Questions and Answers of Fundamentals Of Heat And Mass Transfer

A copper sheet of thickness 2L = 2 mm has an initial temperature of Ti = 118°C. It is suddenly quenched in liquid water, resulting in boiling at its two surfaces. For boiling, Newton’s
Small spherical particles of diameter D = 50 μm contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the
The plasma spray-coating process of Problem 5.25 can be used to produce nanostructured ceramic coatings. Such coatings are characterized by low thermal conductivity, which is desirable in
Shape memory alloys (SMAs) are metals that undergo a change in crystalline structure within a relatively narrow temperature range. A phase transformation from martensite to austenite can induce
A horizontal structure consists of an LA = 10-mm-thick layer of copper and an LB = 10-mm-thick layer of aluminum. The bottom surface of the composite structure receives a heat flux of q" =
A long, highly polished aluminum rod of diameter D = 35 mm is hung horizontally in a large room. The initial rod temperature is Ti = 90°C, and the room air is T∞ = 20°C. At time t1 =
A constant-property, one-dimensional plane slab of width 2L, initially at a uniform temperature, is heated convectively with Bi = 1.(a) At a dimensionless time of Fo1, heating is suddenly
Consider an acrylic sheet of thickness L = 5 mm that is used to coat a hot, isothermal metal substrate at Th = 300°C. The properties of the acrylic are p = 1990 kg/m3, c = 1470 J/kg K, and k = 0.21
Stone mix concrete slabs are used to absorb thermal energy from flowing air that is carried from a large concentrating solar collector. The slabs are heated during the day and release their heat to
Two plates of the same material and thickness L are at different initial temperatures Ti,1 and Ti,2, where Ti,2 > Ti,1. Their faces are suddenly brought into contact. The external surfaces of
Work Problem 5.47 for a cylinder of radius ro and length L = 20 ro.Data From Problem 5.47A constant-property, one-dimensional plane slab of width 2L, initially at a uniform temperature, is heated
A soda lime glass sphere of diameter D1 = 25 mm is encased in a bake lite spherical shell of thickness L = 10 mm. The composite sphere is initially at a uniform temperature, Ti = 40°C, and
Work Problem 5.47 for the case of a sphere of radius ro.Data From Problem 5.47A constant-property, one-dimensional plane slab of width 2L, initially at a uniform temperature, is heated convectively
Consider the plane wall of thickness 2L, the infinite cylinder of radius ro, and the sphere of radius ro. Each configuration is subjected to a constant surface heat flux q"s. Using the approximate
To determine which parts of a spider’s brain are triggered into neural activity in response to various optical stimuli, researchers at the University of Massachusetts Amherst desire to examine the
Derive an expression for the ratio of the total energy transferred from the isothermal surface of an infinite cylinder to the interior of the cylinder, Q/Qo, that is valid for Fo < 0.2. Express
Derive an expression for the ratio of the total energy transferred from the isothermal surface of a sphere to the interior of the sphere Q/Qo that is valid for Fo < 0.2. Express your
Consider Problem 5.9 except now the combined volume of the oil bath and the sphere is Vtot = 1m3. The oil bath is well mixed and well insulated. (a) Assuming the quenching liquid’s properties
Consider a one-dimensional plane wall at a uniform initial temperature Ti. The wall is 10 mm thick, and has a thermal diffusivity of α = 6 x 10–7 m2/s. The left face is insulated, and
Determine the temperature distribution at t = 30 min for the conditions of Problem 5.116.(a) Use an explicit finite-difference technique with a time increment of 600 s and a space increment of 30
A constant-property, one-dimensional plane wall of width 2L, at an initial uniform temperature Ti, is heated convectively (both surfaces) with an ambient fluid at T∞ = T∞ ,1, h = h1. At
Steel-reinforced concrete pillars are used in the construction of large buildings. Structural failure can occur at high temperatures due to a fire because of softening of the metal core. Consider a
The temperature distribution within a laminar thermal boundary layer associated with flow over an isothermal flat plate is shown in the sketch. The temperature distribution shown is located at x =
Consider the rotating disk of Problem 6.16. A diskshaped, stationary plate is placed a short distance away from the rotating disk, forming a gap of width g. The stationary plate and ambient air are
Consider the flow conditions of Example 6.4 for two situations, one in which the flow is completely laminar, and the second for flow that is tripped to turbulence at the leading edge of the plate.
For the situation described in Example 6.4, the boundary layer can be tripped into a turbulent state by applying roughness to the surface of the flat plate at a particular x-location. Hence the
Consider a laminar boundary layer developing over a flat plate. The flow is incompressible.(a) Substitute Equations 6.31 and 6.32 into Equation 6.38 to determine the boundary conditions in
Consider a laminar boundary layer developing over an isothermal flat plate. The flow is incompressible, and viscous dissipation is negligible.(a) Substitute Equations 6.31 and 6.33 into Equation 6.39
Consider parallel flow over a flat plate for air at 300 K and engine oil at 380 K. The free stream velocity is u∞ = 2 m/s. The temperature difference between the surface and the free stream is
Determine the drag force imparted to the top surface of the flat plate of Example 6.4 for water temperatures of 300 K and 350 K. Assume the plate dimension in the z-direction is W = 1m.Example 6.4
A mist cooler is used to provide relief for a fatigued athlete. Water at Ti = 10°C is injected as a mist into a fan airstream with ambient temperature of T∞ = 32°C. The droplet
Experiments have shown that the transition from laminar to turbulent conditions for flow normal to the axis of a long cylinder occurs at a critical Reynolds number of ReD,c ≈ 2 X 105,
Consider the nanofluid of Example 2.2.Example 2.2(a) Calculate the Prandtl numbers of the base fluid and nanofluid, using information provided in the example problem.(b) For a geometry of fixed
Consider Figure 1.3. The heat flux in the x-direction is q"x = 10 W/m2, the thermal conductivity and wall thickness are k = 2.3 W/m · K and L = 20 mm, respectively, and steady-state conditions
A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P = 5 MW of net power production. The compressor, at an average temperature of Tc = 400°C, is driven by the
For a boiling process such as shown in Figure 1.5c, the ambient temperature T∞ in Newton’s law of cooling is replaced by the saturation temperature of the fluid Tsat. Consider a situation where
An internally reversible refrigerator has a modified coefficient of performance accounting for realistic heat transfer processes ofwhere qin is the refrigerator cooling rate, qout is the heat
A wall has inner and outer surface temperatures of 16 and 6°C, respectively. The interior and exterior air temperatures are 20 and 5°C, respectively. The inner and outer convection heat transfer
Pressurized water (pin = 10 bar, Tin = 110°C) enters the bottom of an L = 10-m-long vertical tube of diameter D = 100 mm at a mass flow rate of m = 1.5 kg/s. The tube is located inside a
A household refrigerator operates with cold- and hot-temperature reservoirs of Tc = 5°C and Th = 25°C, respectively. When new, the cold and hot side resistances are Rc,n = 0.05 K/W and Rh,n = 0.04
Heat is transferred by radiation and convection between the inner surface of the nacelle of the wind turbine of Example 1.3 and the outer surfaces of the gearbox and generator. The convection heat
Consider the tube and inlet conditions of Problem 1.36. Heat transfer at a rate of q = 3.89 MW is delivered to the tube. For an exit pressure of p = 8 bar, determine (a) The temperature of the
Consider the wind turbine of Example 1.3. To reduce the nacelle temperature to Ts = 30°C, the nacelle is vented and a fan is installed to force ambient air into and out of the nacelle enclosure.
Consider a carton of milk that is refrigerated at a temperature of Tm = 5°C. The kitchen temperature on a hot summer day is T∞ = 30°C. If the four sides of the carton are of height and width
Assume steady-state, one-dimensional conduction in the axisymmetric object below, which is insulated around its perimeter.If the properties remain constant and no internal heat generation occurs,
A 50 mm X 45 mm X 20 mm cell phone charger has a surface temperature of Ts = 33°C when plugged into an electrical wall outlet but not in use. The surface of the charger is of emissivity ϵ =
The emissivity of galvanized steel sheet, a common roofing material, is ϵ = 0.13 at temperatures around 300 K, while its absorptivity for solar irradiation is αS = 0.65. Would the neighborhood
A photovoltaic panel of dimension 2 m X 4 m is installed on the roof of a home. The panel is irradiated with a solar flux of GS = 700 W/m2, oriented normal to the top panel surface. The
Convection ovens operate on the principle of inducing forced convection inside the oven chamber with a fan. A small cake is to be baked in an oven when the convection feature is disabled. For this
Consider the geometry of Problem 2.14 for the case where the thermal conductivity varies with temperature as k = ko + aT, where ko = 10W/m · K, a= –10–3 W/m · K2, and T is in
Consider a one-dimensional plane wall with constant properties and uniform internal generation . The left face is insulated, and the right face is held at a uniform temperature.(a) Using the
Temperature distributions within a series of one dimensional plane walls at an initial time, at steady state, and at several intermediate times are as shown.For each case, write the appropriate form
A one-dimensional plane wall of thickness 2L = 100 mm experiences uniform thermal energy generation of q = 1000 W/m3 and is convectively cooled at x = ± 50 mm by an ambient fluid characterized
One-dimensional, steady-state conduction with no energy generation is occurring in a cylindrical shell of inner radius r1 and outer radius r2. Under what condition is the linear temperature
Consider a small but known volume of metal that has a large thermal conductivity.(a) Since the thermal conductivity is large, spatial temperature gradients that develop within the metal in response
One-dimensional, steady-state conduction with no energy generation is occurring in a spherical shell of inner radius r1 and outer radius r2. Under what condition is the linear temperature
Consider a one-dimensional plane wall of thickness 2L. The surface at x=–L is subjected to convective conditions characterized by T∞,1, h1, while the surface at x = + L is subjected to
Use IHT to perform the following tasks.(a) Graph the thermal conductivity of pure copper, 2024 aluminum, and AISI 302 stainless steel over the temperature range 300 ≤ T ≤ 600 K. Include all data
Compare and contrast the heat capacity pcp of common brick, plain carbon steel, engine oil, water, and soil. Which material provides the greatest amount of thermal energy storage per unit
A cylindrical rod of stainless steel is insulated on its exterior surface except for the ends. The steady-state temperature distribution is T(x) = a – bx/L, where a = 305 K 8and b = 10K. The
Consider the steady-state temperature distribution within a composite wall composed of Materials A and B.The conduction process is one-dimensional. Within which material does uniform volumetric
Work Problem 3.15 assuming surfaces parallel to the x-direction are adiabatic.Data From Problem 3.15Consider a composite wall that includes an 8-mm-thick hardwood siding, 40 mm by 130-mm hardwood
A long cylindrical rod, initially at a uniform temperature Ti, is suddenly immersed in a large container of liquid at T∞ < Ti. Sketch the temperature distribution within the rod, T(r), at
A composite one-dimensional plane wall is of overall thickness 2L. Material A spans the domain –L < x < 0 and experiences an exothermic chemical reaction leading to a uniform volumetric
A new building to be located in a cold climate is being designed with a basement that has an L = 200-mm-thick wall. Inner and outer basement wall temperatures are Ti = 20°C and
A dormitory at a large university, built 50 years ago, has exterior walls constructed of Ls = 25-mm-thick sheathing with a thermal conductivity of ks = 0.1 W/m · K. To reduce heat losses in the
A t = 10-mm-thick horizontal layer of water has a top surface temperature of Tc = –4°C and a bottom surface temperature of Th = 2°C. Determine the location of the solid–liquid
Ring-porous woods, such as oak, are characterized by grains. The dark grains consist of very low-density material that forms early in the springtime. The surrounding lighter-colored wood is composed
A batt of glass fiber insulation is of density = 28 kg/m3. Determine the maximum and minimum possible values of the effective thermal conductivity of the insulation at T = 300 K, and compare with the
Determine the thermal conductivity of the carbon nanotube of Example 3.4 when the heating island temperature is measured to be Th = 332.6 K, without evaluating the thermal resistances of the
Consider the oven of Problem 1.54. The walls of the oven consist of L = 30-mm-thick layers of insulation characterized by kins = 0.03 W/m · K that are sandwiched between two thin layers of
A particular thermal system involves three objects of fixed shape with conduction resistances of R1 = 1 K/W, R2 = 2 K/W and R3 = 4 K/W, respectively. An objective is to minimize the
The temperature of a flowing gas is to be measured with a thermocouple junction and wire stretched between two legs of a sting, a wind tunnel test fixture. The junction is formed by butt-welding two
Air usually constitutes up to half of the volume of commercial ice creams and takes the form of small spherical bubbles interspersed within a matrix of frozen matter. The thermal conductivity of ice
A carbon nanotube is suspended across a trench of width s = 5 μm that separates two islands, each at T∞ = 300 K. A focused laser beam irradiates the nanotube at a distance ξ from the left
Consider the manufacture of photovoltaic silicon, as described in Problem 1.42. The thin sheet of silicon is pulled from the pool of molten material very slowly and is subjected to an ambient
Determine the density, specific heat, and thermal conductivity of a lightweight aggregate concrete that is composed of 65% stone mix concrete and 35% air by volume. Evaluate properties at T = 300 K.
A one-dimensional plane wall of thickness L is constructed of a solid material with a linear, nonuniform porosity distribution described by ε(x) = εmax(x/L). Plot the steady-state temperature
A homeowner’s wood stove is equipped with a top burner for cooking. The D = 200-mm-diameter burner is fabricated of cast iron (k = 65 W/m · K). The bottom (combustion) side of the burner has 8
A spherical Pyrex glass shell has inside and outside diameters of D1 = 0.1 m and D2 = 0.2 m, respectively. The inner surface is at Ts,1 = 100°C while the outer surface is at Ts,2
Consider the cylindrical bales of hay in Problem 3.82. It is proposed to utilize the microbial energy generation associated with wet hay to heat water. Consider a 30-mm diameter, thin-walled tube
For one of the M = 48 modules of Example 3.13, determine a variety of different efficiency values concerning the conversion of waste heat to electrical energy.(a) Determine the thermodynamic
One of the thermoelectric modules of Example 3.13 is installed between a hot gas at T∞,1 = 450°C and a cold gas at T∞,2 = 20°C. The convection coefficient associated with the flowing
The electric power generator for an orbiting satellite is composed of a long, cylindrical uranium heat source that is housed within an enclosure of square cross section. The only way for heat that is
Triangular and parabolic straight fins are subjected to the same thermal conditions as the rectangular straight fin of Problem 3.134.(a) Determine the length of a triangular fin of unit width and
Rows of the thermoelectric modules of Example 3.13 are attached to the flat absorber plate of Problem 3.108. The rows of modules are separated by Lsep = 0.5 m and the backs of the modules are
Thermoelectric modules have been used to generate electric power by tapping the heat generated by wood stoves. Consider the installation of the thermoelectric module of Example 3.13 on a vertical
Determine the conduction heat flux through various plane layers that are subjected to boundary temperatures of Ts,1 = 301 K and Ts,2 = 299 K at atmospheric pressure.(a) Case A: The plane
Determine the heat transfer rate between two particles of diameter D = 100 μm and temperatures T1 = 300.1 K and T2 = 299.9 K, respectively. The particles are in contact and are surrounded
A nanolaminated material is fabricated with an atomic layer deposition process, resulting in a series of stacked, alternating layers of tungsten and aluminum oxide, each layer being δ = 0.5 nm
A two-dimensional object is subjected to isothermal conditions at its left and right surfaces, as shown in the schematic. Both diagonal surfaces are adiabatic and the depth of the object is L= 100
Determine the conduction heat transfer through an air layer held between two 10 mm X 10 mm parallel aluminum plates. The plates are at temperatures Ts,1 = 305 K and Ts,2 = 295 K,
Determine the parallel plate separation distance L, above which the thermal resistance associated with molecule-surface collisions Rt,m-s is less than 1% of the resistance associated with
The Knudsen number, Kn = λmfp/L, is a dimensionless parameter used to describe potential micro- or nanoscale effects. Derive an expression for the ratio of the thermal resistance due to
A small device is used to measure the surface temperature of an object. A thermocouple bead of diameter D = 120μm is positioned a distance z = 100m from the surface of interest. The two thermocouple
A small water droplet of diameter D = 100 μm and temperature Tmp = 0°C falls on a nonwetting metal surface that is at temperature Ts = 15°C. Determine how long it will take for the
Determine expressions for q(m1,n) → (m,n), q(m1,n) → (m,n), q(m,n1) → (m,n) and q(m,n1) → (m,n) for conduction associated with a control volume that spans two different materials.
An ancient myth describes how a wooden ship was destroyed by soldiers who reflected sunlight from their polished bronze shields onto its hull, setting the ship ablaze. To test the validity of the
A double-glazed window consists of two sheets of glass separated by an L = 0.2-mm-thick gap. The gap is evacuated, eliminating conduction and convection across the gap. Small cylindrical pillars,
Functionally graded materials are intentionally fabricated to establish a spatial distribution of properties in the final product. Consider an L x L two-dimensional object with L = 20 mm. The thermal

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