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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

Reconsider Prob. 3–130. Using EES (or other) software, investigate the effect of the center to center distance of the fins on the rate of heat transfer from the surface and the overall
Consider the conditions of Example 3–14 in the text for two different environments of air and water with convective heat transfer coefficient of 2 W/m2 · K and 20 W/m2 · K, respectively. The
Consider the conditions of Example 3–14 in the text except that the ambient air is at a temperature of 30°C. A person with skin/fat layer thickness of 0.003 m is doing vigorous exercise which
We are interested in steady state heat transfer analysis from a human forearm subjected to certain environmental conditions. For this purpose consider the forearm to be made up of muscle with
What is a conduction shape factor? How is it related to the thermal resistance?
A 20-m-long and 8-cm-diameter hot-water pipe of a district heating system is buried in the soil 80 cm below the ground surface. The outer surface temperature of the pipe is 60°C. Taking the surface
What is the value of conduction shape factors in engineering?
Hot water at an average temperature of 53°C and an average velocity of 0.4 m/s is flowing through a 5-m section of a thin-walled hot-water pipe that has an outer diameter of 2.5 cm. The pipe passes
A thin-walled cylindrical container is placed horizontally on a snow covered ground. The container is 1.5 m long and has a diameter of 10 cm. The container contains chemicals undergoing exothermic
Hot- and cold-water pipes 8 m long run parallel to each other in a thick concrete layer. The diameters of both pipes are 5 cm, and the distance between the centerlines of the pipes is 40 cm. The
A row of 3-ft-long and 1-in-diameter used uranium fuel rods that are still radioactive are buried in the ground parallel to each other with a center-to-center distance of 8 in at a depth of 15 ft
Reconsider Prob. 3–144. Using EES (or other) software, plot the rate of heat transfer between the pipes as a function of the distance between the centerlines of the pipes in the range of 10 cm to
Hot water at an average temperature of 80°C and an average velocity of 1.5 m/s is flowing through a 25-m section of a pipe that has an outer diameter of 5 cm. The pipe extends 2 m in the ambient air
Two flow passages with different cross-sectional shapes, one circular another square, are each centered in a square solid bar of the same dimension and thermal conductivity. Both configurations have
Hot water at an average temperature of 85°C passes through a row of eight parallel pipes that are 4 m long and have an outer diameter of 3 cm, located vertically in the middle of a concrete wall (k
Consider a tube for transporting steam that is not centered properly in a cylindrical insulation material (k = 0.73 W/m ∙ K). The tube diameter is D1 = 20 cm and the insulation diameter is D2 = 40
Consider two tubes of the same diameter (D1 = 20 cm), length, and surface temperature (T1). One tube is properly centered in a cylindrical insulation of D2 = 40 cm; the other tube is placed in
Consider a 25-m-long thick-walled concrete duct (k = 0.75 W/m · K) of square cross section. The outer dimensions of the duct are 20 cm × 20 cm, and the thickness of the duct wall is 2 cm. If the
Consider a house with a flat roof whose outer dimensions are 12 m × 12 m. The outer walls of the house are 6 m high. The walls and the roof of the house are made of 20-cmthick concrete (k = 0.75 W/m
A 3-m-diameter spherical tank containing some radioactive material is buried in the ground (k = 1.4 W/m · K). The distance between the top surface of the tank and the ground surface is 4 m. If the
Radioactive material, stored in a spherical vessel of diameter D = 3.5 m, is buried underground at a depth of 10 m. The radioactive material inside the vessel releases heat at a rate of 1000 W/m3.
The unit thermal resistances (R-values) of both 40-mm and 90-mm vertical air spaces are given in Table 3–9 to be 0.22 m2 · C/W, which implies that more than doubling the thickness of air space in
What is the R-value of a wall? How does it differ from the unit thermal resistance of the wall? How is it related to the U-factor?
What is effective emissivity for a plane-parallel air space? How is it determined? How is radiation heat transfer through the air space determined when the effective emissivity is known?
What is a radiant barrier? What kind of materials are suitable for use as radiant barriers? Is it worthwhile to use radiant barriers in the attics of homes?
Consider a house whose attic space is ventilated effectively so that the air temperature in the attic is the same as the ambient air temperature at all times. Will the roof still have any effect on
The 13-mm-thick wood fiberboard sheathing of the wood stud wall in Prob. 3–161 is replaced by a 25-mm-thick rigid foam insulation. Determine the percent increase in the R-value of the wall as a
Determine the summer R-value and the U-factor of a wood frame wall that is built around 38-mm × 140-mm wood studs with a center-to-center distance of 400 mm. The 140-mm-wide cavity between the studs
The overall heat transfer coefficient (the U-value) of a wall under winter design conditions is U = 2.25 W/m2 · K. Now a layer of 100-mm face brick is added to the outside, leaving a 20-mm air space
Consider a flat ceiling that is built around 38-mm × 90-mm wood studs with a center-to-center distance of 400 mm. The lower part of the ceiling is finished with 13-mm gypsum wallboard, while the
Determine the winter R-value and the U-factor of a masonry cavity wall that consists of 100-mm common bricks, a 90-mm air space, 100-mm concrete blocks made of lightweight aggregate, 20-mm air space,
Repeat Prob. 3–165 assuming one side of both air spaces is coated with a reflective film of ε = 0.05.Data From problem 165Determine the winter R-value and the U-factor of a masonry cavity wall
Determine the winter R-value and the U-factor of a masonry wall that consists of the following layers: 100-mm face bricks, 100-mm common bricks, 25-mm urethane rigid foam insulation, and 13-mm gypsum
Determine the winter R-value and the U-factor of a masonry cavity wall that is built around 4-in-thick concrete blocks made of lightweight aggregate. The outside is finished with 4-in face brick with
The overall heat transfer coefficient (the U-value) of a wall under winter design conditions is U = 1.40 W/m2 · K. Determine the U-value of the wall under summer design conditions.
Determine the summer and winter R-values, in m2 · °C/W, of a masonry wall that consists of 100-mm face bricks, 13-mm of cement mortar, 100-mm lightweight concrete block, 40-mm air space, and 20-mm
The overall heat transfer coefficient of a wall is determined to be U = 0.075 Btu/h · ft2· F under the conditions of still air inside and winds of 7.5 mph outside. What will the U-factor be when
Determine the R-value of a ceiling that consists of a layer of 19-mm acoustical tiles whose top surface is covered with a highly reflective aluminum foil for winter conditions. Assume still air below
A cylindrical nuclear fuel rod of 15 mm in diameter is encased in a concentric hollow ceramic cylinder with inner diameter of 35 mm and outer diameter of 110 mm. This created an air gap between the
A 10-cm-long bar with a square cross-section, as shown in Fig. P3–184, consists of a 1-cm-thick copper layer (k = 400 W/m · K) and a 1-cm-thick epoxy composite layer (k = 0.4 W/m · K). Calculate
A plane wall with surface temperature of 300°C is attached with straight aluminum triangular fins (k = 236 W/m · K). The fins are exposed to an ambient air condition of 25°C and the convection
A 0.2-cm-thick, 10-cm-high, and 15-cm-long circuit board houses electronic components on one side that dissipate a total of 15 W of heat uniformly. The board is impregnated with conducting metal
A row of 10 parallel pipes that are 5 m long and have an outer diameter of 6 cm are used to transport steam at 145°C through the concrete floor (k = 0.75 W/m · K) of a 10-m × 5-m room that is
A 0.6-m-diameter, 1.9-m-long cylindrical tank containing liquefied natural gas (LNG) at 2160°C is placed at the center of a 1.9-m-long 1.4-m × 1.4-m square solid bar made of an insulating material
In a combined heat and power (CHP) generation process, by-product heat is used for domestic or industrial heating purposes. Hot steam is carried from a CHP generation plant by a tube with diameter of
A 1.4-m-diameter spherical steel tank filled with iced water at 0°C is buried underground at a location where the thermal conductivity of the soil is k 5 0.55 W/m · K. The distance between the tank
A thin-walled spherical tank in buried in the ground at a depth of 3 m. The tank has a diameter of 1.5 m, and it contains chemicals undergoing exothermic reaction that provides a uniform heat flux of
Heat is lost at a rate of 275 W per m2 area of a 15-cm thick wall with a thermal conductivity of k = 1.1 W/m · K. The temperature drop across the wall is(a) 37.5°C(b) 27.5°C(c) 16.0°C(d)
Consider a wall that consists of two layers, A and B, with the following values: kA = 0.8 W/m · K, LA = 8 cm, kB = 0.2 W/m · K, LB = 5 cm. If the temperature drop across the wall is 18°C, the rate
Heat is generated steadily in a 3-cm-diameter spherical ball. The ball is exposed to ambient air at 26°C with a heat transfer coefficient of 7.5 W/m2·K. The ball is to be covered with a material of
Consider a 1.5-m-high and 2-m-wide triple pane window. The thickness of each glass layer (k = 0.80 W/m · K) is 0.5 cm, and the thickness of each air space (k = 0.025 W/m · K) is 1 cm. If the inner
Consider two metal plates pressed against each other. Other things being equal, which of the measures below will cause the thermal contact resistance to increase?(a) Cleaning the surfaces to make
A 10-m-long 5-cm-outer-radius cylindrical steam pipe is covered with 3-cm thick cylindrical insulation with a thermal conductivity of 0.05 W/m·K. If the rate of heat loss from the pipe is 1000 W,
A 6-m-diameter spherical tank is filled with liquid oxygen (r = 1141 kg/m3, cp = 1.71 kJ/kg·°C) at 2184°C. It is observed that the temperature of oxygen increases to 2183°C in a 144-hour period.
A 2.5 m-high, 4-m-wide, and 20-cm-thick wall of a house has a thermal resistance of 0.0125°C/W. The thermal conductivity of the wall is(a) 0.72 W/m · K(b) 1.1 W/m · K(c) 1.6 W/m · K(d) 16 W/m ·
Consider two walls, A and B, with the same surface areas and the same temperature drops across their thicknesses. The ratio of thermal conductivities is kA/kB = 4 and the ratio of the wall
A hot plane surface at 100°C is exposed to air at 25°C with a combined heat transfer coefficient of 20 W/m2 · K. The heat loss from the surface is to be reduced by half by covering it with
Consider a large plane wall of thickness L = 0.3 m, thermal conductivity k = 2.5 W/m · K, and surface area A = 12 m2. The left side of the wall at x = 0 is subjected to a net heat flux of q̇0 = 700
A large plane wall has a thickness L = 50 cm and thermal conductivity k = 25 W/m ∙ K. On the left surface (x = 0), it is subjected to a uniform heat flux q̇0 while the surface temperature T0 is
A flat-plate solar collector is used to heat water by having water flow through tubes attached at the back of the thin solar absorber plate. The absorber plate has an emissivity and an absorptivity
A spherical container, with an inner radius r1 = 1 m and an outer radius r2 = 1.05 m, has its inner surface subjected to a uniform heat flux of q̇1 = 7 kW/m2. The outer surface of the container has
A spherical shell, with thermal conductivity k, has inner and outer radii of r1 and r2, respectively. The inner surface of the shell is subjected to a uniform heat flux of q̇1, while the outer
Consider a large plate of thickness L and thermal conductivity k in which heat is generated uniformly at a rate of ėgen. One side of the plate is insulated while the other side is exposed to an
Consider a large plane wall of thickness L and constant thermal conductivity k. The left side of the wall (x = 0) is maintained at a constant temperature T0, while the right surface at x = L is
Reconsider Prob. 2–93. Using the relation obtained for the variation of temperature in the cylinder, plot the temperature as a function of the radius r in the range of r = 0 to r = ro, and discuss
Reconsider Prob. 2–88. Using the relation given for the heat generation in the wall, plot the heat generation as a function of the distance x in the range of x = 0 to x = L, and discuss the
Consider a large plane wall of thickness L = 0.05 m. The wall surface at x = 0 is insulated, while the surface at x = L is maintained at a temperature of 30°C. The thermal conductivity of the wall
Consider a long solid cylinder of radius ro = 4 cm and thermal conductivity k = 25 W/m · K. Heat is generated in the cylinder uniformly at a rate of ėgen = 35 W/cm3. The side surface of the
A cylindrical fuel rod (k = 30 W/m ∙ K) of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel rod generates heat uniformly at a rate of 100 MW/m3, and the average
Consider a homogeneous spherical piece of radioactive material of radius ro = 0.04 m that is generating heat at a constant rate of ėgen = 5 × 107 W/m3. The heat generated is dissipated to the
Reconsider Prob. 2–101. Using the relation obtained for the variation of temperature in the sphere, plot the temperature as a function of the radius r in the range of r = 0 to r = ro. Also, plot
A spherical communication satellite with a diameter of 2.5 m is orbiting around the earth. The outer surface of the satellite in space has an emissivity of 0.75 and a solar absorptivity of 0.10,
Is the thermal conductivity of a medium, in general, constant or does it vary with temperature?
When the thermal conductivity of a medium varies linearly with temperature, is the average thermal conductivity always equivalent to the conductivity value at the average temperature?
The temperature of a plane wall during steady one dimensional heat conduction varies linearly when the thermal conductivity is constant. Is this still the case when the thermal conductivity varies
Consider steady one-dimensional heat conduction in a plane wall in which the thermal conductivity varies linearly. The error involved in heat transfer calculations by assuming constant thermal
A silicon wafer with thickness of 925 mm is being heated with a uniform heat flux at the lower surface. The silicon wafer has a thermal conductivity that varies with temperature and can be expressed
Consider steady one-dimensional heat conduction in a plane wall, long cylinder, and sphere with constant thermal conductivity and no heat generation. Will the temperature in any of these mediums vary
Consider a 1.5-m-high and 0.6-m-wide plate whose thickness is 0.15 m. One side of the plate is maintained at a constant temperature of 500 K while the other side is maintained at 350 K. The thermal
On the left side, a steel plate is subjected to a uniform heat flux of 50 kW/m2 and maintained at a constant temperature of 800 K. On the right side, the temperature is maintained at 600 K. The steel
Consider a plane wall of thickness L whose thermal conductivity varies in a specified temperature range as k(T)= k0(1 + βT2) where k0 and β are two specified constants. The wall surface at x = 0 is
A circular metal pipe has a wall thickness of 10 mm and an inner diameter of 10 cm. The pipe’s outer surface is subjected to a uniform heat flux of 5 kW/m2 and has a temperature of 500°C. The
The thermal conductivity of stainless steel has been characterized experimentally to vary with temperature as k(T) = 9.14 + 0.021T for 273 < T < 1500 K, where k is in W/m∙K and T is in K. Determine
A pipe is used for transporting hot fluid in which the inner surface is at 150°C. The pipe has a wall thickness of 5 mm and an inner diameter of 15 cm. The pipe wall has a variable thermal
A pipe is used for transporting boiling water in which the inner surface is at 100°C. The pipe is situated in surroundings where the ambient temperature is 10°C and the convection heat transfer
A spherical container, with an inner radius of 1 m and a wall thickness of 5 mm, has its inner surface subjected to a uniform heat flux of 7 kW/m2. The outer surface of the container is maintained at
Consider a spherical shell of inner radius r1 and outer radius r2 whose thermal conductivity varies linearly in a specified temperature range as k(T) = k0(1 + βT) where k0 and b are two specified
A spherical vessel is filled with chemicals undergoing an exothermic reaction. The reaction provides a uniform heat flux on the inner surface of the vessel. The inner diameter of the vessel is 5 m
A spherical tank is filled with ice slurry, where its inner surface is at 0°C. The tank has an inner diameter of 9 m and its wall thickness is 20 mm. The tank wall is made of a material with a
Why do we often utilize simplifying assumptions when we derive differential equations?
What is a variable? How do you distinguish a dependent variable from an independent one in a problem?
Can a differential equation involve more than one independent variable? Can it involve more than one dependent variable? Give examples.
What is the geometrical interpretation of a derivative? What is the difference between partial derivatives and ordinary derivatives?
What is the difference between the degree and the order of a derivative?
Consider a function f(x, y) and its partial derivative −f/−x. Under what conditions will this partial derivative be equal to the ordinary derivative df/dx?
Consider a function f(x) and its derivative df/dx. Does this derivative have to be a function of x?
How is integration related to derivation?
What is the difference between an algebraic equation and a differential equation?
What is the difference between an ordinary differential equation and a partial differential equation?
How is the order of a differential equation determined?

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