Convection - Basics
OBJECTIVE
Fundamentals of Convection
Boundary Layer Fundamentals
Velocity and Thermal Boundary Layers
Fundamentals of Convection
So far we have used:
• Newton’s law of cooling Q=hA(Ts-T) as a boundary
condition to the conduction problems
• No details of the actual phenomena of energy transfer
within the fluid has been investigated.
• The equation in this form seems simple, but it is only a
definition of average unit thermal convective
conductance hc rather than a law of heat transfer by
convection.
Convection (Cont’d)
• hc is actually a complicated function of
• Fluid flow
• Thermal properties of the fluid medium, and
• The geometry of the system
• Its value is generally not uniform over a surface and
also depends on the location where the temperature T
is measured
• Thus the study of fluid dynamics is pre-requisite to the
fundamental understanding of convection heat transfer
Energy Transport Mechanism and
Fluid Flow
• The transfer of heat between a solid boundary and a fluid takes
place by a combination of conduction and mass transport
•If the boundary is at higher temperature than the fluid, heat flows
first by conduction from the solid to fluid particles in the very
neighborhood of the wall.
•The energy thus transmitted increases the internal energy of the
fluid and is carried away by the motion of the fluid.
•When the heated fluid particles reach a region at a lower
temperature, heat is again transferred by conduction from warmer
to cooler fluids.
•Thus the flow conditions over the surface are important to know
about.
Energy Transport Mechanism and
Fluid Flow (Cont’d)
• One of the important aspects of the hydrodynamic analysis is to
establish whether the motion of the fluid is laminar or turbulent.
Laminar Flow
• Fluid moves in layers, called stream lines with each fluid particle
following a smooth and continuous path.
•The fluid particles remain in their own layers or streamlines, in
an orderly sequence, without passing one another
•Heat transfer in laminar flow, at a sub-microscopic level, among
the layers is through molecular conduction.
Energy Transport Mechanism and
Fluid Flow (Cont’d)
Turbulent Flow
• In contrast to orderly motion of laminar flow, the motion in
turbulent flow is haphazard and disordered, resembling of a crowd
of people moving in a direction.
•The general trend of the motion is defined, but superimposed
upon this motion are the deviations of individuals according to
their instantaneous direction and their ability to pass the less agile
(strong) members of the crowd.
•Yet, the statistical average of the motion of a large number of
individuals, it would be steady and regular. The same applies to
fluid particles in turbulent flow.
Energy Transport Mechanism and
Fluid Flow (Cont’d)
•The path of any individual particle is zig zag and irregular, but on
a statistical basis the overall motion of the aggregate of the fluid
particles is regular and predictable.
•In turbulent flow, heat transfer by molecular conduction is
modified and aided by small eddies which carry lumps of fluid
across the stream lines.
•These fluid particles act as carriers of energy and transfer heat by
mixing with other particles of the fluid
•Thus increase in rate of mixing (or turbulence) will increase the
rate of heat flow by convection.
Energy Transport Mechanism and
Fluid Flow (Cont’d)
Types of Convection Based on Fluid Motion
Fluid motion can be induced by two processes.
1. By the result of density differences due to
temperature variations in the fluid. (Free or
natural Convection)
2. By the inducement of some external energy,
such as a pump or a blower (Forced
Convection)
Boundary Layer Fundamentals
• Strong viscous effects slow
down the motion of the fluid
particles near the surface.
• Fluid particles near the
surface stick to it and have
zero velocity relative to the
boundary.
• The effect of viscous forces
originating at the boundary
extend into the body of the
fluid but only to a short
distance.
•The fluid contained in the region
of substantial velocity change is
called
the
hydrodynamic
boundary layer.
•The thickness of the b.l. is
defined as the distance from the
surface at which the local velocity
reaches 99% of the external
velocity u
Boundary Layer Fundamentals
(Cont’d)
• In the boundary layer, other particles attempting to slide over
them are retarded due to interaction between faster and
slower moving particles, a phenomena gives rise to shearing
forces.
• In laminar flow these interactions, called viscous shear, takes
place between molecules on a sub-Micronic scale.
• Whereas, in turbulent flow, an interaction of lumps of fluid
on a macroscopic scale, called turbulent shears, is super
imposed on the viscous shear.
Boundary Layer Fundamentals
(Cont’d)
Velocity Profile Within the Boundary Layer
Boundary Layer Fundamentals
(Cont’d)
• Flow within the boundary layer remains laminar only for
a certain distance from the leading edge and then
becomes turbulent.
• The phenomena leading to the growth of disturbance in a
laminar boundary layer can be described.
• As long as these disturbances in a flowing fluid remain
small as compared with the viscous forces, the transition
from laminar to turbulent shall remain delayed.
Boundary Layer Fundamentals
(Cont’d)
• The viscous forces decay the disturbances
• As the boundary layer grows or thickens, the ratio of viscous
forces to inertia forces decreases, and eventually a point is
reached at which disturbances will no longer decay, but will grow
with time and distance
• Then boundary layer becomes unstable and transition from
laminar to turbulent flow begins.
• Eddies and vortexes are formed and destroy the laminar
regularity of the boundary layer motion.
• Quasi-laminar motion, also known as laminar sub-layer, in a
generally turbulent b.l. persists only in a thin layer in the
immediate vicinity of the surface.
Boundary Layer Fundamentals
(Cont’d)
• Region between the laminar sub-layer and
completely turbulent portion of the b.l. is called the
buffer layer.
• The distance from the leading edge at which the
boundary layer becomes turbulent is called the critical
length Xc.
• Critical Reynolds number specifies the critical length
Xc for a particular flow. Rc = U Xc/ is a ratio of
inertial forces to viscous forces at which disturbances
begins to grow.
Boundary Layer Fundamentals
(Cont’d)
• Experimentally, point of transition depends on
the surface conditions:
•Surface contour
•The surface roughness
•The disturbance level
•Heat transfer
Boundary Layer Fundamentals
(Cont’d)
• Without disturbances, a calm laminar flow can persist in the b.l.
at Rc as high as 4x106.
• If the surface is rough, or some other disturbance, the flow may
become turbulent at Rc 3.5x105
• Under avg conditions, the flow over flat plate becomes turbulent
at a distance from from the leading edge Xc where Rc 5x105
Boundary Layer Fundamentals
(Cont’d)
• Separation of b.l. occurs mainly because the k.e. of the fluid in the
boundary layer is dissipated by viscosity within the layer.
• As long as main stream is accelerating, the external pressure is
decreasing along the direction of the flow and the forces at the edge
of the b.l. oppose the retardation of the fluid by the wall shear.
• However, when the flow is decelerating, as for example in a lowspeed diffuser, the external pressure as well as the shearing forces
tend to decelerate the fluid.
• A local reversal of the flow in the b.l. will then occur when the k.e.
of the fluid in the b.l. can no longer over come the adverse pressure
gradient.
• Near this point, the b.l. separates as was shown.
Boundary Layer Fundamentals
(Cont’d)
• Beyond the point of separation, the flow near the
surface consists of highly irregular eddies and vortexes
and can’t be treated by b.l. theory
• Generally speaking, a turbulent b.l. will not separate as
easily as a laminar b.l. because of the higher k.e. of
fluid particles in turbulent layer.
• In a nut shell, the significance of b.l. to the engineer
stems from its relation to the surface shear stress s, and
hence to surface frictional effects.
Boundary Layer Fundamentals
(Cont’d)
•For external flows C =  /(U /2)
f
s

2
•Here, Cf , known as coefficient of friction is a key dimensionless
parameter from which frictional drag may be determined, and
•U is free stream velocity
• Also, assuming Newtonian fluid, the surface shear stress is given as
s= u/y|y=0
•Where  is a fluid property known as dynamic viscosity, and
u/y|y=0 is the velocity gradient at the wall (y=0) surface.
Thermal Boundary Layer
Fluid velocity near the surface is zero.
Heat is transferred to the fluid near the surface
via conduction
• Thus, Qsurface to fluid = -kfAT/y|y=0
• However, from Newton’s law of cooling
Q = hA(Ts-T)
• So we can equate the two, to get
Qs-f = -kfAT/y|y=0= hA(Ts-T)
Thermal Boundary Layer
(Cont’d)
To cater for geometric configuration of the surface,
introducing the characteristic length, L, through which heat
is transferred from the surface, we can write,
• However, from Newton’s law of cooling
hcL/kf = (T/y|y=0)L/(Ts-T)
• In a non dimensional form
hcL/kf = [{(Ts-T)/(Ts-T)}/(y/L)]|y=0
The combination of the convective coefficient hc, the significant
length L, and the thermal conductivity of the fluid kf in the form
hcL/kf is called Nusselt Number, Nu.
Thermal Boundary Layer
(Cont’d)
• Physically, Nu being a dimensionless number, is the ratio of
convective property of the fluid to its conductivity.
• Also, it is a ratio of temperature gradient in the fluid
immediately in contact with the surface to a reference
temperature gradient (Ts-T)/L
• In practice, if Nu is known, heat transfer coefficient can be
calculated from the relation hc= (Nu kf)/L
• The relation shows that for a given Nu, hc is directly
proportional to the kf and inversely proportional to the
characteristic length dimension, L of the system or t, in case
of thermal boundary layer thickness.
Thermal Boundary Layer
(Cont’d)
Velocity Boundary
Layer
Thermal Boundary Layer
CONCLUSION
Fundamentals of Convection
Boundary Layer Fundamentals
Velocity and Thermal Boundary Layers