This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: respectively, find the solution of (*) which satisfies the initial conditions u ( x , o ) = ~ ( x ) and u,(x,o)=y(x) forall  < x < m . b V $ & I M lo p. 40 k w e . 1 Bonus.(25 pts.) A homogeneous solid material occupying D = {(x, y, z) E B3 : 4 i x2 + y2 + z2 i 100) is completely insulated and its initial temperature at position (x, y, z ) in D is 200/,/. (a) Write (without proof or derivation) the partial differential equation and initialhoundary conditions that completely govern the temperature u (x, y, z,t ) at position (x, y, z) in D and time t 2 0. @) Use Gauss' divergence theorem to help show that the heat energy H (t) = IIIcpu (x, y, z, t)dv of D the material in D at time t is a constant function of time. Here c and p denote the (constant) specific heat and mass density, respectively, of the material in D. (c) Compute the (constant) steadystate temperature that the material in D reaches after a long time. 7....
View
Full
Document
This note was uploaded on 01/11/2011 for the course MATH Math 325 taught by Professor Davidfrow during the Fall '10 term at Missouri S&T.
 Fall '10
 DavidFrow
 Math, Equations

Click to edit the document details