2. Introduction
• Convection The process of heat transfer
between a solid surface & the fluid in motion.
• Natural Fluid moves due to density diff.
caused by HT between solid & liquid.
• Forced Fluid motion is imparted by
external means. i.e. pump,fan,slope etc.
3. Mechanism of Forced Convection
• Convection heat transfer is complicated since
it involves fluid motion & heat conduction.
• The fluid motion enhances heat transfer.
• The rate of convection heat transfer is
expressed by Newton’s law of cooling:
4. • The convective heat transfer coefficient h
strongly depends on the fluid properties and
roughness of the solid surface, and the type of
the fluid flow.
5. fig. Forced convection
• It is assumed that the velocity of the fluid is
zero at the wall, this assumption is called
no-slip condition.
6. • As a result, the heat transfer from the solid
surface to the fluid layer adjacent to the
surface is by pure conduction, since the fluid is
motionless.
• Thus h in general, varies along the flow
direction.
• The mean or average convection heat transfer
coefficient for a surface is determined by
(properly) averaging the local heat transfer
coefficient over the entire surface.
7. Velocity Boundary Layer
• laminar flow-The flow in boundary layer
starts as smooth and streamlined
• Turbulent flow-At some distance from the
leading edge, the flow turns chaotic
8. • Transition region-The transition occurs from
laminar to turbulent flow over some region.
• The velocity profile
laminar region - approximately parabolic
turbulent flow- becomes flatter .
• Turbulent region:
1. laminar sublayer- viscous effects are
dominant
2. buffer layer - both laminar and turbulent
effects exist.
3. turbulent layer.
9. Non‐dimensional Groups
• Nusselt number:
• Nu represents the enhancement of HT through
a fluid as a result of convection relative to
conduction across the same fluid layer.
10. • Reynolds number:
At large Re, the inertia forces, which are
proportional to the density & the velocity of the
fluid, are large relative to the viscous forces; thus
the viscous forces cannot prevent the random
and rapid fluctuations of the fluid.
11. • The Reynolds number at which the flow
becomes turbulent is called the critical
Reynolds number.
• For flat plate the critical Re is experimentally
determined to be approximately
Re critical =
• For smooth pipe:
Re < 2000 – Laminar flow
Re > 4000 – Turbulent flow
2000<Re<4000 – Transitional flow
12. • Prandtl number:
Pr is a measure of relative thickness of the
velocity and thermal boundary layer where fluid
properties are:
13. Thermal Boundary Layer
• Similar to VBL, a TBL develops when a fluid
at specific temp. flows over a surface which is
at different temp.
14. • The thickness of the TBL δt is defined as the
distance at which:
• The relative thickness of the VBL & the TBL
is described by the Pr no.
15. • For low Pr fluids, i.e. liquid metals, heat
diffuses much faster than momentum flow
(remember Pr = ν/α<<1) and the VBL is fully
contained within the TBL.
• On the other hand, for high Pr fluids, i.e. oils,
heat diffuses much slower than the momentum
and the TBL is contained within the VBL.
16. Flow Over Flat Plate
• The Cf & h for a flat plate can be determined
by solving the conservation of mass,
momentum, and energy eqns (approximately
or numerically).
• They can also be measured experimentally. It
is found that the Nu can be expressed as:
17. • Laminar Flow-
The Cf & Nu at the location x for laminar flow
over a flat plate are
x - distant from the leading edge of the plate &
Rex = ρV∞x / μ.
18. • The averaged Cf & Nu over the entire
isothermal plate for laminar regime are
19. • Taking the critical Re, the length of the plate
xcr over which the flow is laminar can be
determined from
20. • Turbulent Flow-
The Cf & Nu at location x for turbulent flow
over a flat isothermal plate are
21. • The averaged Cf & Nu over the isothermal
plate in turbulent region are
22. • Combined Laminar and Turbulent
Flow-
If the plate is sufficiently long for the flow to
become turbulent (and not long enough to
disregard the laminar flow region), we should
use the average values for Cf & Nu
23. After performing the integrals and
simplifications, one obtains
The above relationships have been obtained for the case of
isothermal surfaces, but could also be used approximately for the
case of non•]isothermal surfaces. In such cases assume the surface
temperature be constant at some average value.
24. • For isoflux (uniform heat flux) plates, the local
Nusselt number for laminar and turbulent flow
can be found from
• Note the isoflux relationships give values that
are 36% higher for laminar and 4% for
turbulent flows relative to isothermal plate
case.
