上海交通大学：《生物传热学教与学 Bioheat Transfer》课程教学资源（电子讲义）lecture 4 Solve of the Conduction Eq.

3D Conduction Eq. 0T=kV2T+9" PC In Cartesian coordinate systems: oC. T_

2 ''' p T C kTq t       In Cartesian coordinate systems: 3D Conduction Eq. ( ) ( ) ( ) ''' p TT T T C k k kq txx yy z z             

In Cylindrical coordinate systems: ++k+”=c at Y k a2T o2t aT In spherical coordinate systems: k 02T k∂ ot r2 Or sin0 0+r2sing 00 (sing +9 t pCp at

In Cylindrical coordinate systems: In spherical coordinate systems:

It is valid at every point in the material It is the heat equation for conduction in isotropic,constant conductivity material Further simplifications: ·Steady state ·One dimensional ·No energy generation

 It is valid at every point in the material  It is the heat equation for conduction in isotropic, constant conductivity material  Further simplifications:  Steady state  One dimensional  No energy generation

Boundary Conditions and Initial Conditions insulation 0 0 convection,h,T x

Boundary Conditions and Initial Conditions

Fixed surface temperature insulation q 0 0 convection,h,T Tlx=0 To

 Fixed surface temperature