22. Solve the followings problems: a²w a²w Ət² W (0,1)=W (2,1)=0, W(x,0) = 0.05x(2-x), W, (x,0) = 0 du ²u = 3. ,1>0,0 0, 00, u(x,0) d. Find the steady-state temperature distribution for semi infant plate problem if the temperature of the bottom edge is T(x,0) = f(x) = x, the temperature of the other sides is zero, and the width of the plate is 10cm. 2 = 0° 20 Hint: solve Laplace equation + 7 n=1 4 sin(nxx/2) (-1)"+ n 0 < x < 2, 8²T 8²T Əx² ay ² =.0 u(0,1)= u(2x,t) = 0, e sin(nxx /10) hai/10 T= 0° 10 cm T(1,0)=f(x) T = 0.
22. Solve the followings problems: a²w a²w Ət² W (0,1)=W (2,1)=0, W(x,0) = 0.05x(2-x), W, (x,0) = 0 du ²u = 3. ,1>0,0 0, 00, u(x,0) d. Find the steady-state temperature distribution for semi infant plate problem if the temperature of the bottom edge is T(x,0) = f(x) = x, the temperature of the other sides is zero, and the width of the plate is 10cm. 2 = 0° 20 Hint: solve Laplace equation + 7 n=1 4 sin(nxx/2) (-1)"+ n 0 < x < 2, 8²T 8²T Əx² ay ² =.0 u(0,1)= u(2x,t) = 0, e sin(nxx /10) hai/10 T= 0° 10 cm T(1,0)=f(x) T = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
I3
Transcribed Image Text:22. Solve the followings problems:
a²w
a²W
-,t> 0, 0<x<2,
9
at² Əx²
W (0,1)=W (2,1)=0, W(x,0) = 0.05x(2-x), W, (x,0) = 0
ди ²u
3
www =
Ət
a.
b.
C.
Ans. u(x,t) = 40 + ¹+ (−1)″*¹
TC
n=1
n
ди
Ət
= 4
u(x,0): =
²u
,t> 0, 0<x<2, u(0,t) = u(2,t) = 0, u(x,0) = 20.
Əx²
[1
t>0,
0<x<T
(x π < x < 2π
bond
n=1
e
4
n
sin(nmx/2)
0 < x < 2%,
d. Find the steady-state temperature distribution for semi infant plate problem if the
temperature of the bottom edge is T(x,0) = f(x)= x, the temperature of the
other sides is zero, and the width of the plate is 10cm.
2 = 0"
Hint: solve Laplace equation
0²T 8²T
+
Əx² Əy²
Ans. T(x, y) = 20 (-1)^-10 sin(x/10)
7C
=.0
u(0,1)= u(2x,t) = 0,
2
TWO
10 cm
T(x)=f(x)=
T = 0*
Expert Solution
Step by step
Solved in 10 steps with 10 images
Recommended textbooks for you
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
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,
