HEAT&MASS TRANSF. (LL) W/CONNECT<CUSTOM>
6th Edition
ISBN: 9781266141652
Author: CENGEL
Publisher: MCG
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Chapter 1, Problem 17P
A 15-cm-diameter aluminum ball is to be heated form
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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) = ω 2 x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d 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).
The heated rod from Problem 3 is subject to a volumetric heatingh(x) = h0xLin units of [Wm−3], as shown in the figure below. Under theheat supply the temperature of the rod changes along x with thetemperature function T(x). The temperature T(x) is governed by thefollowing equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx 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 heatreservoir at zero temperature.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
A heated rod of length L is subject to a volumetric heating h(x) = h0xLinunits of [Wm−3], as shown in the figure below. Under the heat supply thetemperature of the rod changes along x with the temperature functionT(x). The temperature T(x) is governed by the following equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(3)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. The left end of the bar is in contact with a heatreservoir at zero temperature, while the right end of the bar is thermallyinsulated.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
Chapter 1 Solutions
HEAT&MASS TRANSF. (LL) W/CONNECT<CUSTOM>
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Ch. 1 - Prob. 11CPCh. 1 - An ideal gas is heated from 50C to 80C (a) at...Ch. 1 - What is heat flux? How is it related to the heat...Ch. 1 - What are the mechanisms of energy transfer to a...Ch. 1 - A logic chip used in a computer dissipates 3 W of...Ch. 1 - Consider a 150-W incandescent lamp. 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What...Ch. 1 - Consider a house in Atlanta, Georgia, that is...Ch. 1 - Prob. 120PCh. 1 - A 4m5m6m and room is to be heated by one ton (1000...Ch. 1 - Engine valves (cp=440J/kg.Kandp=7840kg/m3) are to...Ch. 1 - Prob. 123PCh. 1 - Prob. 124PCh. 1 - A 0.3 -cm-thick, 12-cm-high, and 18-cm-long...Ch. 1 - A 40-cm-long, 800-W electric resistance heating...Ch. 1 - It is well known that wind makes the cold air feel...Ch. 1 - An engine block with a surface area measured to be...Ch. 1 - Prob. 129PCh. 1 - Prob. 130PCh. 1 - Prob. 131PCh. 1 - Consider a person standing in a room maintained at...Ch. 1 - Prob. 133PCh. 1 - Prob. 134PCh. 1 - Prob. 135PCh. 1 - Prob. 136PCh. 1 - Prob. 137PCh. 1 - Prob. 138PCh. 1 - Prob. 139PCh. 1 - Prob. 140PCh. 1 - Prob. 141PCh. 1 - Prob. 142PCh. 1 - A 2-kW electric resistance heater submerged in...Ch. 1 - Prob. 144PCh. 1 - A cold bottled drink (m=2.5kg,cp=4200J/kg.K) at...Ch. 1 - Prob. 146PCh. 1 - Air enters a 12-m-long, 7-cm-diameter pipe at 50oC...Ch. 1 - Prob. 148PCh. 1 - Steady heat conduction occurs through a...Ch. 1 - Heat is lost through a brick wall (k=0.72W/m.K),...Ch. 1 - Prob. 151PCh. 1 - A 40-cm-long, 0.4-cm-diameter electric resistance...Ch. 1 - Prob. 153PCh. 1 - Prob. 154PCh. 1 - Over 90 percent of the energy dissipated by an...Ch. 1 - On a still, cleat night, the sky appears to be a...Ch. 1 - Prob. 157PCh. 1 - Prob. 158PCh. 1 - A persons head can be approximated as a...Ch. 1 - A person standing in a room loses heat to the air...Ch. 1 - Write an essay on how microwave ovens work, and...Ch. 1 - Using information form the utility bill for the...Ch. 1 - It is well know that at the same outdoor air...
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