Hello everyone,
I am currently trying to learn PDE's and have some tricky heat flow problems. Can anyone help me out?
Given the following:
du/dt (x,t) = d^2u/dt^2 (x,t) + e^-x, 0 < x < pi, t > 0
u(0,t) = u(pi,t) = 0, t > 0
u(x,0) = sin(2x), 0 < x < pi
Does anyone know what the physical interpretation of the given initial-boundary value problem is?
Does anyone know any good practical examples of the heat equation in engineering?
Thanks, zSXD
You have a typo; the second derivative on the RHS is w.r.t. x. Physically, you have heat conduction in a rod with a prescribed initial temperature distribution, an internal heat source, and zero temperature prescribed at both ends. Since the source is independent of time, this problem is easily solved by decomposing u(x,t) into the sum of a transient part v(x,t) and steady-state part w(x). w takes care of the source, and v has only a nonzero I.C. as a forcing function. The w equation is an ODE, and the v equation is solved using separation of variables.
Have a look at our publications for MEMS
Model Order Reduction for Electro-Thermal MEMS
Evgenii
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