A long, half-round cylinder is placed in an airstream with its flat face downstream. An electrical resistance heater inside the cylinder maintains the cylinder sur- face temperature at 50°C. The cylinder diameter is 5 cm, the air velocity is 31.8 m/s, and the air temperature is 20°C. Determine the power input of the heater per unit length of cylinder. Neglect radiation heat transfer.
> 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
> A large high-power transformer is installed and operated in an electric-power distribution station. To maintain transform efficiency and prevent its failure (burnout), the transformer oil is cooled via a water-cooled, coiled- tube heat exchanger and circ
> Lubricating oil is cooled in a tubular heat exchanger to maintain its viscosity and effectiveness in the journal bearings used in a large steam turbine of an electric power plant. Oil flows at the rate of 0.1 kg/s inside a 12.5-mm-diameter circular tube,
> Determine the rate of heat transfer per meter length to a light oil flowing through a 2.5-cm-ID, 60-cm-long copper tube at a velocity of 0.03 m/s. The oil enters the tube at 16°C, and the tube is heated by steam condensing on its outer surface
> Unused engine oil with a 100°C inlet temperature flows at a rate of 0.25 kg/s through a 5.1-cm-ID pipe that is enclosed by a jacket containing condensing steam at 150°C. If the pipe is 9 m long, determine the outlet temperature of the oil. Also, at what
> Calculate the rate of heat transfer through the composite wall in Problem 1.37 if the temperature difference is 25°C and the contact resistance between the sheets of wood is 0.005 m2 K/W.
> An electronic device is cooled by passing air at 27°C through six small tubular passages drilled through the bottom of the device in parallel as shown. The mass flow rate per tube is 7 * 10-5 kg/s. Heat is generated in the device, resulting in
> Water enters a double-pipe heat exchanger at 60°C. The water flows on the inside through a copper tube of 2.54-cm-ID at an average velocity of 2 cm/s. Steam flows in the annulus and condenses on the outside of the cop- per tube at a temperatur
> The equation: was recommended by H. Hausen (Zeitschr. Ver. Deut. Ing., Beiheft, No. 4, 1943) for forced-convection heat transfer in fully developed laminar flow through tubes maintained at a uniform surface temperature. Compare the values of the Nusselt
> Engine oil flows at a rate of 0.5 kg/s through a 2.5-cm-ID tube. The oil enters at 25°C while the tube wall is at 100°C. (a) If the tube is 4 m long, determine whether the flow is fully developed. (b) Calculate the heat transfer coefficient.
> Repeat Problem 7.10 but assume that one wall is insulated while the temperature of the other wall increases linearly with x.
> Show that for fully developed laminar flow between two flat plates spaced 2a apart, the Nusselt number based on the “bulk mean” temperature and the pas- sage spacing is 4.12 if the temperature of both walls varies line
> To measure the mass flow rate of a fluid in a laminar flow through a circular pipe, a hot-wire-type velocity meter is placed in the center of the pipe. Assuming that the measuring station is far from the entrance of the pipe, the velocity distribution is
> In a metal manufacturing plant and its heat treatment process, a long, hexagonal copper extrusion (or rod) comes out of a heat-treatment furnace at 400°C and is then quenched by immersing it in a 50°C air- stream flowing perpendicul
> An engineer is designing a heating system that consists of multiple tubes placed in a duct carrying the air supply for a building. She decides to perform preliminary tests with a single copper tube of 2-cm OD carrying condensing steam at 100°C
> The Alaska pipeline carries 2 million barrels of crude oil per day from Prudhoe Bay to Valdez, covering a distance of 800 miles. The pipe diameter is 48 in., and it is insulated with 4 in. of fiberglass covered with steel sheathing. Approximately half of
> Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall a
> Repeat Problem 6.5 for water in the temperature range 10°C to 40°C.
> Reconsider the problem described in Example 6.7, where water jets from a nozzle that has a diameter of 6 mm and impinges on a disk of 4 cm in diameter that is subjected to a uniform heat flux of 70,000 W/m2. Instead of water, consider using air and ethyl
> A microprocessor chip 110 mm 3 10 mm square 2 is to be cooled by an impinging circular air jet that is directed on the chip surface by a 5-mm diameter nozzle, placed at a distance of 10 mm. The electrical activity in the microcircuits of the chip r
> In many metal machining operations (cutting or turning) the contact surface at the interface of the tool and metal part is cooled by a liquid coolant that is delivered on the surface by a single round jet. Water at 25°C is used as coolant in one such jet
> An automotive catalytic converter is a packed bed in which a platinum catalyst is coated on the sur- face of small alumina spheres. A metal container holds the catalyst pellets and allows engine exhaust gases to flow through the bed of pellets. The catal
> Suppose the rock bed in Problem 6.50 has been completely discharged and the entire bed is at 10°C. Hot air at 90°C and 0.2 m/s is then used to recharge the bed. How long does it take until the first rocks are back up to 70°C, and what is the total heat t
> One method of storing solar energy for use during cloudy days or at night is to store it in the form of sensible heat in a rock bed, as shown in the sketch. Suppose such a rock bed has been heated to 70°C and it is desired to heat a stream of
> Derive an equation in the form /for the flow of air over a long, horizontal cylinder for the temperature range 0°C to 100°C. Use Eq. (6.3) as a basis.
> Reconsider the heat exchanger of Problem 6.47, and explore the effect of tube center-to-center spacing in the equilateral array of the finned tubes. Consider the tube spacing of 8.75 cm and 10 cm. What is the extent of change in the average heat transfer
> Reconsider the heat exchanger of Problem 6.38 with an externally finned-tube bundle used to enhance the air-side heat transfer coefficient in the pre-heater. If thin circular fins are attached on the outside of the tubes such that the surface extension r
> Repeat Problem 1.35 but assume that instead of sur- face temperatures, the given temperatures are those of the air on the left and right sides of the wall and that the convection heat transfer coefficients on the left and right surfaces are 6 and 10 W/m2
> An attractive method of energy conservation in industrial settings is to utilize waste heat from large- scale power generating equipment. In one such scheme, the exhaust gases from the diesel engine of an industrial power generator are channeled through
> Liquid mercury at a temperature of 315°C flows at a velocity of 10 cm/s over a staggered bank of 5/8-in. 16 BWG stainless steel tubes arranged in an equilateral-triangular array with a pitch-to-diameter ratio of 1.375. If water at 2 atm pressure is
> Estimate the heat transfer coefficient for liquid sodium at 540°C flowing over a 10-row staggered-tube bank of 2.5-cm-diameter tubes arranged in an equilateral- triangular array with a 1.5 pitch-to-diameter ratio. The entering velocity is 0.6 m/s, based
> A blood warmer is often used in certain clinical transfusion procedures. While safely storing and pre- serving blood requires refrigeration, cold blood when used in rapid transfusion procedures could cause clinically dangerous hypothermia in a patient. A
> Consider a heat exchanger consisting of 12.5-mm- OD copper tubes in a staggered arrangement with transverse spacing of 25 mm and longitudinal spacing of 30 mm with nine tubes in the longitudinal direction. Condensing steam at 150°C flows inside the tubes
> Compare the rate of heat transfer and the pressure drop for an in-line and a staggered arrangement of a tube bank consisting of 300 tubes that are 1.8 m long with a 2.5 cm OD. The tubes are to be arranged in 15 rows with longitudinal and transverse spaci
> Carbon dioxide gas at 1 atmosphere pressure is to be heated from 25°C to 75°C by pumping it through a tube bank at a velocity of 4 m/s. The tubes are heated by steam condensing within them at 200°C. The tubes have a 10-mm OD, are in an in-line arrangemen
> Reconsider the problem described in Example 6.5, where methane gas at 20°C flows with an upstream velocity of 10 m/s over a staggered-arrangement tube bundle, with 5 rows of tubes facing the gas flow, and where their surface temperature is maintained at
> An electrical transmission line of 1.2-cm diameter carries a current of 200 amps and has a resistance of 3 * 10-4 ohm per meter of length. If the air around this line is at 16°C, determine the surface temperature on a windy day, assuming a wind blows acr
> Reconsider the heat exchanger of Problem 6.38 with an inline tube arrangement, where the centerlines of the tubes are spaced 7.5 cm apart, both in the longitudinal and transverse directions. Compare the results with those for the staggered tube arrangeme
> Repeat Problem 1.34, including a contact resistance of 0.1 K/W at each of the interfaces.
> A multitube heat exchanger is used in a process plant to pre-heat air before it is enters a combustion chamber, using low pressure steam that flows inside the tubes and condenses. The tube bundle is configured with 6-cm outer diameter tubes in a staggere
> To reduce the carbon footprint of building energy consumption, photovoltaic (PV) cell panels are increasingly being used to provide a solar, self-sustaining source of electricity in both homes and large buildings. However, the semiconductor material that
> To decrease the size of personal computer mother boards, designers have turned to a more compact method of mounting memory chips on the board. The single in-line memory modules, as they are called, essentially mount the chips on their edges so that their
> Suppose the resistor in Problem 6.33 is rotated so that its axis is aligned with the flow. What is the maximum permissible power dissipation?
> An electronic circuit contains a power resistor that dissipates 1.5 W. The designer wants to modify the circuitry in such a way that it is necessary for the resistor to dissipate 2.5 W. The resistor is in the shape of a disk 1 cm in diameter and 0.6-mm t
> Heat transfer from an electronic circuit board is to be determined by placing a model for the board in a wind tunnel. The model is a 15-cm-square plate with embedded electrical heaters. The wind from the tunnel air is delivered at 20°C. Determ
> Estimate the heat transfer coefficient for a spherical fuel droplet injected into a diesel engine at 80°C and 90 m/s. The oil droplet is 0.025 mm in diameter, the cylinder pressure is 4800 kPa, and the gas temperature is 944 K. (b) Estimate the time req
> A method for measuring the convection heat transfer from spheres has been proposed. A 20-mm-diameter copper sphere with an embedded electrical heater is to be suspended in a wind tunnel. A thermocouple inside the sphere measures the sphere surface temper
> Steam at 100 kPa and 100°C is flowing across a 5-cm- OD tube at a velocity of 6 m/s. Estimate the Nusselt number, the heat transfer coefficient, and the rate of heat transfer per meter length of pipe if the pipe is at 200°C.
> A section of a composite wall with the dimensions shown below has uniform temperatures of 200°C and 50°C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA = 70 W/m K, kB = 60
> A copper sphere 2.5 cm in diameter is suspended by a fine wire in the center of an experimental hollow, cylindrical furnace whose inside wall is maintained uniformly at 430°C. Dry air at a temperature of 90°C and a pressure of 1.2 atm is blown steadily t
> In a lead-shot tower, spherical 0.95-cm-diameter BB shots are formed by drops of molten lead, which solidify as they descend in cooler air. At the terminal velocity, i.e., when the drag equals the gravitational force, estimate the total heat transfer coe
> A spherical water droplet of 1.5-mm diameter is freely falling in atmospheric air. Calculate the average convection heat transfer coefficient when the droplet has reached its terminal velocity. Assume that the water is at 50°C and the air is at 20°C. Neg
> A copper sphere initially at a uniform temperature of 132°C is suddenly released at the bottom of a large bath of bismuth at 500°C. The sphere diameter is 1 cm, and it rises through the bath at 1 m/s. How far does the sphere rise b
> An experiment was conducted in which the heat transfer from a sphere in sodium was measured. The sphere, 0.5 in. in diameter, was pulled through a large sodium bath at a given velocity while an electrical heater inside the sphere maintained the temperatu
> Determine the effect of forced convection on heat transfer from a 100-W, spherical glass bulb, incandescent lamp. What would be the glass temperature for air velocities of 0.5, 1, 2, and 4 m/s?
> A 2.5-cm sphere is to be maintained at 50°C in either an airstream or a water stream, both at 20°C and 2 m/s velocity. Compare the rate of heat transfer and the drag on the sphere for the two fluids.
> A hot-wire anemometer consists of a 5-mm-long, 5-mm-diameter platinum wire. The probe is operated at a constant current of 0.03 A. The electrical resistivity of platinum is 17 / cm at 20°C and increases by 0.385% per °C. (a) If the voltage across the wi
> A platinum hot-wire anemometer operated in the constant-temperature mode has been used to mea- sure the velocity of a helium stream. The wire diameter is 20 m, its length is 5 mm, and it is operated at 90°C. The electronic circuit used to maintain the w
> A hot-wire anemometer is used to determine the boundary layer velocity profile in the air flow over a scale model of an automobile. The hot wire is held in a traversing mechanism that moves the wire in a direction normal to the surface of the model. The
> Wearing layers of clothing in cold weather is often recommended because dead-air spaces between the layers keep the body warm. The explanation for this is that the heat loss from the body is less. Compare the rate of heat loss for a single 2-cm-thick lay
> A mercury-in-glass thermometer at 40°C (OD = 1 cm) is inserted through a duct wall into a 3 m/s airstream at 66°C. This can be modelled as a cylinder in cross-flow, as shown in the figure. Estimate the heat transfer coefficient
> The instruction manual for a hot-wire anemometer states that “roughly speaking, the current varies as the one-fourth power of the average velocity at a fixed wire resistance.” Check this statement, using the heat transfer characteristics of a thin wir
> Repeat Problem 6.17 for air flowing over the same two surfaces in the Reynolds number range between 40,000 and 200,000. Neglect radiation.
> Develop an expression for the ratio of the rate of heat transfer to water at 40°C from a thin flat strip of width D/2 and length L at zero angle of attack and from a tube of the same length and diameter D in cross-flow with its axis normal to the wate
> The temperature of air flowing through a 25-cm- diameter duct whose inner walls are at 320°C is to be measured using a thermocouple soldered in a cylindrical steel well of 1.2-cm OD with an oxidized exterior, as shown in the accompanying sketc
> Water at 180°C enters a bare, 15-m-long, 2.5-cm-diameter wrought iron pipe at 3 m/s. If air at 10°C flows perpendicular to the pipe at 12 m/s, determine the outlet temperature of the water. (Note that the temperature difference between the air and the wa
> Repeat Problem 6.13 with glycerol at 20°C flowing over the fin at 2 m/s. The plate temperature is 50°C.
> A stainless steel pin fin 5 cm long and with a 6-mm OD, extends from a flat plate into a 175 m/s air- stream, as shown in the sketch. Estimate (a) the aver- age heat transfer coefficient between air and the fin, (b) the temperature at the end of the fin
> A nuclear reactor fuel rod is a circular cylinder 6 cm in diameter. The rod is to be tested by cooling it with a flow of sodium at 205°C with a velocity of 5 cm/s perpendicular to its axis. If the rod surface is not to exceed 300°C, estimate the maximum
> The human body is typically modelled as a vertical cylinder that is 1.8 m high and is 30 cm in diameter, as shown in the figure. Calculate the average rate of heat loss from this body, which is maintained at 37°C, on a windy day when the airst
> A long wire 0.7 mm in diameter with an emissivity of 0.9 is placed in a large quiescent air space at 270 K. If the wire is at 800 K, calculate the net rate of heat loss. Discuss your assumptions.
> Repeat Problem 6.9 if the extrusion cross-section is elliptical with the major axis normal to the air flow and the same mass per unit length. The major axis of the elliptical cross section is 5.46 cm, and its perimeter is 12.8 cm.
> Determine the heat transfer coefficient at the stagnation point and the average value of the heat transfer coefficient for a single 5-cm-OD, 60-cm-long tube in cross-flow. The temperature of the tube surface is 260°C, the velocity of the fluid flowing pe
> When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indica
> The dimensionless ratio / called the Froude number, is a measure of similarity between an ocean- going ship and a scale model of the ship to be tested in a laboratory water channel. A 150-m-long cargo ship is designed to run at 36 km/h, and a 1.5-m geome
> A scale model of an airplane wing section is tested in a wind tunnel at a Mach number of 1.5. The air pressure and temperature in the test section are 20,000 N/m2 and -30°C, respectively. If the wing section is to be kept at an average temperature of 60°
> The average Reynolds number for air passing in turbulent flow over a 2-m-long, flat plate is 2.4 *106. Under these conditions, the average Nusselt number was found to be equal to 4150. Determine the average heat transfer coefficient for an oil having the
> A satellite reenters the earth’s atmosphere at a velocity of 2700 m/s. Estimate the maximum temperature the heat shield would reach if the shield material is not allowed to ablate and radiation effects are neglected. The temperature of the upper layer of
> A flat plate is placed in a supersonic wind tunnel with air flowing over it at a Mach number of 2.0, a pressure of 25,000 N/m2, and an ambient temperature of -15°C. If the plate is 30 cm long in the direction of flow, calculate the cooling rate per unit
> Air at 15°C and 0.01 atmosphere pressure flows at a velocity of 250 m/s over a thin flat strip of metal that is 0.1 m long in the direction of flow. Determine (a) the surface temperature of the plate at equilibrium and (b) the rate of heat removal requi
> Heat rejection from high-speed racing automobiles is a problem because the required heat exchangers generally create additional drag. Integration of heat rejection into the skin of the vehicle has been pro- posed for a car to be tested at the Bonneville
> A spherical communications satellite, 2 m in diameter, is placed in orbit around the earth. The satellite generates 1000 W of internal power from a small nuclear generator. If the surface of the satellite has an emittance of 0.3, and is shaded from solar
> Air at a static temperature of 21°C and a static pressure of 0.7 kPa (abs) flows at zero angle of attack over a thin, electrically heated flat plate at a velocity of 240 m/s. If the plate is 10 cm long in the direction of flow and 60 cm in the direction
> A highly polished chromium flat plate is placed in a high-speed wind tunnel to simulate flow over the fuselage of a supersonic aircraft. The air flowing in the wind tunnel is at a temperature of 0°C and a pressure of 3500 N/m2 and has a velocity parallel
> A flat plate test section, which is 0.5 m wide and has an electrically heated surface installed 0.5 m away from the leading edge, as depicted in the schematic given, is to be designed for a boundary-layer measurement experiment. The electrically heated s
> A flat plate solar collector is installed flat-flush on the surface of a roof that is inclined 30° from the vertical normal and facing south in order to maximize its performance. The solar collector is a 2.5 m * 2.0 m rectangle and is placed a
> A fluid at temperature T( is flowing at a velocity U( over a flat plate that is at the same temperature as the fluid for a distance x0 from the leading edge but at a higher temperature Ts beyond this point. Show by means of the integral boundary layer eq
> A 4-m2 square flat-plate solar collector for domestic hot-water heating is shown schematically. Solar radiation at a rate of 750 W/m2 is incident on the glass cover, which transmits 90% of the incident flux. Water flows through the tubes soldered to the
> A fluid flows at 5 m/s over a wide, flat plate 15 cm long. For each from the following list, calculate the Reynolds number at the downstream end of the plate. Indicate whether the flow at that point is laminar, transition, or turbulent. Assume all fluid
> An aluminum cooling fin for a heat exchanger is situated parallel to an atmospheric pressure air stream. The fin, as shown in the sketch, is 0.075 m high, 0.005 m thick and 0.45 m in the flow direction. Its base temperature is 88°C, and the ai
> The surface temperature of a thin, flat plate located parallel to an air stream is 90°C. The free-stream velocity is 60 m/s, and the temperature of the air is 0°C. The plate is 60 cm wide and 45 cm long in the direction of the air stream. Neglecting the
> Water at a velocity of 2.5 m/s flows parallel to a 1-m-long horizontal, smooth, and thin, flat plate. Determine the local thermal and hydrodynamic boundary layer thick- nesses and the local friction coefficient at the midpoint of the plate. What is the r
