall thickness of 5 mm. The pipe is covered with a 5-mm-thick layer of insulation (k = 0.15 W/m⋅K). A length of 2 m of the outer surface is exposed to cool air at 1
> Cooling water available at 10°C is used to condense steam at 30°C in the condenser of a power plant at a rate of 0.15 kg/s by circulating the cooling water through a bank of 5-m-long, 1.2-cm internal-diameter thin copper tubes. Water enters the tubes at
> Hot water is being transported in a horizontal pipe (k = 0.15 W/m⋅K, Di = 2.5 cm, Do = 4.5 cm), where the pipe inner surface temperature is at 100°C. A length of 2 m of the pipe’s outer surface is exposed to cool air at 12°C. Assuming that the properties
> What is quality? Does it have any meaning in the superheated vapor region?
> Repeat Prob. 19–63 for a heat transfer coefficient of 40 W/m2⋅K. Data from Prob. 19-63: Combustion gases passing through a 5-cm-internal diameter circular tube are used to vaporize wastewater at atmospheric pressure. Hot gases enter the tube at 115 kPa
> A 1.5-m-diameter, 4-m-long cylindrical propane tank is initially filled with liquid propane, whose density is 581 kg/m3. The tank is exposed to the ambient air at 25°C in calm weather. The outer surface of the tank is polished so that the radi
> Combustion gases passing through a 5-cm-internal diameter circular tube are used to vaporize wastewater at atmospheric pressure. Hot gases enter the tube at 115 kPa and 250°C at a mean velocity of 5 m/s and leave at 150°C. If the average heat transfer co
> What is buoyancy force? Compare the relative magnitudes of the buoyancy force acting on a body immersed in these media: (a) air, (b) water, (c) mercury, and (d) an evacuated chamber.
> Air enters an 18-cm-diameter, 12-m-long underwater duct at 50°C and 1 atm at a mean velocity of 7 m/s and is cooled by the water outside. If the average heat transfer coefficient is 65 W/m2⋅K and the tube temperature is nearly equal to the water temper
> Reconsider Prob. 20–48. Using appropriate software, investigate the effect of the surface temperature of the steam pipe on the rate of heat loss from the pipe and the annual cost of this heat loss. Let the surface temperature vary from
> What is the physical significance of the number of transfer units NTU = hAs/mcp? What do small and large NTU values tell us about a heat transfer system?
> During a visit to a plastic sheeting plant, it was observed that a 45-m-long section of a 2-in nominal (6.03-cm-outer-diameter) steam pipe extended from one end of the plant to the other with no insulation on it. The temperature measurements at several l
> Consider fluid flow in a tube whose surface temperature remains constant. What is the appropriate temperature difference for use in Newton’s law of cooling with an average heat transfer coefficient?
> A 3-mm-diameter and 12-m-long electric wire is tightly wrapped with a 1.5-mm-thick plastic cover whose thermal conductivity and emissivity are k = 0.20 W/m⋅K and ε = 0.9. Electrical measurements indicate that a current of 10 A passes through the wire, an
> A propane tank is filled with a mixture of liquid and vapor propane. Can the contents of this tank be considered a pure substance? Explain.
> When is heat transfer through a fluid conduction and when is it convection? For what case is the rate of heat transfer higher? How does the convection heat transfer coefficient differ from the thermal conductivity of a fluid?
> Reconsider Prob. 20–45. To reduce the cost of heating the pipe, it is proposed to insulate it with enough fiberglass insulation (k = 0.035 W/m⋅K) wrapped in aluminum foil (ε = 0.1) to cut down the heat losses by 85 percent. Assuming the pipe temperature
> What does the logarithmic mean temperature difference represent for flow in a tube whose surface temperature is constant? Why do we use the logarithmic mean temperature instead of the arithmetic mean temperature?
> Thick fluids such as asphalt and waxes and the pipes in which they flow are often heated in order to reduce the viscosity of the fluids and thus to reduce the pumping costs. Consider the flow of such a fluid through a 100-m-long pipe of outer diameter 30
> Consider turbulent forced convection in a circular tube. Will the heat flux be higher near the inlet of the tube or near the exit? Why?
> A 12-m-long section of a 5-cm-diameter horizontal hot-water pipe passes through a large room whose temperature is 27°C. If the temperature and the emissivity of the outer surface of the pipe are 73°C and 0.8, respectively, determine the rate of heat loss
