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Fundamentals of Heat and Mass Transfer 6th Edition Incropera, Dewitt, Bergman, Lavine - Solutions

The average free convection coefficient for the exterior surfaces of a long, horizontal rectangular duct exposed to a quiescent fluid can be estimated from the Hahn-Didion (H-D) correlation [ASHRAE Proceedings. Part 1, pp. 262-67. 1972] where the characteristic length is the half-perimeter
It is desired to estimate the effectiveness of a horizontal, straight fin of rectangular cross section when applied to a surface operating at 45°C in an environment for which the surroundings and ambient air are at 25°C. The fin is to be fabricated from aluminum alloy (2024- T6) with an anodized
Certain wood stove designs rely exclusively on heat transfer by radiation and natural convection to the surroundings. Consider a stove that forms a cubical enclosure, Ls = 1 m on a side, in a large room. The exterior walls of the stove have an emissivity of ε = 0.8 and are at an operating
A plate 1 m by 1 m, inclined at an angle of 45°, is exposed to a net radiation heat flux of 300 W/m 2 at its bottom surface. If the top surface of the plate is well insulated, estimate the temperature the plate reaches when the ambient air is quiescent and at a temperature of 0°C.
A horizontal rod 5 mm in diameter is immersed in water maintained at 18°C. If the rod surface temperature is 56°C, estimate the free convection heat transfer rate per unit length of the rod.
A horizontal uninsulated steam pipe passes through a large room whose walls and ambient air are at 300 K. The pipe of 150-mm diameter has an emissivity of 0.85 and an outer surface temperature of 400 K. Calculate the heat loss per unit length from the pipe.
Examine the conditions of Example 9.4, including the effect of adding insulation of thickness t, thermal conductivity k = 0.026 W/m ∙ K. and emissivity B = 0.85. Compute and plot the surface temperature Ts.2 and the heat loss q' as a function of insulation thickness for 0 < t < 50 mm. In
Beverage in cans 150 mm long and 60 mm in diameter is initially at 27°C and is to be cooled by placement in a refrigerator compartment at 4°e. In the interest of maximizing the cooling rate, should the cans be laid horizontally or vertically in the compartment? As a first approximation, neglect
Consider Problem 8.47. A more realistic solution would account for the resistance to heat transfer due to free convection in the paraffin during melting. Assuming the tube surface to have a uniform temperature of 55°C and the paraffin to be an infinite, quiescent liquid, determine the convection
A long, uninsulated steam line with a diameter of 89 mm and a surface emissivity of 0.8 transports steam at 200°C and is exposed to atmospheric air and large surroundings at an equivalent temperature of 20°C.(a) Calculate the heat loss per unit length for a calm day.(b) Calculate the heat loss on
A horizontal tube of 12.5-mm diameter with an outer surface temperature of 240°C is located in a room with an air temperature of 20°C. Estimate the heat transfer rate per unit length of the tube due to free convection.
Saturated steam at 4 bars absolute pressure with a mean velocity of 3 m/s flows through a horizontal pipe whose inner and outer diameters are 55 and 65 mm, respectively. The heat transfer coefficient for the steam flow is known to be 11,000 W/m2 ∙ K.(a) If the pipe is covered with a 25-mm-thick
A horizontal electrical cable of 25-mm diameter has a heat dissipation rate of 30 W/m. If the ambient air temperature is 27°C, estimate the surface temperature of the cable.
An electric immersion heater, 10 mm in diameter and 300 mm long, is rated at 550 W. If the heater is horizontally positioned in a large tank of water at 20°C, estimate its surface temperature. Estimate the surface temperature if the heater is accidentally operated in air at 20°C.
The maximum surface temperature of the 20-mm. diameter shaft of a motor operating in ambient air al 27°C should not exceed 87°C. Because of power dissipation within the motor housing, it is desirable to reject as much heat as possible through the shaft to the ambient air. In this problem, we will
Consider a horizontal pin fin of 6-mm diameter and 60-mm length fabricated from plain carbon steel (k = 57 W/m ∙ K, 8 = 0.5). The base of the fin is maintained at 150°C, while the quiescent ambient air and the surroundings are at 25°C. Assume the fin tip is adiabatic.(a) Estimate the fin heat
Consider the hot water pipe of Problem 7.56, but under conditions for which the ambient air is not in cross flow over the pipe and is, instead, quiescent. Accounting for the effect of radiation with a pipe emissivity of 8 p = 0.6, what is the corresponding daily cost of heat loss per unit length of
Common practice in chemical processing plants is to clad pipe insulation with a durable, thick aluminum foil. The functions of the foil are to confine the batt insulation and to reduce heat transfer by radiation to the surroundings. Because of the presence of chlorine (at chlorine or seaside
Consider the electrical heater of Problem 7.43. If the blower were to malfunction, terminating airflow while the heater continued to operate at 1000 W/m, what temperature would the heater assume? How long would it take to come within 10°C of this temperature? Allow for radiation exchange between
A computer code is being developed to analyze a 12.5-mm-diameter, cylindrical sensor used to determine ambient air temperature. The sensor experiences free convection while positioned horizontally in quiescent air at T∞ = 27°C. For the temperature range from 30 to 80°C, derive an expression for
A thin-walled tube of 20-mm diameter passes hot fluid at a mean temperature of 45°C in an experimental flow loop. The tube is mounted horizontally in quiescent air at a temperature of 15°C. To satisfy the stringent temperature control requirements of the experiment, it was decided to wind thin
A billet of stainless steel, AISI 316, with a diameter of 150 mm and a length of 500 mm emerges from a heat treatment process at 200°C and is placed in an unstirred oil bath maintained at 20°C.(a) Determine whether it is advisable to position the billet in the bath with its centerline horizontal
Long stainless steel rods of 50-mm diameter are preheated to a uniform temperature of 1000 K before being suspended from an overhead conveyor for transport to a hot forming operation. The conveyor is in a large room whose walls and air are at 300 K.(a) Assuming the linear motion of the rod to have
Hot air flows from a furnace through a 0.15-m-diameter, thin-walled steel duct with a velocity of 3 m/s. The duct passes through the crawlspace of a house, and its uninsulated exterior surface is exposed to quiescent air and surroundings at 0°C.(a) At a location in the duct for which the mean air
A biological fluid moves at a flow rate of m = 0.02 kg/s through a coiled, thin-walled, 5-mm-diameter tube submerged in a large water bath maintained at 50°C. The fluid enters the tube at 25°C.(a) Estimate the length of the tube and the number of coil turns required to provide an exit temperature
Consider a batch process in which 200 liters of a pharmaceutical are heated from 25°C to 70°C by saturated steam condensing at 2.455 bars as it flows through a coiled tube of 15-mm diameter and 15-m length. At any time during the process, the liquid may be approximated as an infinite, quiescent
In the analytical treatment of the fin with uniform cross-sectional area, it was assumed that the convection heat transfer coefficient is constant along the length of the fin. Consider an AISI 316 steel fin of 6-mm diameter and 50-mm length (with insulated tip) operating under conditions for which
A hot fluid at 35°C is to be transported through a tube horizontally positioned in quiescent air at 25°C. Which of the tube shapes, each of equal cross-sectional area, would you use in order to minimize heat losses to the ambient air by free convection?Use the following correlation of Lien hard
Consider a 2-mm-diameter sphere immersed in a fluid at 300 K and 1 atm.(a) If the fluid around the sphere is quiescent and extensive, show that the conduction limit of heat transfer from the sphere can be expressed as NuD, cond = 2.(b) Considering free convection, at what surface temperature will
A sphere of 25-mm diameter contains an embedded electrical heater. Calculate the power required to maintain the surface temperature at 94°C when the sphere is exposed to a quiescent medium at 20°C for:(a) Air at atmospheric pressure,(b) Water, and(c) Ethylene glycol.
Under steady-state operation the surface temperature of a small 20-W incandescent light bulb is 125°C when the temperature of the room air and walls is 25°C. Approximating the bulb as a sphere 40 mm in diameter with a surface emissivity of 0.8, what is the rate of heat transfer from the surface
A 25-mm-diameter copper sphere with a low emissivity coating is removed from an oven at a uniform temperature of 85°C and allowed to cool in a quiescent fluid maintained at 25°C.(a) Calculate convection coefficients associated with the initial condition for immersion in air and water.(b) Using
Consider two long vertical plates maintained at uniform temperatures Ts,1 > Ts,2. The plates are open at their ends and are separated by the distance 2L.(a) Sketch the velocity distribution in the space between the plates.(b) Write appropriate forms of the continuity, momentum, and energy equations
Consider the conditions of Problem 9.9, but now view the problem as one involving free convection between vertical, parallel plate channels. What is the optimum fin spacing S? For this spacing and the prescribed values of t and W, what is the rate of heat transfer from the fins?
A vertical array of circuit boards is immersed in quiescent ambient air at T∞ = 17°C. Although the components protrude from their substrates, it is reasonable, as a first approximation, to assume flat plates with uniform surface heat flux q;. Consider boards of length and width L = W = 0.4 m and
Determined to reduce the $3 per week cost associated with heat loss through their patio window by convection and radiation, the tenants of Problem 9.18 cover the inside of the window with a 50-mm-thick sheet of extruded insulation. Because they are not very handy around the house, the insulation is
The front door of a dishwasher of width 580 mm has a vertical air vent that is 500 mm in height with a20-mm spacing between the inner tub operating at 52°C and an outer plate that is thermally insulated.(a) Determine the heat loss from the tub surface when the ambient air is 27°C.(b) A change in
A natural convection air heater consists of an array of parallel, equally spaced vertical plates, which may be maintained at a fixed temperature Ts by embedded electrical heaters.The plates are of length and width L = W = 300 mm and are in quiescent, atmospheric air at T∞ = 20°C. The total width
A bank of drying ovens is mounted on a rack in a room with an ambient air temperature of 27°C. The cubical ovens are 500 mm to a side, and the spacing between the ovens is 15 mm.(a) Estimate the heat loss from a facing side of an oven when its surface temperature is 47Â°C.(b) Explore the effect
A solar collector consists of a parallel plate channel that is connected to a water storage plenum at the bottom and to a heat sink at the top. The channel is inclined 0 = 30° from the vertical and has a transparent cover plate. Solar radiation transmitted through the cover plate and the water
As is evident from the property data of Tables A.3 and A.4, the thermal conductivity of glass at room temperature is more than 50 times larger than that of air. It is therefore desirable to use windows of double-pane construction, for which the two panes of glass enclose an air space. If heat
A building window pane that is 1.2 m high and 0.8 m wide is separated from the ambient air by a storm window of the same height and width. The air space between the two windows is 0.06 m thick. If the building and storm windows are at 20 and –10oC, respectively, what is the rate of heat loss by
The absorber plate and the adjoining cover plate of a flat-plate solar collector are at 70 and 35°C, respectively, and are separated by an air space of 0.05 m. What is the rate of free convection heat transfer per unit surface area between the two plates if they are inclined at an angle of 60°
Consider a thermal storage system in which the phase change material (paraffin) is housed in a large container whose bottom, horizontal surface is maintained at Ts = 50°C by warm water delivered from a solar collector.(a) Neglecting the change in sensible energy of the liquid phase, estimate the
A rectangular cavity consists of two parallel. 0.5-m- square plates separated by a distance of 50 mm, with the lateral boundaries insulated. The heated plate is maintained at 325 K and the cooled plate at 275 K. Estimate the heat flux between the surfaces for three orientations of the cavity using
Consider a horizontal flat roof section having the same dimensions as a vertical wall section. For both sections, the surfaces exposed to the air gap are at 18°C (inside) and -10oC (outside).(a) Estimate the ratio of the convection heat rate for the horizontal section to that of the vertical
A 50-mm-thick air gap separates two horizontal metal plates that form the top surface of an industrial furnace. The bottom plate is at Th = 200°C and the top plate is at Tc = 50°C. The plant operator wishes to provide insulation between the plates to minimize heat loss. The relatively hot
The space between the panes of a double-glazed window can be filled with either air or carbon dioxide at atmospheric pressure. The window is 1.5 m high and the spacing between the panes can be varied. Develop an analysis to predict the convection heat transfer rate across the window as a function
A vertical, double-pane window, which is I m on a side and has a 25-mm gap filled with atmospheric air, separates quiescent room air at T∞,o = 20°C from quiescent ambient air at T∞,o = - 20°C. Radiation exchange between the window panes, as well as between each pane and its surroundings, may
The top surface (0.5 m x 0.5 m) of an oven is 60°C for a particular operating condition when the room air is 23°C. To reduce heat loss from the oven and to minimize bum hazard, it is proposed to create a 50-mm air space by adding a cover plate.(a) Assuming the same oven surface temperature Ts for
Consider window blinds that are installed in the air space between the two panes of a vertical double-pane window. The window is H = 0.5 m high and w = 0.5 m wide, and includes N = 19 individual blinds that are each L = 25 mm wide. When the blinds are open, 20 smaller, square enclosures are formed
A solar water heater consists of a flat-plate collector that is coupled to a storage tank. The collector consists of a transparent cover plate and an absorber plate that are separated by an air gap.Although much of the solar energy collected by the absorber plate is transferred to a working fluid
Consider the cylindrical, 0.12-m-diameter radiation shield of Example 9.5 that is installed concentric with a 0.10-m-diameter tube carrying steam. The spacing provides an air gap of L = 10 mm.(a) Calculate the heat loss per unit length of the tube by convection when a second shield of 0.14-m
A solar collector design consists of an inner tube enclosed concentrically in an outer tube that is transparent to solar radiation. The tubes are thin walled with inner and outer diameters of 0.10 and 0.15 m, respectively. The annular space between the tubes is completely enclosed and filled with
It has been proposed to use large banks of rechargeable lithium ion batteries to power hybrid electric vehicles. The cylindrical batteries, each of which is of radius r; = 9 mm and length L = 65 mm, undergo exothermic electrochemical reactions while being discharged. Since excessively high
The surfaces of two long, horizontal, concentric thin-walled tubes having radii of 100 and 125 mm are maintained at 300 and 400 K, respectively. If the annular space is pressurized with nitrogen at 5 atm, estimate the convection heat transfer rate per unit length of the tubes.
Liquid nitrogen is stored in a thin-walled spherical vessel of diameter Di = 1 m. The vessel is positioned concentrically within a larger, thin-walled spherical container of diameter Do = 1.10 m and the intervening cavity is filled with atmospheric helium.Under normal operating conditions, the
The human eye contains aqueous humor, which separates the external cornea and the internal iris-lens structure. It is hypothesized that, in some individuals, small flakes of pigment are intermittently liberated from the iris and migrate to, and subsequently damage, the cornea. Approximating the
Water at 35°C with a velocity of 0.05 m/s flows over a horizontal, 50-mm-diameter cylinder maintained at a uniform surface temperature of 20°C. Do you anticipate that heat transfer by free convection will be significant? What would be the situation if the fluid were air at atmospheric pressure?
According to experimental results for parallel airflow over a uniform temperature, heated vertical plate, the effect of free convection on the heat transfer convection coefficient will be 5% when GrL/Re2L = 0.08. Consider a heated vertical plate 0.3 m long, maintained at a surface temperature of
A vertical array of circuit boards of 150-mm height is to be air cooled such that the board temperature does not exceed 60°C when the ambient temperature is 25°C.Assuming isothermal surface conditions, determine the allowable electrical power dissipation per board for the cooling arrangements:(a)
A horizontal l00-mm-diameter pipe passing hot oil is to be used in the design of an industrial water heater. Based on a typical water draw rate, the velocity over the pipe is 0.5 m/s. The hot oil maintains the outer surface temperature at 85°C and the water temperature is 37°C.Investigate the
Determine the heat transfer rate from the steel plates of Problem 7.24 accounting for free convection from the plate surfaces. What is the corresponding rate of change of the plate temperature? Plot the heat transfer coefficient associated with free convection forced convection, and mixed
Square panels (250 mm x 250 mm) with a decorative, highly reflective plastic finish are cured in an oven at 125°C and cooled in quiescent air at 29°C. Quality considerations dictate that the panels remain horizontal and that the cooling rate be controlled. To increase productivity in the plant,
A garment soaked with water is hung up to dry in a warm room at atmospheric pressure. The still air is dry and at a temperature of 40°C. The garment may be assumed to have a temperature of 25°C and a characteristic length of 1 m in the vertical direction. Estimate the drying rate per unit width
A water bath is used to maintain canisters containing experimental biological reactions at a uniform temperature of 37°C. The top of the bath has a width and length of 0.25 m and 0.50 m, respectively, and is uncovered to allow easy access for removal or insertion of the canisters. The bath is
On a very still morning, the surface temperature of a lake used to cool the condenser of a power plant is 30°C while the air temperature is 23°C with a relative humidity of 80%. Assume a surroundings temperature of 285 K. The lake is nominally circular in shape with a diameter of approximately 4
Show that, for water at l-atm pressure with Ts – Tsar = 10oC, the Jakob number is much less than unity. What is the physical significance of this result? Verify that this conclusion applies to other fluids.
The surface of a horizontal, 20-mm-diameter cylinder is maintained at an excess temperature of 5°C in saturated water at 1 atm. Estimate the heat flux using the appropriate free convection correlation and compare your result with the boiling curve of Figure 10.4. For nucleate boiling, estimate the
The role of surface tension in bubble formation can be demonstrated by considering a spherical bubble of pure saturated vapor in mechanical and thermal equilibrium with its superheated liquid.(a) Beginning with an appropriate free-body diagram of the bubble, perform a force balance to obtain an
A long, 1-mm-diameter wire passes an electrical current dissipating 3150 W/m and reaches a surface temperature of 126°C when submerged in water at 1 atm. What is the boiling heat transfer coefficient? Estimate the value of the correlation coefficient Cs,f.
Estimate the nucleate pool boiling heat transfer coefficient for water boiling at atmospheric pressure on the outer surface of a platinum-plated 10-mm-diameter tube maintained 10°C above the saturation temperature.
Plot the nucleate boiling heat flux for saturated water at atmospheric pressure on a large, horizontal polished copper plate, over the excess temperature range 5°C < ∆Te < 30°C. Compare your results with Figure 10.4. Also find the excess temperature corresponding to the critical heat flux.
A simple expression to account for the effect of pressure on the nucleate boiling convection coefficient in water (W/m2∙K) is where p and Po are the system pressure and standard atmospheric pressure, respectively.For a horizontal plate and the range 15
In Example 10.1 we considered conditions for which vigorous boiling occurs in a pan of water, and we determined the electric power (heat rate) required to maintain a prescribed temperature for the bottom of the pan. However, the electric power is, in fact the control (independent) variable, from
Calculate the critical heat flux on a large horizontal surface for the following fluids at 1 atm: mercury, ethanol, and refrigerant R-134a. Compare these results to the critical heat flux for water at 1 atm.
The bottom of a copper pan, 150 mm in diameter, is maintained at 115°C by the heating element of an electric range. Estimate the power required to boil the water in this pan. Determine the evaporation rate. What is the ratio of the surface heat flux to the critical heat flux? What pan temperature
A nickel-coated heater element with a thickness of 15 mm and a thermal conductivity of 50W/m ∙ K is exposed to saturated water at atmospheric pressure. A thermocouple is attached to the back surface, which is well insulated. Measurements at a particular operating condition yield an
Advances in very large scale integration (VLSI) of electronic devices on a chip are often restricted by the ability to cool the chip. For mainframe computers, an array of several hundred chips, each of area 25 mm2, may be mounted on a ceramic substrate. A method of cooling the array is by immersion
Saturated ethylene glycol at 1 atm is heated by a horizontal chromium-plated surface which has a diameter of 200 mm and is maintained at 480 K. Estimate the heating power requirement and the rate of evaporation. What fraction is the power requirement of the maximum power associated with the
Copper tubes 25 mm in diameter and 0.75 m long are used to boil saturated water at 1 atm.(a) If the tubes are operated at 75% of the critical heat flux, how many tubes are needed to provide a vapor production rate of 750 kg/h? What is the corresponding tube surface temperature?(b) Compute and plot
Consider a gas-fired boiler in which five coiled thin-walled, copper tubes of 25-mm diameter and 8-m length are submerged in pressurized water at 4.37 bars. The walls of the tubes are polished and may be assumed to be isothermal. Combustion gases enter each of the tubes at a temperature of Tm,i =
Estimate the current at which a I-mm-diameter nickel wire will bum out when submerged in water at atmospheric pressure. The electrical resistance of the wire is 0.129Ω/m.
Estimate the power (W/m2) required to maintain a brass plate at ∆Te = 15°C while boiling saturated water at 1 atm. What is the power requirement if the water is pressurized to 10 atm? At what fraction of the critical heat flux is the plate operating?
It has been demonstrated experimentally that the critical heat flux is highly dependent on pressure, primarily through the pressure dependence of the fluid surface tension and latent heat of vaporization. Using Equation 10.6, calculate values of q"max for water on a large horizontal surface as a
In applying dimensional analysis, Kutateladze [9] postulated that the critical heat flux varies with the heat of vaporization, vapor density, surface tension, and the bubble diameter parameter given in Equation 10.4a. Verify that dimensional analysis would yield the following expression for the
A dielectric fluid at atmospheric pressure is heated with a 0.5-mm-diameter, horizontal platinum wire. Determine the temperature of the wire when the wire is heated at 50% of the critical heat flux. The properties of the fluid are cp,1 = 1300 J/kg. K ∙ hfg = 142 kJ/kg, k1 = 0.075 W/m ∙ K,
What is the critical heat flux for boiling water at 1 atm on a large horizontal surface on the surface of the moon, where the gravitational acceleration is one-sixth that of the earth?
A heater for boiling a saturated liquid consists of two concentric stainless steel tubes packed with dense boron nitride powder. Electrical current is passed through the inner tube, creating uniform volumetric heating q (W/m3). The exposed surface of the outer tube is in contact with the liquid and
A silicon chip of thickness L = 2.5 mm and thermal conductivity ks = 135 W/m ∙ K is cooled by boiling a saturated fluorocarbon liquid (Tsat = 57°C) on its surface. The electronic circuits on the bottom of the chip produce a uniform heat flux of q"o = 5 x 104 W/m2, while the sides of the chip are
A device for performing boiling experiments consist of a copper bar (k = 400 W/m ∙ K), which is exposed to a boiling liquid at one end, encapsulates an electrical heater at the other end, and is well insulated from its surroundings at all but the exposed surface. Thermocouples inserted in the bar
A small copper sphere, initially at a uniform, elevated temperature T(0) = T;, is suddenly immersed in a large fluid bath maintained at Tsat. The initial temperature of the sphere exceeds the Leiden frost point corresponding to the temperature TD of Figure 10.4.(a) Sketch the variation of the
A sphere made of aluminum alloy 2024 with a diameter of 20 mm and a uniform temperature of 500°C is suddenly immersed in a saturated water bath maintained at atmospheric pressure. The surface of the sphere has an emissivity of 0.25.(a) Calculate the total heat transfer coefficient for the initial
A steel bar, 20 mm in diameter and 200 mm long, with an emissivity of 0.9, is removed from a furnace at 455°C and suddenly submerged horizontally in a water bath under atmospheric pressure. Estimate the initial heat transfer rate from the bar.
Electrical current passes through a horizontal 2-mm-diameter conductor of emissivity 0.5 when immersed in water under atmospheric pressure.(a) Estimate the power dissipation per unit length of the conductor required to maintain the surface temperature at 555°C.(b) For conductor diameters of 1.5,
Consider a horizontal, D = I-mm-diameter platinum wire suspended in saturated water at atmospheric pressure. The wire is heated by an electrical current. Determine the heat flux from the wire at the instant when the surface of the wire reaches its melting point. Determine the corresponding
A heater element of 5-mm diameter is maintained at a surface temperature of 350°C when immersed horizontally in water under atmospheric pressure. The element sheath is stainless steel with a mechanically polished finish having an emissivity of 0.25.(a) Calculate the electrical power dissipation
The thermal energy generated by a silicon chip increases in proportion to its clock speed. The silicon chip of Problem 10.23 is designed to operate in the nucleate boiling regime at approximately 30% of the critical heat flux. A sudden surge in the chip's clock speed triggers film boiling, after
A cylinder of 120-mm diameter at 1000 K is quenched in saturated water at 1 atm. Describe the quenching process and estimate the maximum heat removal rate per unit length during the process.
A 1-mm-diameter horizontal platinum wire of emissivity ε = 0.25 is operated in saturated water at 1-atm pressure.(a) What is the surface heat flux if the surface temperature is Ts = 800 K?(b) For emissivities of 0.1, 0.25, and 0.95, generate a log-log plot of the heat flux as a function of surface

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