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Answers needed for each part with step by step solution thanks ☺:) Solve the heat equation...
This is a question about
Partial differential equation - Heat equation. Please help solving
part (a) and show clear explanations. Thanks!
=K х 7. The temperature T(2,t) in an insulated rod of length L and diffusivity k is given by the heat equation ОТ 22T 0 < x < L. at Əx2' Initially this rod is at constant temperature To, and immediately after t=0 the temperature at x = L is suddenly increased to T1. The temperature at x =...
6. Solve the heat equation (5.17) with initial condition u(x, 0) = H(x)e-x. Write the solution of the Cauchy problem for the heat equation u = kuyx - < x <®, t> 0, (5.17) with initial condition u(t,0) = {(H(x + 1) - H (1 - x)) in terms of the error function Erf () = * e ** dy.
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The solution of the heat equation Uxx = U7, 0 < x < 2,1 > 0, which satisfies the boundary conditions u(0, t) = u(2,t) = 0 and the initial condition u(x, 0) = f(x), (1, 0 < x < 1 L where f(x) = 3 }, is u(x, t) = į bn sin (n7x De 7 ,where bn = 10,1 < x < 2 S n=1 Select one: o a [(-1)] o...
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?
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A mining company considers opening a new excavation site. The project requires an investment of £25 million at the outset, followed by £17 million in 15 months' time. It is expected that the new site will provide income over a 30 year period starting from the end of the second year. Net income from the project will be received continuously at a...
2. Consider the heat equation on a bounded domain with a zero heat-flux condition, 0<a <1 t > 0, u(z,0) = 2(1-2), (0, t) = 0, 14(1, t) = 0, t >0, t > 0, where σ > 0 is a constant. Such an equation is a model for the distribution of head throughout a rod which is thermally insulated on both ends. (a) Find the solution of the above PDE using separation of variables. You may use anything we...
(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...
Solve the heat equation Ut = Uxx
+ Uyy on a square 0 <= x <= 2, 0<= y<= 2 with the
following boundary and initial conditions
2. Solve the heat equation boundary conditions uvw on a square O S r s 2, 0 S vS 2 with the (note the mix of u and tu) and with initial condition 0 otherwise Present your answer as a double trigonometric sum.
2. Solve the heat equation boundary conditions uvw on a...
Solving PDE with separation of variables
3. Solve the heat flow equation on a circle. (10 point) Otu(t,0) = o u(t,0). such that the initial condition is u(0,0) = cos? (0)
Find the solution u(a, t) to the initial boundary value problem for the heat equation 4urx te (0, 00), a e (0,5), with initial condition e [0,) e ,5 | 3, u(0, ar) f(ar) = 4, and with boundary conditions ug (t, 0) = 0, un (t, 5) = 0.
Find the solution u(a, t) to the initial boundary value problem for the heat equation 4urx te (0, 00), a e (0,5), with initial condition e [0,) e ,5 |...