Consider heat conduction in a semiinfinite slab, where the slab is initially ( t = 0 )
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Consider heat conduction in a semiinfinite slab, where the slab is initially (t=0) at a constant temperature um and the end of the slab (at x=0 ) is maintained at the constant temperature uw. The partial differential equation for the temperature distribution u(x,t) for thermal diffusivity κ is
∂u∂t=κ∂2u∂x2,x>0,t>0
with u(x,0)=um,x>0,u(0,t)=uw,t>0,|u(x,t)|0). Using a Laplace transform method:
Transcribed Image Text:
(a) Show that the transformed solution is U(x, s) = (uw-um) S (b) Using the inverse Laplace transform L-1 a =erfc show that the solution is u(x,t) =LU(x,s)}=(u-um)erfe +um-
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Related Book For
Advanced Mathematics For Engineering Students The Essential Toolbox
ISBN: 9780128236826
1st Edition
Authors: Brent J Lewis, Nihan Onder, E Nihan Onder, Andrew Prudil
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