![Question 1 [Total 20 marks] (a) [5 marks] In a steady-state two-dimensional heat flow problem, the temperature, u, at any poi](http://img.homeworklib.com/images/26df5c1e-c7f9-4c2b-8d80-956bc98d736c.png?x-oss-process=image/resize,w_560)
Homework Answers
Any query then comment below...i will help you..
We use central difference approximation of 2nd derivative....
Add Answer to:
Question 1 [Total 20 marks] (a) [5 marks] In a steady-state two-dimensional heat flow problem, th...
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the doma...
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at points a, b, and c using a numerical method. 0 4 4
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at...
The two-dimensional heat equation reduces to Laplace's equation to = 0 if the temperature u is...
The two-dimensional heat equation reduces to Laplace's equation to = 0 if the temperature u is steady-state. u(x, y) is defined in 0<x<2 and 0 Sys2 and satisfy u(x,0) = u(x, 2) = u(0, y) = 0 and u(2, y) = 80 sin my. Answer the following questions. (1) Obtain two ODES (Ordinary Differential Equations) by the method of separation of variables. (2) Find u(x, y) satisfying the boundary condition. (3) Obtain the value of u(1,5).
Consider two-dimensional steady-state heat conduction in a rectangular region of cross-section 2L by 3L subject to...
Consider two-dimensional steady-state heat conduction in a
rectangular region of cross-section 2L by 3L subject to boundary
conditions shown below. By using a mesh size deltax = deltay = L,
write the finite difference equations for this problem, and
calculate the node temperatures T1, T2, T3 and T4.
2 4 3 yL dee itc ft u esu
& 2 The two-dimensional Laplace equation or? ? = 0, describes potentials and steady-state temperature distributions...
& 2 The two-dimensional Laplace equation or? ? = 0, describes potentials and steady-state temperature distributions in a plane. Show that the following function satisfies the two-dimensional Laplace equation f(x y) = -7x + y + 4 में Find for the given function che? #t ax?
Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given ...
Write out the solution
please
Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given set of boundary conditions. ux(0, t)-u(0, t) = 0, u(L, t)-T v(x) =
Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given set of boundary conditions. ux(0, t)-u(0, t) = 0, u(L, t)-T v(x) =
1. Consider the problem of steady state heat flow in the half-plane, 22T a2T + ar2...
1. Consider the problem of steady state heat flow in the half-plane, 22T a2T + ar2 =0 for ER and y>0, ay2 subject to the boundary condition T(3,0) = g(x), and T +0 as yo. You will solve the problem using the Fourier transform in 2, with T(w,y) = ZELT(, y)e-iw= ds 2 (a) Derive an ODE for T. You can assume T +0 as|a . (b) Derive conditions for I at y = 0 and as y. You can...
Consider a two-dimensional, fully-developed, steady viscous flow of water through a duct of constant one-centimeter width...
Consider a two-dimensional, fully-developed, steady viscous flow of water through a duct of constant one-centimeter width in the y-direction. There is no pressure variation through the flow but the water flows in the positive x-direction, which is the direction of the gravity force. $y = 0 and gx = g. (a) Using the continuity and momentum equations, determine the magnitude of the v component of velocity and develop the ordinary differential equation that governs the u component of velocity. (b)...
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the...
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the diffusivity (i) Show that a solution of the form u(x,t)-F )G(t) satisfies the heat equation, provided that 护F and where p is a real constant (ii) Show that u(x,t) has a solution of the form (,t)A cos(pr)+ Bsin(p)le -P2e2 where A and B are constants (b) Consider heat flow in a metal rod of length L = π. The ends of the rod, at...
W The stream function « in a two-dimensional flow field is given as Q = 4x...
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
อาน 02u (a) A two-dimensional plate covering the region -1 5 x 51, 0 Sy s...
อาน 02u (a) A two-dimensional plate covering the region -1 5 x 51, 0 Sy s 1 has a temperature profile which satisfies the heat equation ди 10 + at l@x2' ay Find the value of a such that u(x,y,t) = 60 – 40x + e-at sin(21x) + e-try sin(atx) is a solution to this problem. Give the formula for the steady state part of this solution.
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at points a, b, and c using a numerical method. 0 4 4
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at...
The two-dimensional heat equation reduces to Laplace's equation to = 0 if the temperature u is steady-state. u(x, y) is defined in 0<x<2 and 0 Sys2 and satisfy u(x,0) = u(x, 2) = u(0, y) = 0 and u(2, y) = 80 sin my. Answer the following questions. (1) Obtain two ODES (Ordinary Differential Equations) by the method of separation of variables. (2) Find u(x, y) satisfying the boundary condition. (3) Obtain the value of u(1,5).
Consider two-dimensional steady-state heat conduction in a
rectangular region of cross-section 2L by 3L subject to boundary
conditions shown below. By using a mesh size deltax = deltay = L,
write the finite difference equations for this problem, and
calculate the node temperatures T1, T2, T3 and T4.
2 4 3 yL dee itc ft u esu
& 2 The two-dimensional Laplace equation or? ? = 0, describes potentials and steady-state temperature distributions in a plane. Show that the following function satisfies the two-dimensional Laplace equation f(x y) = -7x + y + 4 में Find for the given function che? #t ax?
Write out the solution
please
Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given set of boundary conditions. ux(0, t)-u(0, t) = 0, u(L, t)-T v(x) =
Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given set of boundary conditions. ux(0, t)-u(0, t) = 0, u(L, t)-T v(x) =
1. Consider the problem of steady state heat flow in the half-plane, 22T a2T + ar2 =0 for ER and y>0, ay2 subject to the boundary condition T(3,0) = g(x), and T +0 as yo. You will solve the problem using the Fourier transform in 2, with T(w,y) = ZELT(, y)e-iw= ds 2 (a) Derive an ODE for T. You can assume T +0 as|a . (b) Derive conditions for I at y = 0 and as y. You can...
Consider a two-dimensional, fully-developed, steady viscous flow of water through a duct of constant one-centimeter width in the y-direction. There is no pressure variation through the flow but the water flows in the positive x-direction, which is the direction of the gravity force. $y = 0 and gx = g. (a) Using the continuity and momentum equations, determine the magnitude of the v component of velocity and develop the ordinary differential equation that governs the u component of velocity. (b)...
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the diffusivity (i) Show that a solution of the form u(x,t)-F )G(t) satisfies the heat equation, provided that 护F and where p is a real constant (ii) Show that u(x,t) has a solution of the form (,t)A cos(pr)+ Bsin(p)le -P2e2 where A and B are constants (b) Consider heat flow in a metal rod of length L = π. The ends of the rod, at...
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
อาน 02u (a) A two-dimensional plate covering the region -1 5 x 51, 0 Sy s 1 has a temperature profile which satisfies the heat equation ди 10 + at l@x2' ay Find the value of a such that u(x,y,t) = 60 – 40x + e-at sin(21x) + e-try sin(atx) is a solution to this problem. Give the formula for the steady state part of this solution.
Most questions answered within 3 hours.
-
The blues made its way into many kinds of music. Eric Clapton,
The Beatles, and Elvis...
asked 7 minutes ago -
If you’re standing at the bottom of a hill and asked to evaluate
it while being...
asked 1 hour ago -
1. Which region has taken the lead in the world of
e-waste handling?
a) European Union...
asked 56 minutes ago -
A 8.15- g bullet from a 9-mm pistol has a velocity of 366.0 m/s.
It strikes...
asked 2 hours ago -
The outstanding bonds of Alpha Extracts have a yield to maturity
of 7.4 percent and a...
asked 2 hours ago -
The Problem: The Case of the Harmonizing Vacations
Your CEO is exploring partnering with a European...
asked 3 hours ago -
A chemical equation is balanced by adding coefficients in front
of some formulas so that the...
asked 3 hours ago -
From the literature (reference your sources): What are the
lattice parameters of calcite and aragonite? Why...
asked 4 hours ago -
Your system is rejecting the question am asking which is
preceded by a case study. It...
asked 4 hours ago -
3. On January 2, 2000, Larry creates a trust with himself as
trustee. Larry as trustee...
asked 4 hours ago -
A member of the volleyball team spikes the ball. During this
process, she changes the velocity...
asked 4 hours ago -
Are adult gamers less likely to use a gaming console (Xbox,
PlayStation, Wii, etc...) than teen...
asked 5 hours ago