Page 178 - Mechanical Engineers' Handbook (Volume 4)

2 Convection Heat Transfer 167

2 CONVECTION HEAT TRANSFER
As discussed earlier, convection heat transfer is the mode of energy transport in which the
energy is transferred by means of fluid motion. This transfer can be the result of the random
molecular motion or bulk motion of the fluid. If the fluid motion is caused by external forces,
the energy transfer is called forced convection. If the fluid motion arises from a buoyancy
effect caused by density differences, the energy transfer is called free convection or natural
convection. For either case, the heat-transfer rate, q, can be expressed in terms of the surface
area, A, and the temperature difference, T, by Newton’s law of cooling:

q hA T
In this expression, h is referred to as the convection heat-transfer coefficient or film coeffi-
cient and a function of the velocity and physical properties of the fluid, and the shape and
nature of the surface. The nondimensional heat-transfer coefficient Nu hL/k is called the
Nusselt number, where L is a characteristic length and k is the thermal conductivity of the
fluid.

2.1 Forced Convection—Internal Flow
For internal flow in a tube or pipe, the convection heat-transfer coefficient is typically defined
as a function of the temperature difference existing between the temperature at the surface
of the tube and the bulk or mixing-cup temperature, T , i.e., T T T can be defined
b
b
s
as
CTd ˙m,
T p
b
Cd ˙m
p
where ˙m is the axial flow rate. Using this value, heat transfer between the tube and the fluid
can be written as q hA(T T ).
b
s
In the entrance region of a tube or pipe, the flow is quite different from that occurring
downstream from the entrance. The rate of heat transfer differs significantly, depending on
whether the flow is laminar or turbulent. From fluid mechanics, the flow is considered to
be turbulent when Re V D/v 2300 for a smooth tube. This transition from laminar to
m
D
turbulent, however, also depends on the roughness of tube wall and other factors. The gen-
erally accepted range for transition is 200 Re 4000.
D
Laminar Fully Developed Flow
For situations where both the thermal and velocity profiles are fully developed, the Nusselt
number is constant and depends only on the thermal boundary conditions. For circular tubes
with Pr 0.6, and x/DRe Pr 0.05, the Nusselt numbers have been shown to be Nu
D
D
3.66 and 4.36, for constant temperature and constant heat flux conditions, respectively. Here,
the fluid properties are based on the mean bulk temperature.
For noncircular tubes, the hydraulic diameter, D 4 the flow cross-sectional area/
h
wetted perimeter, is used to define the Nusselt number Nu and the Reynolds number Re .
D
D
Table 12 shows the Nusselt numbers based on hydraulic diameter for various cross-sectional
shapes.
Laminar Flow for Short Tubes
At the entrance of a tube, the Nusselt number is infinite, and decreases asymptotically to
the value for fully developed flow as the flow progresses down the tube. The Sieder-Tate