hw7_09 - EP 471 – Homework#7 Parabolic PDEs Each problem...

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Unformatted text preview: 04/22/09 EP 471 – Homework #7: Parabolic PDEs Each problem is equally weighted; I’d suggest using Matlab’s pdepe utility for both problems. (1) At the end of Exercise 19, I mentioned some modifications to the transient slab problem we considered there. I’ll change them slightly here. Suppose we have a 10 cm thick slab of density ρ = 1000 kg/m 3 , heat capacity c p =1000 J/kg ⋅° C and thermal conductivity k = 20 W/m ⋅° C. The slab begins from a uniform temperature of 20 ° C. At time t = 0 we activate a spatially uniform heat source within the slab that increases asymptotically with time according to: )] / exp( 1 [ ' ' ' ' ' ' τ t q q o − − = ; 3 5 ' ' ' W/m 10 1 × = o q where τ = s 2 / α , s is the slab thickness of 10 cm and α ≡ k /( ρ c p ) is the thermal diffusivity of the medium. The surrounding medium is also at 20 ° C and heat transfer coefficients on the left and right boundaries are 1000 and 2000 W/m 2 ⋅° C respectively. Modify the scripts you’ve...
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hw7_09 - EP 471 – Homework#7 Parabolic PDEs Each problem...

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