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Find the solution of the heat conduction problem 11(0.1) = 0, u(2,t) = 0, t > 0;
Find the solution of the heat conduction problem u(0,0, 11 (x, 0) =sinOxx)-sin (m), u(1,1)0, t0...
Find the solution of the heat conduction problem u(0,0, 11 (x, 0) =sinOxx)-sin (m), u(1,1)0, t0 0 1 x
** Lon u. that the solution to the heat conduction problem aug , 0<<L t >...
** Lon u. that the solution to the heat conduction problem aug , 0<<L t > 0 u(0,t) - 0, u(L,t) = 0 (u(a,0) = f (3) is given by u(3,4) – È che+n*/2°' sin (182), – Ž Š 5(2) sin (%), vnen. Explicitly show by substitution that this function u(x, t) satisfies the equation aus = U, and all of the given boundary conditions. Note: You can interchange/swap sums and derivatives for this function (that doesn't always work!).
7. Find the solution of the heat conduction problem 100uzz = ut, 0 < x <...
7. Find the solution of the heat conduction problem 100uzz = ut, 0 < x < 1, t > 0; u(0,t) 0, u1,t 0, t>0; In Problem 10, consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t0. Find an expression for the temperature u(,t) if the initial temperature distribution in the rod is the given function. Suppose that a
7. (a) Find the solution of the heat conduction problem: Suxx = ut, 0<x< 5, u(0,...
7. (a) Find the solution of the heat conduction problem: Suxx = ut, 0<x< 5, u(0, 1) = 20, tu(5, 1) = 80, 1>0 u(x,0) = f(x) = 12x + 20 + 13sin(tor) - 5sin(3 tex). (b) Find lim u(2, t). (c) If the initial condition is, instead, u(x,0) = 10x – 20 + 13sin( Tox) - 5sin(3 7ox), will the limit in (b) be different? What would the difference be?
Find the solution of the heat conduction problem and provide a detailed graph showing the initial...
Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 3. ut uxx ux(0, t) 0 ux(1,t) 0 u(x, 0) 1-x Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 4. ut = 2uxx u(0,t) 0 u(10,t) 10 u(x, 0) = 10
Find the solution of the heat conduction problem and...
3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1...
3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1,t)-0, t > 0 and the initial condition u(r,0) f(a) We found the solution to be of the form where (2n-1)n 1,2,3,. TL 20 Now consider the heat conduction problem with the boundary conditions u(0, t) 1,u(T, t)0, t>0 and the initial condition ur,0) 0. Find u(r,t). Hint: First you must find the steady state.
3. In class we discussed the heat conduction problem...
Problem 3 Solve the unsteady heat conduction problem: subject to the boundary conditions: u(0,t)0, (1,t)1; and...
Problem 3 Solve the unsteady heat conduction problem: subject to the boundary conditions: u(0,t)0, (1,t)1; and the initial condition ua, 0) and sketch the form of the complete solution.
5. Find the solution of the heat conduction problem for each initial condition given: Suxxx =...
5. Find the solution of the heat conduction problem for each initial condition given: Suxxx = 0<x<211, tu(0,1) = 0, tu(27,1) = 0, t> 0. (a) u(x,0) =(x) = -2sin(3x) - 3sin(4x) + 17sin(9x/2). (b) u(x,0) = f(x) = 8. (Hint: You may skip the integrations by using the result of #2(b).] (c) In each of cases (a) and (b), find the limit of u( 71,1) ast approaches 0. Are they different? Did you expect them to be different? 6....
Question #5 all parts thanks 5. Find the solution of the heat conduction problem for each...
Question #5 all parts thanks
5. Find the solution of the heat conduction problem for each initial condition given: 0<x <6, t> 0. (a) ux,0)-x)-4sin(x)-3sin(2x) +7sin(570:). (b) ux, 0)-x)-9t (c) In each of cases (a) and (b), find the limit of u(3,1) as t approaches oo. Are they different? Did you 45 expect them to be different?
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) =
Find the solution of the heat conduction problem u(0,0, 11 (x, 0) =sinOxx)-sin (m), u(1,1)0, t0 0 1 x
** Lon u. that the solution to the heat conduction problem aug , 0<<L t > 0 u(0,t) - 0, u(L,t) = 0 (u(a,0) = f (3) is given by u(3,4) – È che+n*/2°' sin (182), – Ž Š 5(2) sin (%), vnen. Explicitly show by substitution that this function u(x, t) satisfies the equation aus = U, and all of the given boundary conditions. Note: You can interchange/swap sums and derivatives for this function (that doesn't always work!).
7. Find the solution of the heat conduction problem 100uzz = ut, 0 < x < 1, t > 0; u(0,t) 0, u1,t 0, t>0; In Problem 10, consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t0. Find an expression for the temperature u(,t) if the initial temperature distribution in the rod is the given function. Suppose that a
7. (a) Find the solution of the heat conduction problem: Suxx = ut, 0<x< 5, u(0, 1) = 20, tu(5, 1) = 80, 1>0 u(x,0) = f(x) = 12x + 20 + 13sin(tor) - 5sin(3 tex). (b) Find lim u(2, t). (c) If the initial condition is, instead, u(x,0) = 10x – 20 + 13sin( Tox) - 5sin(3 7ox), will the limit in (b) be different? What would the difference be?
Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 3. ut uxx ux(0, t) 0 ux(1,t) 0 u(x, 0) 1-x Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 4. ut = 2uxx u(0,t) 0 u(10,t) 10 u(x, 0) = 10
Find the solution of the heat conduction problem and...
3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1,t)-0, t > 0 and the initial condition u(r,0) f(a) We found the solution to be of the form where (2n-1)n 1,2,3,. TL 20 Now consider the heat conduction problem with the boundary conditions u(0, t) 1,u(T, t)0, t>0 and the initial condition ur,0) 0. Find u(r,t). Hint: First you must find the steady state.
3. In class we discussed the heat conduction problem...
Problem 3 Solve the unsteady heat conduction problem: subject to the boundary conditions: u(0,t)0, (1,t)1; and the initial condition ua, 0) and sketch the form of the complete solution.
5. Find the solution of the heat conduction problem for each initial condition given: Suxxx = 0<x<211, tu(0,1) = 0, tu(27,1) = 0, t> 0. (a) u(x,0) =(x) = -2sin(3x) - 3sin(4x) + 17sin(9x/2). (b) u(x,0) = f(x) = 8. (Hint: You may skip the integrations by using the result of #2(b).] (c) In each of cases (a) and (b), find the limit of u( 71,1) ast approaches 0. Are they different? Did you expect them to be different? 6....
Question #5 all parts thanks
5. Find the solution of the heat conduction problem for each initial condition given: 0<x <6, t> 0. (a) ux,0)-x)-4sin(x)-3sin(2x) +7sin(570:). (b) ux, 0)-x)-9t (c) In each of cases (a) and (b), find the limit of u(3,1) as t approaches oo. Are they different? Did you 45 expect them to be different?
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) =
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