Find the steady-state temperature u(r.0) in a circular plate of radius r = 1 if the temperature on the circumference is...
2. Find the steady-state temperature u(r,0) in a semicircular plate of radius r 2 if [10<0< π/2 u(2,0) and the edges 0 = 0 and 0 = T are insulated. 0 /20 T пл sin 2 1 2 + cos(n0) Ans: u(r,0) п
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0< r < 1,0 < z < 1 in a finite cylinder defined by 0 <rs 1,0 < z <1 if the boundary conditions are as given: 0 z< 1 2) u(1, z) = Z, 0, az z 0 0r1
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0< r < 1,0 < z < 1 in a finite cylinder defined by 0 <rs 1,0 < z <1 if the boundary conditions are as given: 0 z< 1 2) u(1, z) = Z, 0, az z 0 0r1
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0
3. A circular plate of unit radius, whose faces are insulated, has half of its boundary kept at constant temperature u, and the other half at temperature uz (see figure). Find the steady state temperature pf the plate. The steady state heat flow is written as oʻu 1du 1 8²u ar?'r or a dz = 0, with the boundary condition 0<¢ <T, luz, < < 21. u(1,0) = {u, After using the proper separation of variable method, we have u=dy...
Estimate the steady state temperature on the plate a quarter
circle radius
r = 1 and f (θ) = θ2 - π shown in the
figure.
(a) Establish the equations to
be solved and their boundary conditions.
(b) Determine the coefficients of the series obtained.
(c) Give the solution to the problem.
VA u=f@) H=0 ON
3. (7 points) Let u(x, y) be the steady-state temperature u(r, y) in a rectangular plate whose vertical r0 and 2 are insulated. When no heat escapes, we have to solve the following the boundary value problem: a(z,0) = 0, u(z,2) = x, 0 < x < 2 (a) By setting u(x, g) -X(x)Y(u), separate the equation into two ODE 0 What ane the sewr homdany condiome hoald Xe) watiy (37)2. (c) Find x(r) for the case when λ-0 and...
9. Find the steady-state temperature distribution in the plate shown below y= x и —D () insulated и 3D Т 1/2 1 и 3D 0
9. Find the steady-state temperature distribution in the plate shown below y= x и —D () insulated и 3D Т 1/2 1 и 3D 0
Problem 1. A circular plate of radius 4 is heated. The temperature at point (x, y) on the plate is given by f(z, y) =2x2 + 3y2-4r +5 Assume (0.0) is the center of the plate. (a) (9 points) Find the hottest and coolest points on the edge of the plate (b) (3 points) Is there a point inside the disc that is hotter? Is there a point that's cooler?
Problem 1. A circular plate of radius 4 is heated....
10. (21 pts]Find the steady-state temperature distribution in a solid cylinder with radius R and height H, if the boundary temperatures are set as 0 on the bottom surface, ugra/R? on the top surface and Uz/H on the curved surface 1 [4 pts) Write the governing equation and boundary conditions 2) [17 pts]Solve the problem
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms of w and plot R versus w; (c) Find Rmax and wmax
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of...