EBK ADVANCED ENGINEERING MATHEMATICS
6th Edition
ISBN: 9781284127003
Author: ZILL
Publisher: JONES+BARTLETT LEARNING,LLC (CC)
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Question
Chapter 13.2, Problem 6E
To determine
The boundary value problem for the temperature
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2. A plane travels 560 km from Los Angeles to San Francisco in 1 hour (h). If the plane's velocity at time t
is v(t) km/h, what is the value of
v(t) dt?
2. Find the temperature distribution inside a solid parallelepiped with sides
(a, b, c) whose faces are kept at zero temperature subject to initial condi-
tion u(x, y, z, 0) = A sin() sin(7) sin().
The steady two-dimensional temperature (7) distribution in an isotropic heat conducting materials is
given by Laplace equation,
H = 6
The side lengths of the domain are L=8 and H=6.
Assuming consistent units are used, boundary conditions are shown in Figure 2. Use the grid indicated
in Figure 2 to solve for the temperature distribution.
L = 8
f'(x) =
T=100
f"(x)=
T=50
T=50
T=100
T=40
T₁
T3
²T ²T
ax² dy²
T=40
Hint: Because of symmetry, T₁-T3 and T2=T4.
Central finite difference formula
f(x+h)-f(x-h)
2h
f(x+h)-2f(x) + f(x-h)
h²
+ =0
T=15
T₂
T4
T=20
ar
Əx
Figure 2 Finite difference nodal scheme
=
X
Chapter 13 Solutions
EBK ADVANCED ENGINEERING MATHEMATICS
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
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- If y In(z- y) then y at the point where y = 0 is equal toarrow_forward4. A 6-cm by 5-cm rectangular silver plate has being uniformly generated at each point at the rate 9 = 1.5 sec. Let x represent the distance along the edge of the plate of length 6 cm and y be the distance along the edge of the plate of length 5 cm. Suppose the temperature u along the edges is kept at cal cm³ the following temperatures: u(x,0) = x(6x), u(x, 5) = 0, u(0, y) = y(5 −y), u(6, y) = 0, 0 ≤ x ≤ 6, 0 ≤ y ≤ 5, where the origin lies at the corner of the plate with coordinates (0,0) and the edges lie along the positive x- and y-axes. The steady-state temperature u = u(x, y) satisfies Poisson's equation: Uxx (x, y) + Uyy (x, y) = q K' 0 < x < 6, 0 < y < 5, where K, the thermal conductivity, is 1.04 difference method with Ax = cal cm.deg.sec 3 and 4y = 2.5. Approximate the temperature u(x, y) using the finitearrow_forwardWhat is the minimum value of y = 3 + cos 2x?arrow_forward
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