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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

How do you distinguish a linear differential equation from a nonlinear one?
How do you recognize a linear homogeneous differential equation? Give an example and explain why it is linear and homogeneous.
How do differential equations with constant coefficients differ from those with variable coefficients? Give an example for each type.
What kind of differential equations can be solved by direct integration?
Consider a third order linear and homogeneous differential equation. How many arbitrary constants will its general solution involve?
A large plane wall, with a thickness L and a thermal conductivity k, has its left surface (x = 0) exposed to a uniform heat flux q̇0. On the right surface (x = L), convection and radiation heat
Consider a long rectangular bar of length a in the x direction and width b in the y-direction that is initially at a uniform temperature of Ti. The surfaces of the bar at x = 0 and y = 0 are
Consider a large plane wall of thickness L = 0.8 ft and thermal conductivity k = 1.2 Btu/h · ft · °F. The wall is covered with a material that has an emissivity of ε = 0.80 and a solar
A spherical vessel has an inner radius r1 and an outer radius r2. The inner surface (r = r1) of the vessel is subjected to a uniform heat flux q̇1. The outer surface (r = r2) is exposed to
Consider a short cylinder of radius ro and height H in which heat is generated at a constant rate of ėgen. Heat is lost from the cylindrical surface at r = ro by convection to the surrounding
In a solar pond, the absorption of solar energy can be modeled as heat generation and can be approximated by ėgen = ė0 e-bx, where ė0 is the rate of heat absorption at the top surface per unit
A spherical metal ball of radius ro is heated in an oven to a temperature of Ti throughout and is then taken out of the oven and allowed to cool in ambient air at T∞ by convection and radiation.
Heat is generated in a long wire of radius ro at a constant rate of ėgen per unit volume. The wire is covered with a plastic insulation layer. Express the heat flux boundary condition at the
It is stated that the temperature in a plane wall with constant thermal conductivity and no heat generation varies linearly during steady one-dimensional heat conduction. Will this still be the case
Consider one-dimensional heat conduction through a large plane wall with no heat generation that is perfectly insulated on one side and is subjected to convection and radiation on the other side. It
Consider a solid cylindrical rod whose side surface is maintained at a constant temperature while the end surfaces are perfectly insulated. The thermal conductivity of the rod material is constant
Consider the base plate of an 800-W household iron with a thickness of L = 0.6 cm, base area of A = 160 cm2, and thermal conductivity of k = 60 W/m·K. The inner surface of the base plate is
Consider a solid cylindrical rod whose ends are maintained at constant but different temperatures while the side surface is perfectly insulated. There is no heat generation. It is claimed that the
Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 1.8 W/m·K, and surface area A = 30 m2. The left side of the wall is maintained at a constant temperature of T1 = 90°C
Consider a 20-cm-thick large concrete plane wall (k = 0.77 W/m · K) subjected to convection on both sides with T∞1 = 27°C and h1 = 5 W/m2 · K on the inside, and T∞2 = 8°C and h2 = 12
The outer surface of an engine is situated in a place where oil leakage can occur. Some oils have autoignition temperatures of approximately above 250°C. When oil comes in contact with a hot engine
Electrically heated draw batch furnaces are commonly used in the heat treatment industry. Consider a draw batch furnace front made of a 20-mm thick steel plate with a thermal conductivity of 25
A large steel plate having a thickness of L = 4 in, thermal conductivity of k = 7.2 Btu/h·ft·°F, and an emissivity of ε = 0.7 is lying on the ground. The exposed surface of the plate at x = L is
Consider a solid cylindrical rod of length 0.15 m and diameter 0.05 m. The top and bottom surfaces of the rod are maintained at constant temperatures of 20°C and 95°C, respectively, while the side
Consider a chilled-water pipe of length L, inner radius r1, outer radius r2, and thermal conductivity k. Water flows in the pipe at a temperature Tf and the heat transfer coefficient at the inner
Consider a steam pipe of length L = 30 ft, inner radius r1 = 2 in, outer radius r2 = 2.4 in, and thermal conductivity k = 7.2 Btu/h·ft·°F. Steam is flowing through the pipe at an average
A pipe in a manufacturing plant is transporting superheated vapor at a mass flow rate of 0.3 kg/s. The pipe is 10 m long, has an inner diameter of 5 cm and pipe wall thickness of 6 mm. The pipe has a
Liquid ethanol is a flammable fluid that has a flashpoint at 16.6°C. At temperatures above the flashpoint, ethanol can release vapors that form explosive mixtures, which could ignite when source of
In subsea oil and natural gas production, hydrocarbon fluids may leave the reservoir with a temperature of 70°C and flow in subsea surrounding of 5°C. As a result of the temperature difference
A spherical container of inner radius r1 = 2 m, outer radius r2 = 2.1 m, and thermal conductivity k = 30 W/m · K is filled with iced water at 0°C. The container is gaining heat by convection from
A stainless steel spherical container, with k = 15 W/m∙K is used for storing chemicals undergoing exothermic reaction. The reaction provides a uniform heat flux of 60 kW/m2 to the container’s
In a food processing facility, a spherical container of inner radius r1 = 40 cm, outer radius r2 = 41 cm, and thermal conductivity k = 1.5 W/m·K is used to store hot water and to keep it at 100°C
Reconsider Prob. 2–76. Using the relation obtained for the variation of temperature in the container material, plot the temperature as a function of the radius r in the range of r = r1 to r = r2,
What is heat generation? Give some examples.
Does heat generation in a solid violate the first law of thermodynamics, which states that energy cannot be created or destroyed? Explain.
Consider uniform heat generation in a cylinder and a sphere of equal radius made of the same material in the same environment. Which geometry will have a higher temperature at its center? Why?
An iron is left unattended and its base temperature rises as a result of resistance heating inside. When will the rate of heat generation inside the iron be equal to the rate of heat loss from the
Consider the uniform heating of a plate in an environment at a constant temperature. Is it possible for part of the heat generated in the left half of the plate to leave the plate through the right
Consider a large 5-cm-thick brass plate (k = 111 W/m·K) in which heat is generated uniformly at a rate of 2 × 105 W/m3. One side of the plate is insulated while the other side is exposed to an
Reconsider Prob. 2–83. Using EES (or other) software, investigate the effect of the heat transfer coefficient on the highest and lowest temperatures in the plate. Let the heat transfer coefficient
Consider a large 3-cm-thick stainless steel plate (k = 15.1 W/m·K) in which heat is generated uniformly at a rate of 5 × 105 W/m3. Both sides of the plate are exposed to an environment at 30°C
In a nuclear reactor, 1-cm-diameter cylindrical uranium rods cooled by water from outside serve as the fuel. Heat is generated uniformly in the rods (k = 29.5 W/m · K) at a rate of 4 × 107 W/m3. If
Heat is generated uniformly at a rate of 3 kW per ft length in a 0.08-in-diameter electric resistance wire made of nickel steel (k = 5.8 Btu/h · ft · °F). Determine the temperature difference
A 2-kW resistance heater wire with thermal conductivity of k = 20 W/m·K, a diameter of D = 4 mm, and a length of L = 0.9 m is used to boil water. If the outer surface temperature of the resistance
A cylindrical nuclear fuel rod of 1 cm in diameter is encased in a concentric tube of 2 cm in diameter, where cooling water flows through the annular region between the fuel rod (k = 30 W/m · K) and
Consider a solid stainless steel wire with a thermal conductivity of 14 W/m · K. The wire has a diameter of 1 mm, a resistivity of 45 × 10-8 Ω·m, and carries a current of 120 A.(a) Determine the
A long homogeneous resistance wire of radius ro = 0.6 cm and thermal conductivity k = 15.2 W/m·K is being used to boil water at atmospheric pressure by the passage of electric current. Heat is
A 6-m-long 3-kW electrical resistance wire is made of 0.2-cm-diameter stainless steel (k = 15.1 W/m·K). The resistance wire operates in an environment at 20°C with a heat transfer coefficient of
A long homogeneous resistance wire of radius ro = 5 mm is being used to heat the air in a room by the passage of electric current. Heat is generated in the wire uniformly at a rate of 5 × 107 W/m3
Is heat transfer a scalar or vector quantity? Explain. Answer the same question for temperature.
Does a heat flux vector at a point P on an isothermal surface of a medium have to be perpendicular to the surface at that point? Explain.
From a heat transfer point of view, what is the difference between isotropic and anisotropic materials?
What is heat generation in a solid? Give examples.
Heat generation is also referred to as energy generation or thermal energy generation. What do you think of these phrases?
In order to size the compressor of a new refrigerator, it is desired to determine the rate of heat transfer from the kitchen air into the refrigerated space through the walls, door, and the top and
In order to determine the size of the heating element of a new oven, it is desired to determine the rate of heat loss through the walls, door, and the top and bottom section of the oven. In your
Consider a round potato being baked in an oven. Would you model the heat transfer to the potato as one-, two-, or three-dimensional? Would the heat transfer be steady or transient? Also, which
Consider an egg being cooked in boiling water in a pan. Would you model the heat transfer to the egg as one-, two-, or three-dimensional? Would the heat transfer be steady or transient? Also, which
Consider a hot dog being cooked in boiling water in a pan. Would you model the heat transfer to the hot dog as one-, two-, or three dimensional? Would the heat transfer be steady or transient? Also,
Consider the cooking process of a roast beef in an oven. Would you consider this to be a steady or transient heat transfer problem? Also, would you consider this to be one-, two-, or
Consider heat loss from a 200-L cylindrical hot water tank in a house to the surrounding medium. Would you consider this to be a steady or transient heat transfer problem? Also, would you consider
Consider a cold canned drink left on a dinner table. Would you model the heat transfer to the drink as one-, two-, or three-dimensional? Would the heat transfer be steady or transient? Also, which
Heat flux meters use a very sensitive device known as a thermopile to measure the temperature difference across a thin, heat conducting film made of kapton (k = 0.345 W/m·K). If the thermopile can
Consider a large 3-cm-thick stainless steel plate in which heat is generated uniformly at a rate of 5 × 106 W/m3. Assuming the plate is losing heat from both sides, determine the heat flux on the
In a nuclear reactor, heat is generated uniformly in the 5-cm-diameter cylindrical uranium rods at a rate of 2 × 108 W/m3. If the length of the rods is 1 m, determine the rate of heat generation in
The resistance wire of an 800-W iron is 15 in long and has a diameter of D = 0.08 in. Determine the rate of heat generation in the wire per unit volume, in Btu/h·ft3, and the heat flux on the outer
Write down the one-dimensional transient heat conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable
Write down the one-dimensional transient heat conduction equation for a long cylinder with constant thermal conductivity and heat generation, and indicate what each variable represents.
Starting with an energy balance on a rectangular volume element, derive the one-dimensional transient heat conduction equation for a plane wall with constant thermal conductivity and no heat
Starting with an energy balance on a cylindrical shell volume element, derive the steady one-dimensional heat conduction equation for a long cylinder with constant thermal conductivity in which heat
Consider a medium in which the heat conduction equation is given in its simplest form as(a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there
Consider a medium in which the heat conduction equation is given in its simplest form as(a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there
Starting with an energy balance on a volume element, derive the two-dimensional transient heat conduction equation in rectangular coordinates for T(x, y, t) for the case of constant thermal
Starting with an energy balance on a ring-shaped volume element, derive the two-dimensional steady heat conduction equation in cylindrical coordinates for T(r, z) for the case of constant thermal
Starting with an energy balance on a disk volume element, derive the one-dimensional transient heat conduction equation for T(z, t) in a cylinder of diameter D with an insulated side surface for the
What is a boundary condition? How many boundary conditions do we need to specify for a two-dimensional heat conduction problem?
What is an initial condition? How many initial conditions do we need to specify for a two-dimensional heat conduction problem?
What is a thermal symmetry boundary condition? How is it expressed mathematically?
Consider an aluminum pan used to cook stew on top of an electric range. The bottom section of the pan is L = 0.25 cm thick and has a diameter of D = 18 cm. The electric heating unit on the range top
Consider a medium in which the heat conduction equation is given in its simplest form as(a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there
Starting with an energy balance on a spherical shell volume element, derive the one-dimensional transient heat conduction equation for a sphere with constant thermal conductivity and no heat
Consider a medium in which the heat conduction equation is given in its simplest form as(a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there
Consider a medium in which the heat conduction equation is given in its simplest form as(a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there
Consider a medium in which the heat conduction equation is given in its simplest form as(a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there
Consider a medium in which the heat conduction equation is given in its simplest form as(a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there
How is the boundary condition on an insulated surface expressed mathematically?
It is claimed that the temperature profile in a medium must be perpendicular to an insulated surface. Is this a valid claim? Explain.
Why do we try to avoid the radiation boundary conditions in heat transfer analysis?
Consider a steel pan used to boil water on top of an electric range. The bottom section of the pan is L = 0.3 cm thick and has a diameter of D = 20 cm. The electric heating unit on the range top
Consider the East wall of a house that has a thickness of L. The outer surface of the wall exchanges heat by both convection and radiation. The interior of the house is maintained at T∞1, while the
Consider a long pipe of inner radius r1, outer radius r2, and thermal conductivity k. The outer surface of the pipe is subjected to convection to a medium at T∞ with a heat transfer coefficient of
A 2-kW resistance heater wire whose thermal conductivity is k = 10.4 Btu/h·ft·R has a radius of ro = 0.06 in and a length of L = 15 in, and is used for space heating. Assuming constant thermal
Water flows through a pipe at an average temperature of T∞ = 90°C. The inner and outer radii of the pipe are r1= 6 cm and r2 = 6.5 cm, respectively. The outer surface of the pipe is wrapped with a
Consider a spherical container of inner radius r1, outer radius r2, and thermal conductivity k. Express the boundary condition on the inner surface of the container for steady one dimensional
Consider a spherical shell of inner radius r1, outer radius r2, thermal conductivity k, and emissivity ε. The outer surface of the shell is subjected to radiation to surrounding surfaces at Tsurr,
A container consists of two spherical layers, A and B, that are in perfect contact. If the radius of the interface is ro, express the boundary conditions at the interface.
A spherical metal ball of radius ro is heated in an oven to a temperature of Ti throughout and is then taken out of the oven and dropped into a large body of water at T∞ where it is cooled by
Infiltration of cold air into a warm house during winter through the cracks around doors, windows, and other openings is a major source of energy loss since the cold air that enters needs to be
A logic chip used in a computer dissipates 3 W of power in an environment at 120°F, and has a heat transfer surface area of 0.08 in2. Assuming the heat transfer from the surface to be uniform,
Solve this system of three equations with three unknowns using EES: xy − z = x − 3y0.5 + xz = x + y − z = 4.2 x+y 1.5 −2 -2

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