1 of 6 5.21-D Diffusion Equation ExampleAluminum rod. 10 cm long, 1 cm diameter Initially at 20ºC Apply BCs for 0≥t1-D Diffusion Equation 22xTtT∂∂=∂∂α⎟⎟⎠⎞⎜⎜⎝⎛=scm2971.0αI.C. ()200,=xTB.C.s ()100,0=tT()0,10=tT()0≥tSolve numerically for the rod temperature ()txT,Choose say cmx2=ΔSix ixlocations Choose say sec1=ΔtTime steps 00=t, 11=t, 22=t, … Consider one time step from ktto 1+kttttkkΔ+=+1cmx2=Δsec1=ΔtPerform a grid-independence check later NotationArbitrary time ktArbitrary location ix()kikiTtxT=,5,,2,1,0K=iK,2,1,0=kno limit – predict Tover the time range of interest Superscript – time Subscript – position Tsolution at “new” time 1+kt(unknown)Tsolution at “old” time kt(known – starting from the ICs)
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