Page 66 - Modelling in Transport Phenomena A Conceptual Approach

3.2. HEAT TRANSFER COEFFICIENT 47

where (h) is the heat transfer coefficient averaged over the area of the plate and is
defined by

Jd" Jd" h dxdn 1
w
L
(h) = = wL Jd Jd hdxdz (3.2-6)
Jd" Jd" dxdz
Equation (3.2-5) can be generalized in the form

(3.2-7)

where AH is the heat transfer area and (AT),, is the characteristic temperature
difference.

3.2.1.1 Physical interpretation of heat transfer coefficient

According to Fourier's law of heat conduction, Eq. (2.1-4)) the molecular energy
flux at the wall is expressed as

(3.2-8)

Combination of Eqs. (3.2-4) and (3.2-8) gives

h=- (3.2-9)

The convection heat transfer coefficient can be determined from Eq. (3.2-9) if the
thermal conductivity of the fluid, the overall temperature difference, and the tem-
perature gradient at the wall are known. Since the calculation of the temperature
gradient at the wall requires the determination of the temperature distribution in
the fluid phase, the actual case is idealized as shown in Figure 3.4.

a) Actual case b) Idealized case
Figure 3.4 The film model for energy transfer.