Roadmap To Completing A Transient Heat Conduction Problem

Roadmap to Completing a Transient Heat Transfer Problem Examine geometry of object

Not enough info. to calculate Bi? Assume Bi < 0.1 and then verify afterwards.

Has all finite surfaces

Use lumped capacitance:

Bi < 0.1

Find Bi =

(Eqn. 5.6)

Energy generation?

If Bi does not < 0.1, you can not use the LC method.

(Eqn. 5.25) Has ONE surface that extends to infinity

Semi-infinite medium: See App. B.2 for solving erf functions.

Constant Ts = T(0,t)

Bi > 0.1

Fo > 0.2

Calculate Fo =

Heisler charts

OR

Fo < 0.2

Use entire series: 2D or 3D heat transfer

(Eqn. 5.39a) (requires extensive computation; computer software needed)

One-term approximation: See Table 5.1 to find values for C1 and Z1, and Appendix B.4 to find values for J0.

Plane wall:

Multi-dimensional effects: See Chp. 5 Suppl. section 2, Fig. 5S.11 for all geometries. Semi-infinite:

Plane wall:

Cylinder:

(Eqn. 5.40a)

Infinite cylinder:

(Eqn. 5.57)

Constant heat flux

(Eqn. 5.49a)

(Eqn. 5.59)

2D ex.:

Surface convection

3D ex.:

(Eqn. 5.60)

Sphere: (Eqn. 5.50a)