Question

Solve the heat equation given below with the associated boundary conditions and initial condition: $\frac{\partial^2 u}{\partial x^2} + \sin(x) = \frac{\partial u}{\partial t}$, $0 < x < \pi$, $t > 0$ $u(0, t) = 400$, $u(\pi, t) = 200$, $t > 0$ $u(x, 0) = 400 + \sin(x)$, $0 < x < \pi$

          Solve the heat equation given below with the associated boundary conditions and initial condition:
$\frac{\partial^2 u}{\partial x^2} + \sin(x) = \frac{\partial u}{\partial t}$, $0 < x < \pi$, $t > 0$
$u(0, t) = 400$, $u(\pi, t) = 200$, $t > 0$
$u(x, 0) = 400 + \sin(x)$, $0 < x < \pi$

Solve the heat equation given below with the associated boundary conditions and initial condition:
(∂^2 u)/(∂ x^2) + sin(x) = (∂ u)/(∂ t), 0 < x < π, t > 0
u(0, t) = 400, u(π, t) = 200, t > 0
u(x, 0) = 400 + sin(x), 0 < x < π

Added by Glenda E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

02/20/2023

Step 1

Step 1: The heat equation in one dimension is given by: \[ u_t = \alpha^2 u_{xx} \] where $ \alpha^2 $ is the thermal diffusivity. Show more…

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Subject Advanced Engneering analysis. Solve the heat equation given below with the associated boundary conditions and initial condition: 0<7>x>0 at u0,t=400,utt=200 t>0 ux,0=400+sinx0<x<