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(Solved): Heat Equation: a) The two-dimensional heat equation is the following partial differential equation: ...
Heat Equation: a) The two-dimensional heat equation is the following partial differential equation:
k((del^(2)T)/(delx^(2))+(del^(2)T)/(dely^(2)))=(delT)/(delt)Prove that:
T(x,y,t)=e^(-kt)(cosx+cosy)is a solution of the two-dimensional heat equation. b) Sketch the surfaces given by
z=T(x,y,t_(0)), for
t_(0)=0,1,10. If
T(x,y,t)describes the temperature of a plate over time
t, what happens to the temperature of the plate after a long period of time?
