Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 3, Problem 3.11P
Determine the thermal conductivity of the carbon nanotube of Example 3.4 when the heating island temperature is measured to be
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PROBLEM 1:
The block of 304 stainless steel shown below is well insulated on the front and back surfaces, and the temperature in the block varies
linearly in both the x- and y-directions. Find:
(a) The heat fluxes and heat flows in the x- and y-directions.
(b) The magnitude and direction of the heat flux vector.
15°C
5°C
5 cm
y
5 cm-
10 cm
The thermal conductivity of 304 stainless steel is 14.4 W/m K.
10°C
0°C
What is the analogical reason between heat transfer by conduction and flow of electricity through ohmic resistance? Use a composite wall of a building to illustrate the concept. A composite slab with three layers of thermal conductivities k1, k2, k3 and thickness ti, t2, të respectively, are placed in a close contact. Derive an expression from the first principle for the heat flow through the composite slab per unit surface area in terms of the overall temperature difference across the slab.
1. The four sides of a square plate of side 12 cm, made of homogeneous material,
are kept at constant temperature and as shown in Fig. Using a (very wide) grid
of mesh 4 cm and applying Gauss-Seidel iteration with ek < 0.0001, find the
(steady-state) temperature at the mesh (interior) points.
y
u = 0
12
u = 100
u = 100
R
12
u = 100
Chapter 3 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 3 - Consider the plane wall of Figure 3.1, separating...Ch. 3 - A new building to be located in a cold climate is...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - A dormitory at a large university, built 50 years...Ch. 3 - In a manufacturing process, a transparent film is...Ch. 3 - The walls of a refrigerator are typically...Ch. 3 - A t=10-mm -thick horizontal layer of water has a...Ch. 3 - A technique for measuring convection heat transfer...Ch. 3 - The wind chill, which is experienced on a cold,...
Ch. 3 - Determine the thermal conductivity of the carbon...Ch. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Consider the composite wall of Problem 3.13 under...Ch. 3 - Consider a composite wall that includes an...Ch. 3 - Work Problem 3.15 assuming surfaces parallel to...Ch. 3 - Consider the oven of Problem 1.54. The walls of...Ch. 3 - The composite wall of an oven consists of three...Ch. 3 - The wall of a drying oven is constructed by...Ch. 3 - The t=4-mm-thick glass windows of an automobile...Ch. 3 - The thermal characteristics of a small, dormitory...Ch. 3 - In the design of buildings, energy conservation...Ch. 3 - When raised to very high temperatures. many...Ch. 3 - A firefighter's protective clothing, referred to...Ch. 3 - A particular thermal system involves three objects...Ch. 3 - A composite wall separates combustion gases at...Ch. 3 - Approximately 106 discrete electrical components...Ch. 3 - Two stainless steel plates 10 mm thick are...Ch. 3 - Consider a plane composite wall that is composed...Ch. 3 - The performance of gas turbine engines may be...Ch. 3 - A commercial grade cubical freezer, 3 m on a side,...Ch. 3 - Physicists have determined the theoretical value...Ch. 3 - Consider a power transistor encapsulated in an...Ch. 3 - Ring-porous woods, such as oak, are characterized...Ch. 3 - A batt of glass fiber insulation is of density...Ch. 3 - Air usually constitutes up to half of the volume...Ch. 3 - Determine the density, specific heat, and thermal...Ch. 3 - A one-dimensional plane wall of thickness L is...Ch. 3 - The diagram shows a conical section fabricated...Ch. 3 - A truncated solid cone is of circular cross...Ch. 3 - From Figure 2.5 it is evident that, over a wide...Ch. 3 - Consider a tube wall of inner and outer radii ri...Ch. 3 - Measurements show that steady-state conduction...Ch. 3 - A device used to measure the surface temperature...Ch. 3 - A steam pipe of 0.12-m outside diameter is...Ch. 3 - Consider the water heater described in Problem...Ch. 3 - To maximize production and minimize pumping costs....Ch. 3 - A thin electrical heater is wrapped around the...Ch. 3 - A stainless steel (AISI 304) tube used to...Ch. 3 - A thin electrical heater is inserted between a...Ch. 3 - A 2-mm-diameter electrical wire is insulated by a...Ch. 3 - Electric current flows through a long rod...Ch. 3 - A composite cylindrical wall is composed of two...Ch. 3 - An electrical current of 700 A flows through a...Ch. 3 - A 0.20-m-diameter. thin-walled steel pipe is used...Ch. 3 - An uninsulated. thin-walled pipe of 100-mm...Ch. 3 - Steam flowing through a long. thin-walled pipe...Ch. 3 - A storage tank consists of a cylindrical section...Ch. 3 - Consider the liquid oxygen storage system and the...Ch. 3 - A spherical Pyrex glass shell has inside and...Ch. 3 - In Example 3.6. an expression was derived for the...Ch. 3 - A hollow aluminum sphere. with an electrical...Ch. 3 - A spherical tank for storing liquid oxygen on the...Ch. 3 - A spherical, cryosurgical probe may be imbedded in...Ch. 3 - Prob. 3.70PCh. 3 - Prob. 3.71PCh. 3 - A composite spherical shell of inner radius...Ch. 3 - The energy transferred from the anterior chamber...Ch. 3 - The outer surface of a hollow sphere of radius r2...Ch. 3 - A spherical shell of inner and outer radii r1 and...Ch. 3 - Prob. 3.76PCh. 3 - Prob. 3.77PCh. 3 - Prob. 3.78PCh. 3 - The air inside a chamber at T,i=50C is heated...Ch. 3 - Prob. 3.80PCh. 3 - A plane wall of thickness 0.1 m and thermal...Ch. 3 - Large, cylindrical bales of hay used to feed...Ch. 3 - Prob. 3.83PCh. 3 - Consider one-dimensional conduction in a plane...Ch. 3 - Consider a plane composite wall that is composed...Ch. 3 - An air heater may be fabricated by coiling...Ch. 3 - Prob. 3.87PCh. 3 - Consider uniform thermal energy generation inside...Ch. 3 - A plane wall of thickness and thermal conductivity...Ch. 3 - A nuclear fuel element of thickness 21, is covered...Ch. 3 - In Problem 3.79 the strip heater acts to guard...Ch. 3 - The exposed surface (x=0) of a plane wall of...Ch. 3 - A quartz window of thickness L serves as a viewing...Ch. 3 - For the conditions described in Problem 1.44....Ch. 3 - A cylindrical shell of inner and outer radii, ri...Ch. 3 - The cross section of a long cylindrical fuel...Ch. 3 - A long cylindrical rod of diameter 200 mm with...Ch. 3 - A radioactive material of thermal conductivity k...Ch. 3 - Radioactive wastes are packed in a thin-walled...Ch. 3 - Radioactive wastes (ktw=20W/mK) are stored in a...Ch. 3 - Unique characteristics of biologically active...Ch. 3 - Consider the plane wall, long cylinder, and sphere...Ch. 3 - One method that is used to grow nanowires...Ch. 3 - Consider the manufacture of photovoltaic silicon,...Ch. 3 - Copper tubing is joined to a solar collector plate...Ch. 3 - A thin flat plate of length L thickness t. and...Ch. 3 - The temperature of a flowing gas is to be measured...Ch. 3 - A thin metallic wire of thermal conductivity k,...Ch. 3 - A motor draws electric power Pelec from a supply...Ch. 3 - Consider the fuel cell stack of Problem 158. The...Ch. 3 - Consider a rod of diameter D, thermal conductivity...Ch. 3 - A carbon nanotube is suspended across a trench of...Ch. 3 - A probe of overall length L=200mm and diameter...Ch. 3 - A metal rod of length 2L diameter D, and thermal...Ch. 3 - A very long rod of 5-mm diameter and uniform...Ch. 3 - From Problem 1.71, consider the wire leads...Ch. 3 - Turbine blades mounted to a rotating disc in a...Ch. 3 - Prob. 3.127PCh. 3 - Prob. 3.128PCh. 3 - Prob. 3.129PCh. 3 - A brass rod 100 mm long and 5 mm in diameter...Ch. 3 - The extent to which the tip condition affects the...Ch. 3 - A pin fin of uniform. cross-sectional area is...Ch. 3 - The extent to which the tip condition affects the...Ch. 3 - A straight tin fabricated from 2024 aluminum alloy...Ch. 3 - Triangular and parabolic straight tins are...Ch. 3 - Two long copper rods of diameter D=10mm are...Ch. 3 - Circular copper rods of diameter D=1mm and length...Ch. 3 - During the initial stages of the growth of the...Ch. 3 - Consider two long, slender rods of the same...Ch. 3 - A 40-mm-long, 2-mm-diameter pin fin is fabricated...Ch. 3 - An experimental arrangement for measuring the...Ch. 3 - Finned passages are frequently formed between...Ch. 3 - The fin array of Problem 3.142 is commonly found...Ch. 3 - An isothermal silicon chip of width W=20mm on a...Ch. 3 - As seen in Problem 3.109, silicon carbide...Ch. 3 - A homeowner's wood stove is equipped with a top...Ch. 3 - Water is heated by submerging 50-mm-diameter,...Ch. 3 - As a means of enhancing heat transfer from...Ch. 3 - Consider design B of Problem 3.151. Over time....Ch. 3 - Determine the percentage increase in heat transfer...Ch. 3 - Aluminum fins of triangular profile are attached...Ch. 3 - An annular aluminum fin of rectangular profile is...Ch. 3 - Annular aluminum fins of rectangular profile are...Ch. 3 - It is proposed to air-cool the cylinders of a...Ch. 3 - Prob. 3.165PCh. 3 - Prob. 3.166PCh. 3 - Prob. 3.168PCh. 3 - Prob. 3.173PCh. 3 - Prob. 3.174PCh. 3 - Prob. 3.175PCh. 3 - A nanolaminated material is fabricated with an...
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