Re: [理工] 高等工數有關熱對流
※ 引述《cyc647 (小G)》之銘言：
: 代PO,不妥請告知刪文
: A solid cylinder.0<r<b,0<z<c,is initially at temperature F(r,z).For times
: t>0,the boundary at z=0 is insulated, the boundary at z=c is dissipating heat
: by convection into a medium at zero temperature, and the boundary at r=b is
: kept at zero temperature. Obtain an expression for the temperature
: distribution T(r,z,t) in the solid for times t>0.
: 本題是求溫度T(r,z,t),應該是用PDE
: 同學完全不知道如何下手
: 有大大知道怎麼解嗎????
Heat conduction problem
r=b kept zero temprature
z=0 was insulated
z=c was cooling by convection of the surroundings
Laplacian T = k dT/dt
With the axial-symmetric polar coordinate description
d^2T/dr^2+1/r*dT/dr = k dT/dt
I.C.s
T(r,z,0)=F(r,z)
B.C.s
dT/dr = 0 where z=0 (no heat flux passing)
T =0 where r= b (zero temprature)
Newton cooling law (dQ/dt = h (T-Ts))
h is convecton coefficient
and Ts is temprature of surroundings
Let you try
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