Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 13.2, Problem 6E
To determine
The boundary value problem for the temperature
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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
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
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 30ECh. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Prob. 11ECh. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - Prob. 23ECh. 13.5 - Prob. 1ECh. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 22ECh. 13.6 - Prob. 1ECh. 13.6 - Prob. 2ECh. 13.6 - Prob. 5ECh. 13.6 - Prob. 6ECh. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Prob. 12ECh. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Prob. 17ECh. 13.6 - Prob. 18ECh. 13.6 - Prob. 19ECh. 13.6 - Prob. 20ECh. 13.7 - Prob. 1ECh. 13.7 - Prob. 2ECh. 13.7 - Prob. 3ECh. 13.7 - Prob. 4ECh. 13.7 - Prob. 5ECh. 13.7 - Prob. 7ECh. 13.7 - Prob. 8ECh. 13.7 - Prob. 9ECh. 13.8 - Prob. 1ECh. 13.8 - Prob. 2ECh. 13.8 - Prob. 3ECh. 13.8 - Prob. 4ECh. 13 - Prob. 1CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Prob. 11CRCh. 13 - Prob. 12CRCh. 13 - Prob. 13CRCh. 13 - Prob. 14CRCh. 13 - Prob. 15CRCh. 13 - Prob. 16CRCh. 13 - Prob. 17CRCh. 13 - Prob. 18CRCh. 13 - Prob. 19CRCh. 13 - Prob. 20CR
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
- 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
- The steady two-dimensional temperature (7) distribution in an isotropic heat conducting materials is given by Laplace equation, The side lengths of the domain are I=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. H=6 T=100 T=50 T=50 T=100 L=8 T=40 T₁ T3 T=40 &T O'T Central finite difference formula f'(x)= f(x+h)-f(x-h) 2h ƒ"(x) = f(x+h)−2ƒ (x) + f(x−h) T=15 T₂ T₁ T=20 Figure 2 Finite difference nodal scheme बे -6 xarrow_forward4. An engineer is planning a reinforced concrete ring on their computer (see picture below). The concrete ring has an inner radius r, outer radius R and height h. Such a ring has a volume of V = Th(R² – r²). The engineer is increasing the inner radius r and the height h by 1 m/sec at a certain time to. (a) What is the rate of change of the volume V at to if the engineer fixes R to have a constant value? (your answer should possibly involve r, R and h). (b) The engineer only has a fixed amount of concrete, so they fix V = 10500T m³. If r = 10 m, h = 20 m, what is the rate of change of R at to? Reinforced concrete ring - illustration.arrow_forward4. An imaginary ant is walking on an imaginary cartesian plane so that at any point (x, y) it moves in the direction of maximum temperature increase. If the temperature at any point (x, y) is T(x, y) = -e2y cos x, find an equation of the form y = f(x) for the path of the ant if it was originally located at (T/4,0).arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY