Question: One method of storing solar energy for
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 air by blowing it through the bed. If the air inlet temperature is 10°C and the mass velocity of the air in the bed is 0.5 kg/s m2, how long must the bed be in order for the initial outlet air temperature to be 65°C? Assume that the rocks are spherical, 2 cm in diameter, and that the bed void fraction is 0.5. (Hint: The surface area of the rocks per unit volume of the bed 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
> 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
> 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
> 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, an
> 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
