Thermodynamics: An Engineering Approach
8th Edition
ISBN: 9780073398174
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 2.8, Problem 85P
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The heated rod from Problem 3 is subject to a volumetric heating
h(x) = h0
x
L in units of [Wm−3], as shown in the figure below. Under the
heat supply the temperature of the rod changes along x with the
temperature function T (x). The temperature T (x) is governed by the
d
following equations:
−
dx (q(x)) + h(x) = 0 PDE
q(x) =−k dT
dx Fourier’s law of heat conduction (4)
where q(x) is the heat flux through the rod and k is the (constant)
thermal conductivity. Both ends of the bar are in contact with a heat
reservoir at zero temperature.
Determine:
1. Appropriate BCs for this physical problem.
2. The temperature function T (x).
3. The heat flux function q(x).
Side Note: Please see that both ends of bar are in contact with a heat reservoir at zero temperature so the boundary condition at the right cannot be du/dx=0 because its not thermally insulated. Thank you
The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω2x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement d u(x) is governed by the following equations: dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L. Determine: 1. Appropriate BCs for this physical problem. 2. The displacement function u(x). 3. The stress function σ(x). SIDE QUESTION: I saw a tutor solve it before but I didn't understand why the tutor did not divide E under the second term (c1x) before finding u(x). The tutor only divided E under first term. please explain and thank you
calculate the total power required to go 80 mph in a VW Type 2 Samba Bus weighing 2310 lbs. with a Cd of 0.35 and a frontal area of 30ft^2. Consider the coefficient of rolling resistance to be 0.018. What is the increase in power required to go the same speed if the weight is increased by 2205 pounds (the rated carrying capacity of the vehicle). If the rated power for the vehicle is 49 bhp, will the van be able to reach 80 mph at full carrying capacity?
Chapter 2 Solutions
Thermodynamics: An Engineering Approach
Ch. 2.8 - What is total energy? Identify the different forms...Ch. 2.8 - List the forms of energy that contribute to the...Ch. 2.8 - How are heat, internal energy, and thermal energy...Ch. 2.8 - What is mechanical energy? How does it differ from...Ch. 2.8 - Natural gas, which is mostly methane CH4, is a...Ch. 2.8 - Portable electric heaters are commonly used to...Ch. 2.8 - Prob. 7PCh. 2.8 - Prob. 8PCh. 2.8 - 2–9E Calculate the total potential energy, in Btu,...Ch. 2.8 - Prob. 10P
Ch. 2.8 - Prob. 11PCh. 2.8 - At a certain location, wind is blowing steadily at...Ch. 2.8 - A water jet that leaves a nozzle at 60 m/s at a...Ch. 2.8 - Prob. 14PCh. 2.8 - Prob. 15PCh. 2.8 - Consider a river flowing toward a lake at an...Ch. 2.8 - When is the energy crossing the boundaries of a...Ch. 2.8 - Consider an automobile traveling at a constant...Ch. 2.8 - A gas in a pistoncylinder device is compressed,...Ch. 2.8 - A room is heated by an iron that is left plugged...Ch. 2.8 - A room is heated as a result of solar radiation...Ch. 2.8 - Prob. 23PCh. 2.8 - A small electrical motor produces 5 W of...Ch. 2.8 - Prob. 25PCh. 2.8 - 2–26C Lifting a weight to a height of 20 m takes...Ch. 2.8 - Prob. 27PCh. 2.8 - Prob. 28PCh. 2.8 - Prob. 29PCh. 2.8 - Prob. 30PCh. 2.8 - Prob. 31PCh. 2.8 - Prob. 32PCh. 2.8 - Prob. 33PCh. 2.8 - A ski lift has a one-way length of 1 km and a...Ch. 2.8 - The engine of a 1500-kg automobile has a power...Ch. 2.8 - Prob. 36PCh. 2.8 - What are the different mechanisms for transferring...Ch. 2.8 - On a hot summer day, a student turns his fan on...Ch. 2.8 - Prob. 39PCh. 2.8 - A vertical pistoncylinder device contains water...Ch. 2.8 - At winter design conditions, a house is projected...Ch. 2.8 - A water pump increases the water pressure from 15...Ch. 2.8 - Prob. 43PCh. 2.8 - Prob. 44PCh. 2.8 - A university campus has 200 classrooms and 400...Ch. 2.8 - Prob. 46PCh. 2.8 - Consider a room that is initially at the outdoor...Ch. 2.8 - Prob. 48PCh. 2.8 - 2-49 The 60-W fan of a central heating system is...Ch. 2.8 - Prob. 50PCh. 2.8 - An escalator in a shopping center is designed to...Ch. 2.8 - Prob. 52PCh. 2.8 - How is the combined pumpmotor efficiency of a pump...Ch. 2.8 - Prob. 54PCh. 2.8 - Can the combined turbinegenerator efficiency be...Ch. 2.8 - Consider a 2.4-kW hooded electric open burner in...Ch. 2.8 - Prob. 57PCh. 2.8 - Prob. 58PCh. 2.8 - Prob. 59PCh. 2.8 - A geothermal pump is used to pump brine whose...Ch. 2.8 - Prob. 62PCh. 2.8 - Prob. 63PCh. 2.8 - The water in a large lake is to be used to...Ch. 2.8 - A 7-hp (shaft) pump is used to raise water to an...Ch. 2.8 - At a certain location, wind is blowing steadily at...Ch. 2.8 - Reconsider Prob. 265. Using appropriate software,...Ch. 2.8 - Water is pumped from a lake to a storage tank 15 m...Ch. 2.8 - Prob. 69PCh. 2.8 - A hydraulic turbine has 85 m of elevation...Ch. 2.8 - Prob. 71PCh. 2.8 - Water is pumped from a lower reservoir to a higher...Ch. 2.8 - Prob. 73PCh. 2.8 - An oil pump is drawing 44 kW of electric power...Ch. 2.8 - How does energy conversion affect the environment?...Ch. 2.8 - What is acid rain? Why is it called a rain? How do...Ch. 2.8 - Why is carbon monoxide a dangerous air pollutant?...Ch. 2.8 - What is the greenhouse effect? How does the excess...Ch. 2.8 - What is smog? What does it consist of? How does...Ch. 2.8 - Prob. 80PCh. 2.8 - Consider a household that uses 14,000 kWh of...Ch. 2.8 - When a hydrocarbon fuel is burned, almost all of...Ch. 2.8 - Prob. 83PCh. 2.8 - A typical car driven 20,000 km a year emits to the...Ch. 2.8 - What are the mechanisms of heat transfer?Ch. 2.8 - Which is a better heat conductor, diamond or...Ch. 2.8 - How does forced convection differ from natural...Ch. 2.8 - What is a blackbody? How do real bodies differ...Ch. 2.8 - Define emissivity and absorptivity. What is...Ch. 2.8 - Does any of the energy of the sun reach the earth...Ch. 2.8 - The inner and outer surfaces of a 5-m 6-m brick...Ch. 2.8 - The inner and outer surfaces of a 0.5-cm-thick 2-m...Ch. 2.8 - Reconsider Prob. 292. Using appropriate software,...Ch. 2.8 - Prob. 94PCh. 2.8 - Prob. 95PCh. 2.8 - Prob. 96PCh. 2.8 - Prob. 97PCh. 2.8 - For heat transfer purposes, a standing man can be...Ch. 2.8 - Prob. 99PCh. 2.8 - Prob. 100PCh. 2.8 - A 1000-W iron is left on the ironing board with...Ch. 2.8 - A 7-cm-external-diameter, 18-m-long hot-water pipe...Ch. 2.8 - A thin metal plate is insulated on the back and...Ch. 2.8 - Reconsider Prob. 2103. Using appropriate software,...Ch. 2.8 - The outer surface of a spacecraft in space has an...Ch. 2.8 - Prob. 106PCh. 2.8 - A hollow spherical iron container whose outer...Ch. 2.8 - Consider a vertical elevator whose cabin has a...Ch. 2.8 - Consider a homeowner who is replacing his...Ch. 2.8 - Prob. 110RPCh. 2.8 - Prob. 111RPCh. 2.8 - Prob. 112RPCh. 2.8 - 2–113 The U.S. Department of Energy estimates that...Ch. 2.8 - Prob. 114RPCh. 2.8 - Prob. 115RPCh. 2.8 - Prob. 116RPCh. 2.8 - Prob. 117RPCh. 2.8 - Consider a TV set that consumes 120 W of electric...Ch. 2.8 - Water is pumped from a 200-ft-deep well into a...Ch. 2.8 - Prob. 120RPCh. 2.8 - Prob. 121RPCh. 2.8 - In a hydroelectric power plant, 65 m3/s of water...Ch. 2.8 - The demand for electric power is usually much...Ch. 2.8 - The pump of a water distribution system is powered...Ch. 2.8 - On a hot summer day, the air in a well-sealed room...Ch. 2.8 - Prob. 126FEPCh. 2.8 - A 2-kW electric resistance heater in a room is...Ch. 2.8 - A 900-kg car cruising at a constant speed of 60...Ch. 2.8 - Prob. 129FEPCh. 2.8 - Prob. 130FEPCh. 2.8 - Prob. 131FEPCh. 2.8 - A 2-kW pump is used to pump kerosene ( = 0.820...Ch. 2.8 - Prob. 133FEPCh. 2.8 - Prob. 134FEPCh. 2.8 - Prob. 135FEPCh. 2.8 - Prob. 136FEPCh. 2.8 - Prob. 137FEPCh. 2.8 - Heat is transferred steadily through a...Ch. 2.8 - The roof of an electrically heated house is 7 m...
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