若条件只有BC只能有一为nonhomogeneous(doc)-下载

若条件只有BC只能有一为nonhomogeneous(doc)-下载 1. equation 為linear & homogeneous若條件只有B.C.只能有一為nonhomogeneous 若條件中有I.C. ,B.C.,只能有I.C.是nonhomogeneous 2,T,T,,ex. ,T(0,t)=0, T(L ,t)=0, T(x,0)=10 2,t,x 11. 令T1(x)+T2(x,t) 2,T1,T1(L),，T1(x)，x,0=> B.C. T(0)=100, …解ODE,02,x,x 2,T2,T2,T2(L,t),,，T2(x,t) T2(0,t)=0 T2(x,0)=50,02,t,x,x 用variation解PDE 12. 令T=T1(x)+T2(x,y) 2,T1,,x=> T1(0)=0 T1(L)=10 separation解ODE2,x 22,T2(x,0),T2,T2,0 T2(0,y)=0 ,T2(L,y)=0 ,T2(x,H)=f(x)-T1(x) , ，,022,y,y,x 令T2=X(x)Y(y)代入解separation PDE =>T=T1(x)+T2(x,y)即得 4. q,A,,t,q,A,,t,q,p,,x,t,,Cp,A,,x,T,,Cp,A,,x,Txx，,xx，,xx T(x,0)=100 T(0,t)=20 T(L,t)=20 ,Tq,,kBy Fourier’s law: x,x By heat convension:q=h(T-T) 0 2,T,T,,(T,20),,, ,,,皆為constant2,x,t T(x,0)=100 T(0,t)=20 T(L,t)=20 設T=T-20 1 2,T,T11,,,T, 12,x,t T(x,0)=80 1 T(0,t)= 0 1 T(L,t)= 0 1 設T,X,1 ,,,,,''',X,X,X ''',,,,X2,,,,,,,k,,,,X,, ,''2？X,,,k , '2,,,？，k,0 ？T,X,1 5. sol: in-out+gen-dep=acc,取一部分?x,?y,?z為系統 q?y?z -q?y?z +q?x?z -q?x?z +xy?x?y?z =0 yy，,yxx，,x (?steady state) ?x,，0,?y,，0,?z,，0 ,0?x?L,0?y?H 22,q,q,T,Txy,T,Tyx,，--+xy=0 (?q=-k?q=-k),，++=0yx22,xk,y,y,y,x,x T(x,0)=0,T(x,H)=0,T(0,y)=0,T(L,y)=0 22,T,TT,,,取+=0, T(x,0)=0,T(x,H)=0 T(0,y)=0,T(L,y)=0, 設22,y,x ,n,，，T,AYsinX去計算=, ,nLn,1,2,,Tn,,,,AsinXn,2,,n1yL,,代回原式並求B n,2,2，，,,,,Tnn,,,,,,,,,AsinXn2,,,,,n1,,xLL,,,，，,, T,,,又T(x,0)=0,T(x,H)=0代回B,,此題解為 ？,nnnn1,