Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 1, Problem 1.11P
The heat flux that is applied to one face of a plane wallis
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
A ball with a mass of 5.0 kg is hanging from a string and is initially at rest.
A bullet with a mass of 10.0 g and a velocity of 200.0 m/s is fired at the ball.
The bullet embeds itself inside the ball.
How high (h) do the ball and the bullet rise?
Gravitational acceleration: g=9.81g = 9.81g=9.81 m/s².
Don't use chatgpt.
Need handwritten solution.
Mechanical engineering
Chapter 1 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 1 - The thermal conductivity of a sheet of rigid,...Ch. 1 - The heat flux that is applied to the left face of...Ch. 1 - A concrete wall, which has a surface area of 20m2...Ch. 1 - The concrete slab of a basement is 11 in long. 8...Ch. 1 - Consider Figure 1.3. The heat flux in the...Ch. 1 - The heal flux through a wood slab 50 mm thick,...Ch. 1 - The inner and outer surface temperatures of a...Ch. 1 - A thermodynamic analysis of a proposed Brayton...Ch. 1 - A glass window of width W=1m and height H=2m is 5...Ch. 1 - A freezer compartment consists of a cubical cavity...
Ch. 1 - The heat flux that is applied to one face of a...Ch. 1 - An inexpensive food and beverage container is...Ch. 1 - What is the thickness required of a masonry wall...Ch. 1 - A wall is made from an inhomogeneous...Ch. 1 - The 5-mm-thick bottom of a 200-mm-diameter panmay...Ch. 1 - A square silicon chip (k=150W/mK) is of width...Ch. 1 - For a boiling process such as shown in Figure 1.5...Ch. 1 - You’ve experienced convection cooling if you’ve...Ch. 1 - Air at 40°C flows over a long, 25-mm-diameter...Ch. 1 - A wall has inner and outer surface temperatures of...Ch. 1 - An electric resistance heater is embedded in a...Ch. 1 - The free convection heat transfer coefficient on a...Ch. 1 - A transmission case measures W=0.30m on a sideand...Ch. 1 - A cartridge electrical heater is shaped as a...Ch. 1 - A common procedure for measuring the velocity of...Ch. 1 - A square isothermal chip is of width w=5mm on...Ch. 1 - The temperature controller for a clothes dryer...Ch. 1 - An overhead 25-m-long, uninsulated industrial...Ch. 1 - Under conditions for which the same room...Ch. 1 - A spherical interplanetary probe of 0.5-m diameter...Ch. 1 - An instrumentation package has a spherical outer...Ch. 1 - Consider the conditions of Problem 1.22. However,...Ch. 1 - If TsTsur in Equation 1.9, the radiation heat...Ch. 1 - A vacuum system, as used ¡n sputtering...Ch. 1 - An electrical resistor is connected to a battery,...Ch. 1 - Pressurized water (pin=10bar,Tin=110C) enters...Ch. 1 - Consider the tube and inlet conditions of Problem...Ch. 1 - An internally reversible refrigerator has a...Ch. 1 - A household refrigerator operates with cold-...Ch. 1 - Chips of width L=15mm on a side are mounted to...Ch. 1 - Consider the transmission case of Problem 1...Ch. 1 - One method for growing thin silicon sheets for...Ch. 1 - Heat is transferred by radiation and convection...Ch. 1 - Radioactive wastes are packed in a long,...Ch. 1 - An aluminum plate 4 mm thick is mounted in a...Ch. 1 - A blood warmer is to be used during the...Ch. 1 - Consider a carton of milk that is refrigerated at...Ch. 1 - Prob. 1.48PCh. 1 - Liquid oxygen, which has a boiling into of 90 K...Ch. 1 - The emissivity of galvanized steel sheet, a...Ch. 1 - Three electric resistance heaters of length...Ch. 1 - A hair dryer may be idealized as a circular duct...Ch. 1 - In one stage of an annealing process, 304...Ch. 1 - Convection ovens operate on the principle of...Ch. 1 - Annealing, an important step ¡n semiconductor...Ch. 1 - In the thermal processing of semiconductor...Ch. 1 - A furnace tor processing semiconductor materials...Ch. 1 - Prob. 1.58PCh. 1 - Consider the wind turbine of Example 1.3. To...Ch. 1 - Consider the conducting rod of Example 1.4...Ch. 1 - A long bus bar (cylindrical rod used for making...Ch. 1 - A 50mm45mm20mm cell phone chargerhas a surface...Ch. 1 - A spherical, stainless steel (AISI 302) canister...Ch. 1 - A freezer compartment is covered with a...Ch. 1 - A vertical slab of Wood’s metal is joined to a...Ch. 1 - A photovoltaic panel of dimension 2m4m isinstalled...Ch. 1 - Following the hot vacuum forming of a...Ch. 1 - Prob. 1.69PCh. 1 - A computer consists of an array of five printed...Ch. 1 - Prob. 1.71PCh. 1 - The roof of a car in a parking lot absorbs a solar...Ch. 1 - Consider the conditions of Problem 1.22,but the...Ch. 1 - Most of the energy we consume as food ¡s converted...Ch. 1 - Prob. 1.75PCh. 1 - The wall of an oven used to cure plastic parts is...Ch. 1 - An experiment to determine the convection...Ch. 1 - A thin electrical heating element provides a...Ch. 1 - A rectangular forced air healing duct is suspended...Ch. 1 - Consider the steam pipe of Example 1.2. The...Ch. 1 - During its manufacture, plate glass at 600°C is...Ch. 1 - The curing press of Example 1.9 involves exposure...Ch. 1 - The diameter and surface emissivity of an...Ch. 1 - Prob. 1.84PCh. 1 - A solar flux of 700W/m2K is incident on a...Ch. 1 - In considering the following problems involving...
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