Homework Answers
![Hence Solution (4) reduces to ucast) 을 sin (2m-) 4 (2m-1) Ta &mas) ²+ in je IT mol u cart) 4 (2 m 1971 sin((2m-1) 2] e-(2m-2)](http://img.homeworklib.com/questions/4dd6d100-5505-11eb-9f26-f5f86095ca34.png?x-oss-process=image/resize,w_560)
Add Answer to:
Show that for the completely insulated bar (including the ends), ux(0,t) = 0, uz(L,t) 0, and...
(a) The heat flux through the faces at the ends of bar is found to be...
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
* Exercise 4: Let k,l 〉 0. The temperature of a rod insulated at the ends...
* Exercise 4: Let k,l 〉 0. The temperature of a rod insulated at the ends with an expo- nentially decreasing heat source in it satisfies the following problem: ux (0, t) u(z,0) 0 = ux (1, t), φ(z) Find the solution to this problem by writing u as a cosine series: Ao(t) u(x, t) An(t) cos and determine limt-Hou(z, t
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t)...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...
Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends...
Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends are also insulated, assuming the same initial temperature profile as in Problem 5. Hint: remember that if the end points are thermally insulated, there is no heat flow. Hence, the temperature gradient must vanish at the endpoints! Problem 5 Find the temperature in a laterally insulated bar of length whose ends are kept at 0° Celsius, assuming that the initial temperature distribution is in...
Problem 1 (Submit): Longitudinal vibrations of an elastic bar with zero strain and stress at both...
Problem 1 (Submit): Longitudinal vibrations of an elastic bar with zero strain and stress at both ends satisfies the following initial-boundary value problem ras ux(0, t) = uz(r,t) 0 u(z,0) = 5 cos(x), ut(z,0) = 1-cos(2r). (a) Use the method of separation of variables to solve this problem. (b) Find the D'Alembert's solution for this initial-boundary value problem and compare it to the solution you found in (a).
Problem 1 (Submit): Longitudinal vibrations of an elastic bar with zero strain...
5. [8] A bar of length a cm is insulated at both ends. Find the temperature...
5. [8] A bar of length a cm is insulated at both ends. Find the temperature u(x,t), when 3, and u(x,0) = f(x) = x. Find and give an interpretation of the steady state solution. a =
Find the temperature u(x, t) in a rod of length L if the initial temperature is...
Find the temperature u(x, t) in a rod of length L if the initial temperature is f(x) throughout and if the ends x = 0 and x = L are insulated. Solve if L = 2 and f(x) = Jx, 0<x< 1 10, 1<x< 2. ux, t) = + ŠL n = 1
a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0)...
a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0) = cos 3x, u(,0) = 21 b) Consider the heat equation диди 0<x<1, t > 0, at ax? with boundary conditions uz (0,t) = 0, uz(1,t) = 0, > 0, and initial conditions u(x,0) = { 0, 2.0, 0<r < 0.5, 0.5 <<1. Use the method of separation of variables to solve the equation.
2. Consider the initial-boundary value problem 0 0, t >0 Uz uェェ, Uz(0, t) _ u(0, t) = 0. a(z, 0...
PDE questions. Please show all
steps in detail.
2. Consider the initial-boundary value problem 0
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
* Exercise 4: Let k,l 〉 0. The temperature of a rod insulated at the ends with an expo- nentially decreasing heat source in it satisfies the following problem: ux (0, t) u(z,0) 0 = ux (1, t), φ(z) Find the solution to this problem by writing u as a cosine series: Ao(t) u(x, t) An(t) cos and determine limt-Hou(z, t
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...
Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends are also insulated, assuming the same initial temperature profile as in Problem 5. Hint: remember that if the end points are thermally insulated, there is no heat flow. Hence, the temperature gradient must vanish at the endpoints! Problem 5 Find the temperature in a laterally insulated bar of length whose ends are kept at 0° Celsius, assuming that the initial temperature distribution is in...
Problem 1 (Submit): Longitudinal vibrations of an elastic bar with zero strain and stress at both ends satisfies the following initial-boundary value problem ras ux(0, t) = uz(r,t) 0 u(z,0) = 5 cos(x), ut(z,0) = 1-cos(2r). (a) Use the method of separation of variables to solve this problem. (b) Find the D'Alembert's solution for this initial-boundary value problem and compare it to the solution you found in (a).
Problem 1 (Submit): Longitudinal vibrations of an elastic bar with zero strain...
5. [8] A bar of length a cm is insulated at both ends. Find the temperature u(x,t), when 3, and u(x,0) = f(x) = x. Find and give an interpretation of the steady state solution. a =
Find the temperature u(x, t) in a rod of length L if the initial temperature is f(x) throughout and if the ends x = 0 and x = L are insulated. Solve if L = 2 and f(x) = Jx, 0<x< 1 10, 1<x< 2. ux, t) = + ŠL n = 1
a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0) = cos 3x, u(,0) = 21 b) Consider the heat equation диди 0<x<1, t > 0, at ax? with boundary conditions uz (0,t) = 0, uz(1,t) = 0, > 0, and initial conditions u(x,0) = { 0, 2.0, 0<r < 0.5, 0.5 <<1. Use the method of separation of variables to solve the equation.
PDE questions. Please show all
steps in detail.
2. Consider the initial-boundary value problem 0
Most questions answered within 3 hours.
-
A motor produces a torque of 0.25 N m at an angular velocity of
7200 revolutions...
asked 3 minutes ago -
***Please answer the below java question***
Are static methods inheritable? Can they be overridden?
asked 6 minutes ago -
In reaching her destination, a backpacker walks with an average
velocity of 1.13 m/s, due west....
asked 6 minutes ago -
Write two C programs that run a
server program and a client program concurrently.
Server program:...
asked 5 minutes ago -
Executive Program Practical Connection Assignment
Subject : Operations Security.
Assignment:
Provide a reflection of at least...
asked 15 minutes ago -
Every time Casey is at bat he has a 0.4 probability of
getting on base (assume...
asked 23 minutes ago -
The Walston Company is to be liquidated and has the following
liabilities:
Income taxes
$
9,400...
asked 30 minutes ago -
If
the more comprehensive data is available in MEPS, why does the NHIS
still exist? How...
asked 52 minutes ago -
Koo argues that the Japanese economy in the 1990s suffered from
a balance sheet recession. What...
asked 45 minutes ago -
Automobile mechanics conduct diagnosis tests on 150 new cars of
particular make and model to determine...
asked 39 minutes ago -
11) Find the proceeds of a 5 year non-interest
bearing note for $6500 discounted 2.5 years...
asked 46 minutes ago -
Required: Prepare the consolidated financial statements of
Griffin Ltd at 30 June 2019.
Griffin Ltd is...
asked 55 minutes ago