Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat equation au =u, for 00. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u (0,t)=u (L,t)=0 for t>0. The condition u (0,t) = 0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition).

Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat equation au =u, for 00. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u (0,t)=u (L,t)=0 for t>0. The condition u (0,t) = 0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 4. Let y' = 4y – y². Find all equilibria and use the local stability criterion to determine if each…

Q: 1. Complete the table below. Ordinary or Partial Linear or Non- Order Degree Linear Independent…

A: Order of a differential equation is the order of the highest derivative and the degree of the…

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: 3. a.) Find the partial derivative of the function f(x, y) = x² tan y + In( sin xy) 1 b.) IF ƒ(x, y)…

Q: 1.(3.3) Let f(x, y) = x² - 3xy + 5x + 6y² - 2y+8. (1) Find critical point(s) of f. (2) Find the…

A: Step 1 Step 2: Step 3: Step 4:

Q: Find the first partial derivatives of the following functions: 5. y = Vx? – y2 6. z = In(x + /x? –…

Q: A thin rectangular plate coincides with the region defined by 0<x <1, 0< y<1. The left and right…

A: The given problem is to set up an boundary value problem with given initial conditions and boundary…

Q: The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, −10 ≤ y ≤ 10 is given by the…

A: The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, -10 ≤ y ≤ 10 is given bythe…

Q: 5. A particle of mass m moves in the one-dimensional potential x2 U(x) = U, Se-x/a Sketch U(x).…

Q: 2. Find the steady state temperature distribution v'T = 0 in a rectangular plate covering the area…

A: Given ∇2T=0 with 0<x<4,0<y<1with boundary conditions…

Q: 5. Use the separation of variables method to solve the heat equation Ut = 0 0 u(0, t) = u(27, t)…

A: Let the solution here be u(x,t)=G(x)·Y(t), where G(x) is a function of x only and Y(t) is the…

Q: (a) Given a surface function, z(x, y) == + xy with x cos0 and y= sin 0, 2 %3D az and əz (i) find ax…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the values of x, y and z that correspond to the critical point of the function ƒ(x, y) = 2x² +…

Q: (a) The temperature distribution u(x, t) of the one-dimensional silver rod is governed by the heat…

Q: 2) Given the joint pmff(x.y): X 0 X 5 X 6 X -1 X 2 Y=-3 0.1 0.25 0 0.2 0 Y-1 0 0.1 0.05 0 0 0.1 0.05…

A: Given Joint pmf f(x,y) as shown belowThe marginal pmfs are calculated using the formulas shown below

Q: Consider the multivariable function g(x, y) = x2 – 3y*x? + sin(cy). Find the following partial 12.…

A: here given as gx, y=x2-3y4x2+sin xy Thus gx=∂∂xx2-3y4x2+sin xy treat y as constant=2x-6xy4+ycos xy…

Q: Find an antiderivative F(x) with F′(x)=f(x)=11+24x^3+21x^6 and F(1)=0. Include a "+C" if…

Q: 3. Use the Chain Rule to find the indicated partial derivatives. (a) w = x² + y² + z², x = st, y = s…

A: Note- As per company guidelines for multiple questions posted we are allowed to solve only one…

Q: 11) If f(x,y) = xe' – y In(x² +1) find af af and dy

Q: There is a partial insurance policy that pays $80,000 upon the bad drought state (and $0 in the…

Q: . Find all second order partial derivatives of the functions given below. (a) f(x,y) = xe + y + 1 Y…

Q: Solve the heat transfer equation for a metal rod in one dimension, assuming a constant cross-section…

Q: (t) = A cos(wt) + B sin(wt)? b) An undamped oscillation under the influence of external force is…

Q: 1. The heat equation is an equation involving the partial derivatives of a function u(r,t): du Fu at…

A: The heat equation is ∂u∂t=∂2u∂x2. To show: ux, t=cosnxe-n2t satisfies the heat equation.…

Q: 3. (Free-driving force, damped mass-spring system). Recall that the underdamped motion of the system…

Question

100%

Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat
equation au =u, for 0<x<L and t>0. Use separation of variables method to
find the unsteady state temperature distribution in the strip given that the initial
condition
is
u(x,0) =x
and
the
boundary
conditions
u (0,t)=u (L,t)=0 for t>0.
The
condition
u, (0,t) = 0
expresses
mathematically the constraint that no heat flows through the left boundary (insulated
end condition).
-H.W. Problems P.327 "wylie" Q.5,7,8

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Double Integration$

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

Provide the General Solution of each differential equations. Box your Final Answer and show your solutions:
(a) Find the indicated partial derivatives for f(x,y,2) = xln(xy²z') (1) f.y (ii) fax (b) Use az the Chain Rule to find and if as at () Z=tan u=2s+31, v =3s-21.
2. For z = ln y? dz calculate the partial derivatives az 2 — ет and he
2" Q2: Find the Partial Derivatives of the functions with respect to each variable x and y and z: 1. f(x,y) = sin²(x – 2y) %3D
Consider the heat equation Ut = auxx, a € R⁰, 00 with boundary conditions ur(0,t) = ur(L,t)=0, t>0. i. Give a meaningful interpretation of the boundary conditions.
1. Please rewire the expression below without the summation operator. 2. Example: For the numbers 2, 3, 6, and 9, please find а. ai b. a? W-