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engineering
heat and mass transfer fundamentals and applications
Questions and Answers of
Heat And Mass Transfer Fundamentals And Applications
A potato may be approximated as a 5.7-cm-diameter solid sphere with the properties ρ = 910 kg/m3, cp = 4.25 kJ/kg·K, k = 0.68 W/m · K, and α = 1.76 × 10-7 m2/s. Twelve such potatoes initially at
When water, as in a pond or lake, is heated by warm air above it, it remains stable, does not move, and forms a warm layer of water on top of a cold layer. Consider a deep lake (k = 0.6 W/m · K, cp
A large chunk of tissue at 35°C with a thermal diffusivity of 1 × 10-7 m2/s is dropped into iced water. The water is well-stirred so that the surface temperature of the tissue drops to 0 °C at
The 40-cm-thick roof of a large room made of concrete (k = 0.79 W/m · K, α = 5.88 × 10-7 m2/s) is initially at a uniform temperature of 15°C. After a heavy snow storm, the outer surface of the
Citrus trees are very susceptible to cold weather, and extended exposure to subfreezing temperatures can destroy the crop. In order to protect the trees from occasional cold fronts with subfreezing
With powerful computers and software packages readily available, do you think obtaining analytical solutions to engineering problems will eventually disappear from engineering curricula?
What are the limitations of the analytical solution methods?
Consider a heat conduction problem that can be solved both analytically, by solving the governing differential equation and applying the boundary conditions, and numerically, by a software package
What is the basis of the energy balance method? How does it differ from the formal finite difference method? For a specified nodal network, will these two methods result in the same or a different
How do numerical solution methods differ from analytical ones? What are the advantages and disadvantages of numerical and analytical methods?
Two engineers are to solve an actual heat transfer problem in a manufacturing facility. Engineer A makes the necessary simplifying assumptions and solves the problem analytically, while engineer B
Define these terms used in the finite difference formulation: node, nodal network, volume element, nodal spacing, and difference equation.
The finite difference formulation of steady two dimensional heat conduction in a medium with heat generation and constant thermal conductivity is given byin rectangular coordinates. Modify this
For a one dimensional steady state variable thermal conductivity heat conduction with uniform internal heat generation, develop a generalized finite difference formulation for the interior nodes,
In many engineering applications variation in thermal properties is significant especially when there are large temperature gradients or the material is not homogeneous. To account for these
Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The nodal network of the medium consists of nodes 0, 1, 2, 3, and 4
Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and constant thermal conductivity, as shown in Fig. P5–12 on the next page. The nodal network of the
Explain how the finite difference form of a heat conduction problem is obtained by the energy balance method.
What are the basic steps involved in solving a system of equations with Gauss-Seidel method?
Consider a medium in which the finite difference formulation of a general interior node is given in its simplest form as(a) Is heat transfer in this medium steady or transient?(b) Is heat transfer
How is an insulated boundary handled in finite difference formulation of a problem? How does a symmetry line differ from an insulated boundary in the finite difference formulation?
How can a node on an insulated boundary be treated as an interior node in the finite difference formulation of a plane wall? Explain.
In the energy balance formulation of the finite difference method, it is recommended that all heat transfer at the boundaries of the volume element be assumed to be into the volume element even for
Consider steady heat conduction in a plane wall whose left surface (node 0) is maintained at 30°C while the right surface (node 8) is subjected to a heat flux of 1200 W/m2. Express the finite
Consider steady heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The nodal network of the medium consists of nodes 0, 1, 2, 3, and 4 with a uniform
Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The nodal network of the medium consists of nodes 0, 1, 2, 3, 4, and 5
Consider steady one-dimensional heat conduction in a pin fin of constant diameter D with constant thermal conductivity. The fin is losing heat by convection to the ambient air at T∞ with a
Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and variable thermal conductivity. The nodal network of the medium consists of nodes 0, 1, and 2 with a
Consider steady one-dimensional heat conduction in a pin fin of constant diameter D with constant thermal conductivity. The fin is losing heat by convection to the ambient air at T∞ with a heat
Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The nodal network of the medium consists of nodes 0, 1, 2, 3, 4, and 5
Consider the base plate of a 800 W household iron having a thickness of L = 0.6 cm, base area of A = 160 cm2, and thermal conductivity of k = 20 W/m · K. The inner surface of the base plate is
Consider a large plane wall of thickness L = 0.3 m, thermal conductivity k = 2.5 W/m · K, and surface area A = 24 m2. The left side of the wall is subjected to a heat flux of q̇0 = 350 W/m2 while
Consider a large uranium plate of thickness 5 cm and thermal conductivity k = 28 W/m · K in which heat is generated uniformly at a constant rate of ė = 6 × 105 W/m3. One side of the plate is
Repeat Prob. 5–29 using EES (or other) software.Data From problem 29Consider a large uranium plate of thickness 5 cm and thermal conductivity k = 28 W/m · K in which heat is generated uniformly at
Steam is being condensed at 60°C by a 15-m-long horizontal copper tube with a diameter of 25 mm. The tube surface temperature is maintained at 40°C. Determine the condensation rate of the steam
Consider a non-boiling gas-liquid two-phase flow in a tube, where the ratio of the mass flow rate is ṁl/ṁg = 300. Determine the flow quality (x) of this non-boiling two-phase flow.
Consider a non-boiling gas-liquid two-phase flow in a 102-mm diameter tube, where the superficial gas velocity is one-third that of the liquid. If the densities of the gas and liquid are ρg = 8.5
A non-boiling two-phase flow of air and engine oil in a 25-mm diameter tube has a bulk mean temperature of 140°C. If the flow quality is 2.1 × 10-3 and the mass flow rate of the engine oil is 0.9
Turkeys with a water content of 64 percent that are initially at 1°C and have a mass of about 7 kg are to be frozen by submerging them into brine at 229°C. Using Figure 4–56, determine how long
Long aluminum wires of diameter 3 mm (ρ = 2702 kg/m3, cp = 0.896 kJ/kg · K, k = 236 W/m · K, and α = 9.75 × 10-5 m2/s) are extruded at a temperature of 350°C and exposed to atmospheric air at
Repeat Prob. 4–140 for a copper wire (ρ = 8950 kg/m3, cp = 0.383 kJ/kg · K, k = 386 W/m · K, and α = 1.13 × 10-4 m2/s).Data from problem 140Long aluminum wires of diameter 3 mm (ρ = 2702
The thermal conductivity of a solid whose density and specific heat are known can be determined from the relation k = α/ρcp after evaluating the thermal diffusivity a. Consider a 2-cm-diameter
Consider a 2-m-long and 0.7-m-wide stainless-steel plate whose thickness is 0.1 m. The left surface of the plate is exposed to a uniform heat flux of 2000 W/m2 while the right surface of the plate is
A stainless steel plane wall (k = 15.1 W/m · K) of thickness 1 m experiences a uniform heat generation of 1000 W/m3. The left side of the wall is maintained at a constant temperature of 70°C, and
Consider a 1-D steady state heat conduction in a composite wall made up of two different materials A (k= 45 W/m · K) and B (k = 28 W/m · K). There is a heating element passing through the material
A 1-m-long and 0.1-m-thick steel plate of thermal conductivity 35 W/m · K is well insulated on its both sides, while the top surface is exposed to a uniform heat flux of 5500 W/m2. The bottom
A plane wall with surface temperature of 350°C is attached with straight rectangular fins (k = 235 W/m · K). The fins are exposed to an ambient air condition of 25°C and the convection heat
Consider a stainless steel spoon (k = 15.1 W/m · K, ε = 0.6) that is partially immersed in boiling water at 95°C in a kitchen at 25°C. The handle of the spoon has a cross section of about 0.2 cm
A circular fin of uniform cross section, with diameter of 10 mm and length of 50 mm, is attached to a wall with surface temperature of 350°C. The fin is made of material with thermal conductivity of
A cylindrical aluminum fin with adiabatic tip is attached to a wall with surface temperature of 300°C, and is exposed to ambient air condition of 15°C with convection heat transfer coefficient of
A circular fin (k = 240 W/m · K) of uniform cross section, with diameter of 10 mm and length of 50 mm, is attached to a wall with surface temperature of 350°C. The fin tip has a temperature of
A DC motor delivers mechanical power to a rotating stainless steel shaft (k = 15.1 W/m · K) with a length of 25 cm and a diameter of 25 mm. The DC motor is in a surrounding with ambient air
One side of a 2-m-high and 3-m-wide vertical plate at 80°C is to be cooled by attaching aluminum fins (k= 237 W/m · K) of rectangular profile in an environment at 35°C. The fins are 2 cm long, 0.3
A hot surface at 100°C is to be cooled by attaching 3-cm-long, 0.25-cm-diameter aluminum pin fins (k = 237 W/m · K) with a center-to-center distance of 0.6 cm. The temperature of the surrounding
Repeat Prob. 5–45 using copper fins (k = 386 W/m · K) instead of aluminum ones.Data from problem 45A hot surface at 100°C is to be cooled by attaching 3-cm-long, 0.25-cm-diameter aluminum pin
Consider an aluminum alloy fin (k = 180 W/m · K) of triangular cross section whose length is L = 5 cm, base thickness is b = 1 cm, and width w in the direction normal to the plane of paper is very
Reconsider Prob. 5–47. Using EES (or other) software, investigate the effect of the fin base temperature on the fin tip temperature and the rate of heat transfer from the fin. Let the temperature
Reconsider Prob. 5–49. Using EES (or other) software, investigate the effects of the steam temperature and the outer heat transfer coefficient on the flange tip temperature and the rate of heat
Two 3-m-long and 0.4-cm-thick cast iron (k = 52 W/m · K, ε = 0.8) steam pipes of outer diameter 10 cm are connected to each other through two 1-cm-thick flanges of outer diameter 20 cm. The steam
Using EES (or other) software, solve these systems of algebraic equations. (a) (b) 3x₁x₂ + 3x3 = 0 -X₁ + 2x₂ + x3 = 3 2X₁ X₂ X3 = 2 4x₁2x2 +0.5x3 = -2 xx₂ + x3 = 11.964 - x₁ + x₂
Using EES (or other) software, solve these systems of algebraic equations. (a) 3x₁ + 2x₂ - x3 + x₁ = 6 X₁ + 2x₂x₁ = -3 -2x₁ + x₂ + 3x3 + x₁ = 2 3x₂ + x3 4x4 = -6 (b) - 3x₁ + x²
Using EES (or other) software, solve these systems of algebraic equations. (a) (b) 4x₁ - x₂ + 2x3 + x₂ = -6 x₁ + 3x₂x3 + 4x4 = -1 -X₁ + 2x₂ + 2x₂ - 4x3 2x₁ + x2x3 + x4 = 1 x² +
What is an irregular boundary? What is a practical way of handling irregular boundary surfaces with the finite difference method?
Consider a medium in which the finite difference formulation of a general interior node is given in its simplest form as(a) Is heat transfer in this medium steady or transient?(b) Is heat transfer
Consider a medium in which the finite difference formulation of a general interior node is given in its simplest form as(a) Is heat transfer in this medium steady or transient?(b) Is heat transfer
Starting with an energy balance on a volume element, obtain the steady two-dimensional finite difference equation for a general interior node in rectangular coordinates for T(x, y) for the case of
Consider steady two-dimensional heat transfer in a square cross section (3 cm × 3 cm) with the prescribed temperatures at the top, right, bottom, and left surfaces to be 100°C, 200°C, 300°C, and
Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The measured temperatures at selected points of the outer surfaces are as shown. The
Consider steady two-dimensional heat transfer in a long solid bar of(a) Square(b) Rectangular cross sections as shown in the figure. The measured temperatures at selected points of the outer surfaces
Consider steady two-dimensional heat conduction in a square cross section (3 cm × 3 cm, k = 20 W/m · K, a= 6.694 × 10-6 m2/s) with constant prescribed temperature of 100°C and 300°C at the top
Consider steady two-dimensional heat transfer in a rectangular cross section (60 cm × 30 cm) with the prescribed temperatures at the left, right, and bottom surfaces to be 0°C, and the top surface
Consider a rectangular metal block (k = 35 W/m · K) of dimensions 100 cm × 75 cm subjected to a sinusoidal temperature variation at its top surface while its bottom surface is insulated. The two
Consider a long bar of rectangular cross section (60 mm by 90 mm on a side) and of thermal conductivity 1 W/m · K. The top surface is exposed to a convection process with air at 100ºC and a
Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in Fig. P5–65. The temperatures at the selected nodes and the thermal conditions on the boundaries
Repeat Prob. 5–65 using EES (or other) software.Data from problem 65Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in Fig. P5–65. The temperatures
Reconsider Prob. 5–65. Using EES (or other) software, investigate the effects of the thermal conductivity and the heat generation rate on the temperatures at nodes 1 and 3, and the rate of heat
Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The temperatures at the selected nodes and the thermal conditions at the boundaries are
Repeat Prob. 5–68 using EES (or other) software.Data from problem 68Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The temperatures
Consider a 5-m-long constantan block (k = 23 W/m · K) 30 cm high and 50 cm wide (Fig. P5–70). The block is completely submerged in iced water at 0°C that is well stirred, and the heat transfer
Consider steady two-dimensional heat transfer in a long solid bar (k = 25 W/m · K) of square cross section (3 cm × 3 cm) with the prescribed temperatures at the top, right, bottom, and left
Consider steady two-dimensional heat transfer in a long solid bar of square cross section in which heat is generated uniformly at a rate of ė = 0.19 × 105 Btu/h·ft3. The cross section of the bar
Hot combustion gases of a furnace are flowing through a concrete chimney (k = 1.4 W/m · K) of rectangular cross section. The flow section of the chimney is 20 cm × 40 cm, and the thickness of the
Repeat Prob. 5–73 by disregarding radiation heat transfer from the outer surfaces of the chimney.Data from problem 73Hot combustion gases of a furnace are flowing through a concrete chimney (k =
A thin film 500 W electrical heater of negligible thickness and dimensions 100 mm × 100 mm is sandwiched between two slabs made of copper alloy (k = 120 W/m · K) and stainless steel (15 W/m · K).
The wall of a heat exchanger separates hot water at TA = 90°C from cold water at TB = 10°C. To extend the heat transfer area, two-dimensional ridges are machined on the cold side of the wall, as
Consider steady two-dimensional heat transfer in two long solid bars whose cross sections are given in the figure. The measured temperatures at selected points on the outer surfaces are as shown. The
Consider a long concrete dam (k = 0.6 W/m · K, αs = 0.7) of triangular cross section whose exposed surface is subjected to solar heat flux of q̇s = 800 W/m2 and to convection and radiation to the
Consider a long solid bar whose thermal conductivity is k = 5 W/m · K and whose cross section is given in the figure. The top surface of the bar is maintained at 50°C while the bottom surface is
Consider steady two-dimensional heat transfer in an L-shaped solid body whose cross section is given in the figure. The thermal conductivity of the body is k = 45 W/m · K, and heat is generated in
Sintering is a metallurgical process used to create metal objects with better physical properties by holding powdered material in a mold and heating it to a temperature slightly below its melting
Reconsider Prob. 5–83E. Using EES (or other) software, investigate the effects of the temperatures at the top and bottom surfaces on the temperature in the middle of the insulated surface. Let the
A hot brass plate is having its upper surface cooled by impinging jet of air at temperature of 15°C and convection heat transfer coefficient of 220 W/m2 · K. The 10-cm-thick brass plate (ρ = 8530
Consider a large uranium plate of thickness L = 9 cm, thermal conductivity k = 28 W/m · K, and thermal diffusivity α = 12.5 × 10-6 m2/s that is initially at a uniform temperature of 100°C. Heat
Consider a house whose windows are made of 0.375-in-thick glass (k = 0.48 Btu/h·ft·°F and α = 4.2 × 10-6 ft2/s). Initially, the entire house, including the walls and the windows, is at the
Reconsider Prob. 5–107. Using EES (or other) software, investigate the effect of the cooling time on the temperatures of the left and right sides of the plate. Let the time vary from 5 min to 60
Consider a refrigerator whose outer dimensions are 1.80 m × 0.8 m × 0.7 m. The walls of the refrigerator are constructed of 3-cm-thick urethane insulation (k = 0.026 W/m · K and α = 0.36 × 10-6
Reconsider Prob. 5–111. Using EES (or other) software, plot the temperature inside the refrigerator as a function of heating time as time varies from 1 h to 10 h, and discuss the results.Data from
Consider two-dimensional transient heat transfer in an L-shaped solid bar that is initially at a uniform temperature of 140°C and whose cross section is given in the figure. The thermal conductivity
Reconsider Prob. 5–113. Using EES (or other) software, plot the temperature at the top corner as a function of heating time as it varies from 2 min to 30 min, and discuss the results.Data from
Consider a long solid bar (k = 28 W/m · K and α = 12 × 10-6 m2/s) of square cross section that is initially at a uniform temperature of 32°C. The cross section of the bar is 20 cm × 20 cm in
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