Find the temperature distribution at equilibrium in a rectangular plate (0 ≤ x ≤ L, 0...

Find the temperature distribution at equilibrium in a rectangular plate (0 ≤ x ≤ L, 0 ≤ y ≤ H) when the side at y = 0 is subject to the prescribed temperature g(x) = 2x, the sides at x = 0 and x = L are maintained at zero temperature, and the side at y = H is insulated, by using the method of separation of variables.

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Find the temperature distribution at equilibrium in a rectangular plate (0 ≤ x ≤ L, 0...

Find the temperature distribution at equilibrium in a rectangular plate (0 ≤ x ≤ L, 0 ≤ y ≤ H) when the side at x = 0 is subject to the prescribed temperature f(y) = 1 + y, and the sides at x = L, y = 0 and y = H are insulated, by using the method of separation of variables.

Find the steady state temperature function on a pi x pi rectangular plate, where the temperature...

Find the steady state temperature function on a pi x pi rectangular plate, where the temperature at the top edge is kept at sin(4x)oC and the remaining 3 sides are kept at 0oC

A thin rectangular plate coincides with the region defined by 0 ≤ x ≤ π, 0...

A thin rectangular plate coincides with the region defined by 0 ≤ x ≤ π, 0 ≤ y ≤ 1. The left end and right end of the plate are insulated. The bottom of the plate is held at temperature zero and the top of the plate is held at temperature f(x) = 4 cos(6x) + cos(7x). Set up an initial-boundary value problem for the steady-state temperature u(x, y).

a rectangular plate OPQR is bounded by the lines x=0, y=0 x=4, y=4 determine the potential...

a rectangular plate OPQR is bounded by the lines x=0, y=0 x=4, y=4 determine the potential distribution u(x,y) over the rectangular using the laplace equation uxx+uyy=0 boundary conditions are u(4,y), u(x,0)=0, u(x,0)=x(4-x) usimg separation of variables

a. If ? ~ ?(?,?), find the distribution (name and parameters) of ?=?X+?. b. If ?~?(0,?),...

a. If ? ~ ?(?,?), find the distribution (name and parameters) of ?=?X+?. b. If ?~?(0,?), find the density of ?=|?|. c. If ? ~ ?amma(?,?), find the distribution (name and parameters) of ?=?X. d. If ? ~ Uniform(0,1), find the density function of ?=√?. e. If Θ ~ Uniform(−?/2,?/2), find cdf and the density function of ?=tan(Θ).

Find the solution to the heat equation on 0 < x < l, with u(0, t)...

Find the solution to the heat equation on 0 < x < l, with u(0, t) = 0, ux(l, t) = 0, and u(x, 0) = phi(x). This is sometimes called a "mixed" boundary condition.

Find -A continuous r.v. X follows uniform distribution , that is ? ~ ???????(?=0,?=1), Find the...

Find -A continuous r.v. X follows uniform distribution , that is ? ~ ???????(?=0,?=1), Find the following probability (a) P(0 < X < 0.3) (b) P(0.5 < X < 1) (c) Find the mean and variance of X - A continuous r.v. X follows the pdf: ?(?)= 2?3, 1≤?≤2. (a) Find the cdf of X for 1≤?≤2. (b) Find the mean and variance of X. (c) Find P(X = 1.22) -Suppose that in a particular traffic environment, the distribution of...

Consider a rectangular plate of width L and height W. Three of the sides (left, bottom,...

Consider a rectangular plate of width L and height W. Three of the sides (left, bottom, and right side) are maintained at a constant temperature of T1 whereas the top side is maintained at T2. Write a general computer program to solve for the steady state temperature solution of the plate using finite difference techniques and the Gauss-Seidel iterative method for any arbitrary grid mesh m x n. Obtain a temperature solution using a grid mesh of 10x10, 20x20, and...

Ant on a metal plate. The temperature at a point ( x, y) on a metal...

Ant on a metal plate. The temperature at a point ( x, y) on a metal plate is T(x, y) = 4x2 - 4xy + y2 . An ant on the plate walks around the circle of radius 10 centered at the origin. a) What are the highest and lowest temperatures encountered by the ant? b) Suppose the ant has changed its trajectory and is walking around the circle of radius 5. Is the highest temperature encountered by the ant...

A.) 1 L of oxygen gas has a temperature of 0

Subjects