View/Open

3.3.1.2 Heat balance at the outer surface of the heating plate
Figure 3.9 Heating plate heat balance
The heat generated by the heating element transfers to the heating plate (Figure 3.5).
The thermal conduction resistance for each of these components can be expressed as:
l
R
k A
47
(3.19)
The overall resistance from heating element to heating plate is added up in table below:
Table 3.2 Overall resistance from heating element to heating plate [19]
Component
l(m)
(Thickness)
k[W/(m·K)]
(Thermal
conductivity)
A(m²)
(Area)
R(K/W)
(Thermal
resistance)
Ceramic substrate 0.000635 24 0.0025 0.01058
3M thermal conductive tape 0.00025 0.6 0.00567 0.07349
Aluminium heating plate 0.0012 237 0.01033 0.00049
Total from Ceramic to Plate 0.08456
The heat balance on the top of the heating plate can be written as (Figure 3.9):
(3.20)
QHE QBw QHp T T
HE Hp
HE
(3.21)
RHS
Q
Because of the assumption that the ambient air is quiescent, the model is simplified to
have only natural convection on all the outer surface area. For the outer circumferential
vertical surface of the heating plate, the rim (Figure 3.9), Sparrow and Gregg have
demonstrated that a vertical cylinder can be considered as flat vertical plate for the