Chapter 6 explores the fascinating world of forced convection, a dominant mode of heat and mass transfer driven by external forces, such as fans or pumps, in a fluid flow. This chapter provides a comprehensive and detailed examination of the underlying principles, mathematical models, and practical...
Forsberg Heat Transfer
Chapter 6
Forced Convection
Dimensionless Numbers
Experimental data for forced convection
is correlated by three dimensionless
parameters: the Reynolds Number,
the Prandtl number,and the Nusselt Number.
VL
Reynolds Number = Re =
= fluid density V = fluid velocity
L = characteristic length of geometry
= fluid absolute viscosity
= / = fluid kinematic viscosity, so
VL
Reynolds Number = Re =
1
, cp
Prandtl Number = Pr =
k
cp = fluid specific heat at constant pressure
= fluid absolute viscosity
k = fluid thermal conductivity
hL
Nusselt Number = Nu =
k
h = convective coefficient
We are looking for h so the convective heat
transfer can be determined. Thus, correlation
of experimental data gives Nu as a function
of Re and Pr : Nu = f (Re, Pr)
Nu = f (Re, Pr)
The functional relationship is often
of the form Nu = C Rea Prb
Fluid velocities for natural convection are much
smaller that those for forced convection. The
Reynolds Number is no longer significant. It is
replaced by the Grashof Number:
2
, g (Ts − T ) L3
Grashof Number = Gr =
2
g = acceleration of gravity
= coefficient of thermal expansion of fluid
L = characteristic length of geometry
Ts = surface temperature
T = fluid temperature
= fluid kinematic viscosity
hL
Nu = = f (Gr, Pr)
k
Forced Convection - External Flow
Flow Over a Flat Plate
3
, There are three flow regions: laminar, transition,
and turbulent. If the plate is short, there might only be
a laminar region on it. The transition region is short, and
often the flow is modeled as only laminar and turbulent;
the "critical length", xc , being the location of the change
from laminar to turbulent.
= boundary layer thickness
For flow over a flat plate, the Renolds Number at location x is
u x u x
Re x = =
The critical distance is typically the distance where the Reynolds
Number is 5 x 10 5 .
(5 x 105 ) (5 x 105 )
That is, xc = =
u u
The boundary layer thickness varies with x. It is usually defined
as the distance from the surface at which the x-component of
velocity, u, is 99% of the free-stream velocity u .
u
At y = , = 0.99
u
4
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