Differential Equations Lecture Work Solutions 5

Differential Equations Lecture Work Solutions 5 - 1.2...

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1.2 Applications 1.3 Conduction of Heat in a Rod 1.4 Boundary Conditions Problems 1. Suppose the initial temperature of the rod was u ( x, 0) = 2 x 0 x 1 / 2 2(1 x )1 / 2 x 1 and the boundary conditions were u (0 ,t )= u (1 )=0 , what would be the behavior of the rod’s temperature for later time? 2. Suppose the rod has a constant internal heat source, so that the equation describing the heat conduction is u t = ku xx + Q, 0 <x< 1 . Suppose we Fx the temperature at the boundaries u (0 u (1 )=1 . What is the steady state temperature of the rod? (Hint: set u t =0 . ) 3. Derive the heat equation for a rod with thermal conductivity
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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