Questions and Answers of Fundamentals Of Heat And Mass Transfer

Consider fully developed conditions in a circular tube with constant surface temperature Ts < Tm. Determine whether a small- or large-diameter tube is more effective in minimizing heat
An engineer proposes to insert a solid rod of diameter Di into a circular tube of diameter Do to enhance heat transfer from the flowing fluid of temperature Tm to the outer tube wall of
Consider the laminar thermal boundary layer development near the entrance of the tube shown in Figure 8.4. When the hydrodynamic boundary layer is thin relative to the tube diameter, the inviscid
Consider Problem 7.113. Estimate the heat transfer rate to the air, accounting for both the increase in the air temperature as it flows through the foam and the thermal resistance associated with
The metallic foam of Problem 7.113 is brazed to the surface of a silicon chip of width W = 25 mm on a side. The foam heat sink is L = 10 mm tall. Air at Ti 27°C, V = 5 m/s impinges on the
The extremely high temperatures needed to trigger nuclear fusion are proposed to be generated by laser irradiating a spherical pellet of deuterium and tritium fuel of diameter Dp = 1.8 mm.(a)
A proposed method for generating electricity from solar irradiation is to concentrate the irradiation into a cavity that is placed within a large container of a salt with a high melting temperature.
Consider Problem 4.51.(a) The students are each given a flat, first-surface silver mirror with which they collectively irradiate the wooden ship at location B. The reflection from the mirror is
Consider a two-color pyrometer such as in Problem 12.89 that operates at λ1 = 0.65 μm and λ2 = 0.63 λm. Using Wien’s law (see Problem 12.27) determine the temperature of a sheet of
An experiment involves heating a very small sphere that is suspended by a fine string in air with a laser beam in order to induce the highest sphere temperature possible. After inspecting
A probe, used to measure the velocity of air in a low speed wind tunnel, is fabricated of an L = 100 mm long, D = 8-mm outside diameter horizontal aluminum tube. Power resistors are inserted into the
The surface of a horizontal, 7-mm-diameter cylinder is maintained at an excess temperature of 5°C in saturated water at 1 atm. Estimate the heat flux using an appropriate free convection correlation
Estimate the heat transfer coefficient, h, associated with Points A, B, C, D, and E in Figure 10.4. Which point is associated with the largest value of h? Which point correspond to the smallest value
Consider wave-free laminar condensation on a vertical isothermal plate of length L, providing an average heat transfer coefficient of hL. If the plate is divided into N smaller plates, each of length
The tube of Problem 10.58 is modified by milling sharp-cornered grooves around its periphery, as in Figure 10.15. The 2-mm-deep grooves are each 2 mm wide with a pitch of S = 4 mm. Estimate the
Consider the situation of Problem 10.67 at relatively high vapor velocities, with a fluid mass flow rate of m = 2.5 kg/s.(a) Determine the heat transfer coefficient and condensation rate per unit
Refrigerant R-22 with a mass flow rate of m = 8.75 10-3 kg/s is condensed inside a 7-mm-diameter tube. Annular flow is observed. The saturation temperature of the pressurized refrigerant is Tsat
Wetting of some metallic surfaces can be inhibited by means of ion implantation of the surface prior to its use, thereby promoting dropwise condensation. The degree of wetting inhibition and, in
As part of a senior project, a student was given the assignment to design a heat exchanger that meets the following specifications:Like many real-world situations, the customer hasn’t revealed, or
The hot and cold inlet temperatures to a concentric tube heat exchanger are Th,i = 200C, Tc,i = 100°C, respectively. The outlet temperatures are Th,o = 110°C and Tc,o = 125°C. Is the
A concentric tube heat exchanger of length L = 2m is used to thermally process a pharmaceutical product flowing at a mean velocity of um,c = 0.1 m/s with an inlet temperature of Tc,i =
Consider a coupled shell-in-tube heat exchange device consisting of two identical heat exchangers A and B. Air flows on the shell side of heat exchanger A, entering at Th,i,A = 520 K and
Consider Problem 11.36.(a) For mc,A = mh,B = 10kg/s, determine the outlet air and ammonia temperatures, as well as the heat transfer rate.(b) Plot the outlet air and outlet
An automobile radiator may be viewed as a cross-flow heat exchanger with both fluids unmixed. Water, which has a flow rate of 0.05 kg/s, enters the radiator at 400 K and is to leave at 330 K. The
Fluid enters a tube with a flow rate of 0.015 kg/s and an inlet temperature of 20°C. The tube, which has a length of 6 m and diameter of 15 mm, has a surface temperature of 30°C.(a) Determine the
Consider a circular tube of diameter D and length L, with a mass flow rate of .(a) For constant heat flux conditions, derive an expression for the ratio of the temperature difference between the tube
A liquid food product is processed in a continuousflow sterilizer. The liquid enters the sterilizer at a temperature and flow rate of Tm,i,h = 20°C, m = 1 kg/s, respectively. A
NaK (45%/55%), which is an alloy of sodium and potassium is used to cool fast neutron nuclear reactors. The NaK flows at a rate of m = 1 kg/s through a D = 50-mmdiameter tube that has a surface
A circular tube of diameter D = 0.2 mm and length L = 100 mm imposes a constant heat flux of q" = 20 X 103 W/m2 on a fluid with a mass flow rate of m = 0.1 g/s. For an inlet temperature of
Consider pressurized liquid water flowing at m = 0.1 kg/s in a circular tube of diameter D = 0.1 m and length L = 6m.(a) If the water enters at Tm,i = 500 K and the surface temperature of the
Repeat Problem 8.66 for a circular tube of diameter D = 2 mm, an applied heat flux of q" = 200,000 W/m2, and a mass flow rate of m = 10 g/s.Data From Problem 8.66A circular tube of diameter D = 0.2
Consider laminar flow of a fluid with Pr = 4 that undergoes a combined entrance process within a constant surface temperature tube of length L< xfd,t with a flow rate of . An engineer
To maintain pump power requirements per unit flow rate below an acceptable level, operation of the oil pipeline of Problem 8.63 is subject to the constraint that the oil exit temperature
Consider laminar, fully developed flow in a channel of constant surface temperature Ts. For a given mass flow rate and channel length, determine which rectangular channel, b/a = 1.0, 1.43, or 2.0,
An ideal gas flows within a small diameter tube. Derive an expression for the transition density of the gas pc below which microscale effects must be accounted for. Express your result in terms
Consider air flowing in a small-diameter steel tube. Graph the Nusselt number associated with fully developed laminar flow with constant surface heat flux for tube diameters ranging from 1 μm ≤ D
The onset of turbulence in a gas flowing within a circular tube occurs at ReD,c ≈ 2300, while a transition from incompressible to compressible flow occurs at a critical Mach number of Mac ≈
Many of the solid surfaces for which values of the thermal and momentum accommodation coefficients have been measured are quite different from those used in micro- and nanodevices. Plot the Nusselt
A mass transfer operation is preceded by laminar flow of a gaseous species B through a circular tube that is sufficiently long to achieve a fully developed velocity profile. Once the fully developed
Dry air is inhaled at a rate of 10 liter/min through a trachea with a diameter of 20 mm and a length of 125 mm. The inner surface of the trachea is at a normal body temperature of 37°C and may be
Determine the tube diameter that corresponds to a 10% reduction in the convection heat transfer coefficient for thermal and momentum accommodation coefficients of αt = 0.92 and αp = 0.89,
The one-dimensional plane wall of Figure 3.1 is of thickness L = 75 mm and thermal conductivity k = 5W/m · K. The fluid temperatures are T∞,1 = 200°C and T∞,2 = 100°C, respectively.
For laminar free convection flow on a vertical plate, the recommended values of C and n for use in the correlation of Equation 9.24 are 0.59 and 1/4, respectively Derive the values of C from the
To reduce heat losses, a horizontal rectangular duct that is W = 0.80 m wide and H = 0.3 m high is encased in a metal radiation shield. The duct wall and shield are separated by an air gap of
Consider laminar flow about a vertical isothermal plate of length L, providing an average heat transfer coefficient of hL. If the plate is divided into N smaller plates, each of length, LN =
As discussed in Section 5.2, the lumped capacitance approximation may be applied if Bi < 0.1, and, when implemented in a conservative fashion for a long cylinder, the characteristic length is
The effective thermal conductivity keff for concentric cylinders and concentric spheres is provided in Equations 9.59 and 9.62, respectively. Derive expressions for the critical Rayleigh numbers
A proposed method to reduce heat losses from a horizontal, isothermal cylinder placed within a large room is to encase it within a larger cylinder, as shown in the schematic, with all surfaces
Free convection occurs between concentric spheres. The inner sphere is of diameter Di = 50 mm and temperature Ti = 50°C, while the outer sphere is maintained at To = 20°C. Air is in the
Consider the phase change material (PCM) of Problems 8.47 and 9.57. The PCM is housed in a long, horizontal, and insulated cylindrical enclosure of diameter De = 200 mm, which in turn includes a
A horizontal, 25-mm diameter cylinder is maintained at a uniform surface temperature of 35°C. A fluid with a velocity of 0.05 m/s and temperature of 20°C is in cross flow over the cylinder.
An energy storage system is proposed to absorb thermal energy collected during the day with a solar collector and release thermal energy at night to heat a building. The key component of the system
For health reasons, public spaces require the continuous exchange of a specified mass of stale indoor air with fresh outdoor air. To conserve energy during the heating season, it is expedient to
Cooling of outdoor electronic equipment such as in telecommunications towers is difficult due to seasonal and diurnal variations of the air temperature, and potential fouling of heat exchange
Untapped geothermal sites in the United States have the estimated potential to deliver 100,000 MW (electric) of new, clean energy. The key component in a geothermal power plant is a heat exchanger
Solve Problem 8.109a using the effectiveness-NTU method.Data From Problem 8.109(a) For the operating conditions prescribed in Problem 8.107 and a chip thermal conductivity of kch = 140 W/m ·
Derive the expression for the modified effectivenessε*, given in Comment 4 of Example 11.8.Example 11.8 Spherical steel balls of diameter D = 10 mm are cooled from an initial temperature of Thi =
Work Problem 7.29, taking into account the increase in temperature of the water as it flows through the heat sink. Properties of water are listed in Problem 7.29, along with p = 995 kg/m3 and
Consider Problem 3.144a.(a) Using an appropriate correlation from Chapter 8, determine the air inlet velocity for each channel in the heat sink. Assume laminar flow and evaluate air properties at T =
Estimate the total, hemispherical emissivity for polished stainless steel at 800 K using Equation 12.43 along with information provided in Figure 12.17. Assume that the hemispherical emissivity is
The top surface of an L = 5-mm-thick anodized aluminum plate is irradiated with G = 1000 W/m2 while being simultaneously exposed to convection conditions characterized by h = 40 W/m2 · K
Neglecting the effects of radiation absorption, emission, and scattering within their atmospheres, calculate the average temperature of Earth, Venus, and Mars assuming diffuse, gray behavior. The
A frictionless piston of diameter Dp = 50 mm, thickness δ = 10 mm, and density p = 8000 kg/m3 is placed in a vertical cylinder of total length L = 100 mm. The cylinder is bored into a
Rework Problem 13.21 but with both disks having diameter D = 0.20 m. Next, consider the coaxial disks to be replaced by aligned squares of length X on a side so that X2 = π D2/4. Using a software
A small oven consists of a cubical box of dimension L = 0.1 m, as shown. The floor of the box consists of a heater that supplies P = 400 W. The remaining walls lose heat to the surroundings
Consider the attic of a home located in a hot climate. The floor of the attic is characterized by a width of L1 = 10 m while the roof makes an angle of θ = 30°from the horizontal direction,
Long, cylindrical bars are heat-treated in an infrared oven. The bars, of diameter D = 50 mm, are placed on an insulated tray and are heated with an overhead infrared panel maintained at temperature
Plant leaves possess small channels that connect the interior moist region of the leaf to the environment. The channels, called stomata, pose the primary resistance to moisture transport through the
Determine the temperatures of surfaces 1 through 4 of the furnace cavity of Example 13.3 if the entire furnace experiences a uniform heat flux corresponding to a total power of 1522 W.Example 13.3A
Noting from Figure 13.16 that gas emissivity can be increased by adding water vapor, it is proposed to enhance heat transfer by injecting saturated steam at 100C at the entrance of the pipe of
Pure, solid silicon is produced from a melt, as, for example, in Problem 1.42. Solid silicon is semitransparent, and the spectral absorption coefficient distribution for pure silicon may be
Two convex objects are inside a large vacuum enclosure whose walls are maintained at T3 = 300 K. The objects have the same area, 0.2 m2, and the same emissivity, 0.2. The view factor from object
A double-glazed window consists of two panes of glass, each of thickness t = 6 mm. The inside room temperature is Ti = 20°C with hi = 7.7 W/m2 · K, while the outside temperature is
Cylindrical pillars similar to those of Problem 4.22 are positioned between the glass sheets with a pillar to- pillar spacing of W. The inside surface of one glass sheet is treated with a
Consider a vertical, double-pane window for the conditions prescribed in Problem 9.94. That is, vertical panes at temperature of T1 = 22°C and T2 = 20°C are separated by atmospheric air,
Plot the mass diffusivity, DAB, versus the molecular weight of Substance A for Substance B being air at p = 1.5 atm, T = 320 K. Substance A is each of the first 8 entries of Table A.8. Is your plot
Consider Problem 14.41.(a) How long should the bubbles remain in the water to achieve an average vapor concentration that is 95% of the maximum value?(b) How long should the bubbles remain in the
A pharmaceutical product is designed to be absorbed in the gastrointestinal tract. The active ingredient is pressed into a tablet with a density of pA = 15 kg/m3 while the remainder of the
Consider atmospheric air at 25°C and a velocity of 25 m/s flowing over both surfaces of a 1-m-long flat plate that is maintained at 125°C. Determine the rate of heat transfer per unit width from
Consider laminar, parallel flow past an isothermal flat plate of length L, providing an average heat transfer coefficient of hL. If the plate is divided into N smaller plates, each of length
Repeat Problem 7.11 for the case when the boundary layer is tripped to a turbulent condition at its leading edge.Data From Problem 7.11Consider laminar, parallel flow past an isothermal flat plate of
Consider the photovoltaic solar panel of Example 3.3. The heat transfer coefficient should no longer be taken to be a specified value.(a) Determine the silicon temperature and the electric power
Calculate the value of the average heat transfer coefficient for the plate of Problem 7.21 when the entire plate is rotated 90° so that half of the leading edge consists of a very smooth portion (A)
Consider a thin, 50 mm X 50 mm fuel cell similar to that of Example 1.5, with air in parallel flow over its surfaces. Very small-diameter wires are stretched across both sides of the fuel cell at a
The boundary layer associated with parallel flow over an isothermal plate may be tripped at any x-location by using a fine wire that is stretched across the width of the plate. Determine the value of
An L = 1-m-long vertical copper tube of inner diameter Di = 20 mm and wall thickness t = 2 mm contains liquid water at Tw ≈ 0°C. On a winter day, air at V = 3 m/s, T∞ =–20°C
Pin fins are to be specified for use in an industrial cooling application. The fins will be subjected to a gas in cross flow at V = 10 m/s. The cylindrical fin has a diameter of D = 15 mm, and the
In a manufacturing process, long aluminum rods of square cross section with d = 25 mm are cooled from an initial temperature of Ti = 400°C. Which configuration in the sketch should be used to
Determine the convection heat loss from both the top and the bottom of a flat plate at Ts = 80°C with air in parallel flow at T∞ = 25°C, u∞ = 3 m/s. The plate is t = 1 mm thick, L =
Consider two very long, straight fins of uniform cross section, as shown in Figure 3.17. The rectangular fin has dimensions t = 1 mm and w = 20 mm. The circular pin fin has the same cross-sectional
Repeat Problem 7.94, but with NL = 7, NT = 10, and V = 10.5 m/s.Data From Problem 7.94A tube bank uses an aligned arrangement of 30-mmdiameter tubes with ST = SL = 60 mm and
Heating and cooling with miniature impinging jets has been proposed for numerous applications. For a single round jet, determine the minimum jet diameter for which Equation 7.71 may be applied for
A cryogenic probe is used to treat cancerous skin tissue. The probe consists of a single round jet of diameter De = 2 mm that issues from a nozzle conscentrically situated within a larger,
The porosity of a packed bed can be decreased by vibrating the containment vessel as the vessel is filled with the particles. The vibration promotes particle settling. (a) Consider the air
Packed beds of spherical particles can be sintered at high temperature to form permeable, rigid foams. A foam sheet of thickness t = 10mm is comprised of sintered bronze spheres, each of diameter D =
Consider the physical system of Problem 7.119 (a series of water-filled trays heated radiatively), but under operating conditions for which each tray is 0.25 m long by 1 m wide and is uniformly
For each of the following cases, determine an appropriate characteristic length Lc and the corresponding Biot number Bi that is associated with the transient thermal response of the solid object.
Calculate the thermal conductivity of air, hydrogen, and carbon dioxide at 300 K, assuming ideal gas behavior. Compare your calculated values to values from Table A.4.
A flaked cereal is of thickness 2L = 1.2 mm. The density, specific heat, and thermal conductivity of the flake are 700 kg/m3, cp = 2400 J/kg · K, and k = 0.34 W/m · K, respectively. The
Molecular electronics is an emerging field associated with computing and data storage utilizing energy transfer at the molecular scale. At this scale, thermal energy is associated exclusively with

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