Page 64 - Modelling in Transport Phenomena A Conceptual Approach

3.2. HEAT TRANSFER COEFFICIENT 45

The friction factor can be determined from Eq. (3.1-13) if the physical properties of
the fluid (viscosity and density), the approach velocity of the fluid, and the velocity
gradient at the wall are known. Since the calculation of the velocity gradient
requires determination of the velocity distribution in the fluid phase, the actual case
is idealized as shown in Figure 3.2. The entire resistance to momentum transport
is assumed to be due to a laminar film of thickness S next to the wall.

Laminar film
'L,

a) Actual case b) Idealized case
Figure 3.2 The film model for momentum transfer.

The velocity gradient in the film is constant and is equal to

v, (3.1-14)

Substitution of Eq. (3.1-14) into Eq. (3.1-13) and multiplication of the resulting
equation by the characteristic length, Lch, yields

(3.1-15)

where the dimensionless term Re is the Reynolds number defined by
&=- Lchvcvp (3.1-16)
c1
Equation (3.1-15) indicates that the product of the friction factor with the Reynolds
number is directly proportional to the characteristic length and inversely propor-
tional to the thickness of the momentum boundary layer.

3.2 HEAT TRANSFER COEFFICIENT

3.2.1 Convection Heat Transfer Coefficient
Let us consider a flat plate suspended in a uniform stream of velocity v, and
temperature T, as shown in Figure 3.3. The temperature at the surface of the
plate is kept constant at T,.