1. differential equations of heat transfer

4. boundary conditions
isothermal BC
insulated BC
combined BC

5. 1-D steady state conduction
plane wall
hollow cylinder
hollow sphere

6. 1-D conduction in a circular cylinder with internal generation of energy
BC; 1) at center, 2) at wall
Cylindrical solid with homogeneous energy generation
Plane wall with variable energy generation

7. heat transfer from extended surfaces
assumption; T is a function of x only
; valid when the cross section is thin or when k is large

8. fin of uniform cross section
-> total heat transfer from an extended surface -> fin efficiency

9. 2-D systems

10. unsteady-state conduction
lumped parameter analysis
T is a function of time & position
; if T varies with time only (large k)
error in lumped parameter analysis is less than 5% for Bi less than 0.1
; systems with negligible internal resistance

11. negligible surface resistance
; surface temperature is constant for Bi>>1

12. heating a body with finite surface and internal resistance

13. heat transfer to a semi-infinite wall

14. Separation of Variables
Unsteady state heat conduction in a rubber sheet
292oF
292oF x
x0=1/4”
Curing at 292oF
for 50min

15. Temperature profiles in rubber sheet
Separation of Variables
Temperature profiles in rubber sheet
300
10min
292oF
5min
1min
200
Temperature, oF
18.7 min
100
1/4
1/2
3/4 1
center
surface
Distance, n(=x/x0)

17. Gurney-Lurie Chart
m is zero because the assumption of constant surface temperature implies that surface resistance to heat transfer is negligible (h=∞).

18. Gurney-Lurie Chart
From Fig. 19-3,
we obtain
cf min