Unsteady-State Conduction of Heat in Two Dimensions

Manipulate[Module[{plt,sol},sol=NDSolve[{ D[T[x,y,t],{t,1}]==alpha (D[T[x,y,t],{x,2}]+D[T[x,y,t],{y,2}]),T[x,y,0]== 400-400 Exp[-100000 x^2 y^2 (x-1)^2 (y-1)^2]+350 Exp[-100000 x^2  (x-1)^2],
T[x,0,t]== 350 Exp[-100000 x^2  (x-1)^2],T[x,1,t]== 350 Exp[-100000 x^2  (x-1)^2],T[0,y,t]== 350,T[1,y,t]== 350},{T[x,y,t]},{x,0,1},{y,0,1},{t,0,100},PrecisionGoal->2];plt=ContourPlot[T[x,y,t]/.sol/.t-> time,{x,0,1},{y,0,1},ColorFunction->"Pastel",Contours-> 8,PlotLabel->"temperature profile"]],{{time,5,"time"},5,100,0.05,Appearance-> "Labeled"},
{{alpha,0.002,"thermal diffusivity in (cm^2)/s"},0.001,0.005,0.001,Appearance-> "Labeled"},TrackedSymbols:>{alpha,time}]

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Unsteady-State Conduction of Heat in Two Dimensions" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/UnsteadyStateConductionOfHeatInTwoDimensions/

Contributed by: Housam Binous

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