Short Notes: Free and Forced Convection | Short Notes for Mechanical Engineering PDF Download

 Page 1


Free and Forced Convection 
Convection is the mechanism of heat transfer through a fluid in the presence of 
bulk fluid motion. Convection is classified as natural (or free) and forced 
convection depending on how the fluid motion is initiated.
In natural convection, any fluid motion is caused by natural means such as the 
buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in 
forced convection, the fluid is forced to flow over a surface or in a tube by external 
means such as a pump or fan.
Forced Convection
• The rate of convection heat transfer is expressed by Newton’s law of cooling:
q;^ = h iz - T j ( ft/»j 2)
Q 'cm=hA(Ts- T j (W) •
• 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 
(laminar or turbulent).
Page 2


Free and Forced Convection 
Convection is the mechanism of heat transfer through a fluid in the presence of 
bulk fluid motion. Convection is classified as natural (or free) and forced 
convection depending on how the fluid motion is initiated.
In natural convection, any fluid motion is caused by natural means such as the 
buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in 
forced convection, the fluid is forced to flow over a surface or in a tube by external 
means such as a pump or fan.
Forced Convection
• The rate of convection heat transfer is expressed by Newton’s law of cooling:
q;^ = h iz - T j ( ft/»j 2)
Q 'cm=hA(Ts- T j (W) •
• 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 
(laminar or turbulent).
' Zero velocity 
at the surface.
• It is assumed that the velocity of the fluid is zero at the wall, this assumption 
is called no-slip condition. 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,
ST
4 c o m Q c o n d * f.u d
cy
q ^ = h \ T ; - T j
- k
J:-Q
¦ — > h - -
cT
cv
T. ~ T
[w hn2 .K)
• The convection heat transfer coefficient, 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.
Thermal Boundary Layer
• Similar to velocity boundary layer, a thermal boundary layer develops when a 
fluid at specific temperature flows over a surface which is at different 
temperature.
U» T*
a
Pr = 1
Pr < 1 
ft < 6 ,
ft = fix
The thickness of the thermal boundary layer 5t is defined as the distance at which:
--------^ = 0.99
• The relative thickness of the velocity and the thermal boundary layers is 
described by the Prandtl number.
• For low Prandtl number fluids, i.e. liquid metals, heat diffuses much faster 
than momentum flow (remember Pr = v /a « 1 ) and the velocity boundary
Page 3


Free and Forced Convection 
Convection is the mechanism of heat transfer through a fluid in the presence of 
bulk fluid motion. Convection is classified as natural (or free) and forced 
convection depending on how the fluid motion is initiated.
In natural convection, any fluid motion is caused by natural means such as the 
buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in 
forced convection, the fluid is forced to flow over a surface or in a tube by external 
means such as a pump or fan.
Forced Convection
• The rate of convection heat transfer is expressed by Newton’s law of cooling:
q;^ = h iz - T j ( ft/»j 2)
Q 'cm=hA(Ts- T j (W) •
• 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 
(laminar or turbulent).
' Zero velocity 
at the surface.
• It is assumed that the velocity of the fluid is zero at the wall, this assumption 
is called no-slip condition. 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,
ST
4 c o m Q c o n d * f.u d
cy
q ^ = h \ T ; - T j
- k
J:-Q
¦ — > h - -
cT
cv
T. ~ T
[w hn2 .K)
• The convection heat transfer coefficient, 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.
Thermal Boundary Layer
• Similar to velocity boundary layer, a thermal boundary layer develops when a 
fluid at specific temperature flows over a surface which is at different 
temperature.
U» T*
a
Pr = 1
Pr < 1 
ft < 6 ,
ft = fix
The thickness of the thermal boundary layer 5t is defined as the distance at which:
--------^ = 0.99
• The relative thickness of the velocity and the thermal boundary layers is 
described by the Prandtl number.
• For low Prandtl number fluids, i.e. liquid metals, heat diffuses much faster 
than momentum flow (remember Pr = v /a « 1 ) and the velocity boundary
layer is fully contained within the thermal boundary layer.
• For high Prandtl number fluids, i.e. oils, heat diffuses much slower than the 
momentum and the thermal boundary layer is contained within the velocity 
boundary layer.
Flow Over Flat Plate
• The friction and heat transfer coefficient for a flat plate can be determined by 
solving the conservation of mass, momentum, and energy equations (either 
approximately or
numerically). They can also be measured experimentally. It is found that the N 
usselt number can be expressed as:
Nu = — = CRe* P rr ‘ 
k
where C, m, and n are constants and L is the length of the flat plate. The properties 
of the fluid are usually evaluated at the film temperature defined as:
T, =
T;~TS
2
Laminar Flow
• The local friction coefficient and the Nusselt number at the location x for 
laminar flow over a flat plate are
Nuz = — = 0.332 Re* 2 P r1 ; Pr > 0.6 
1 k
0.664
^ ~ R e1 :'2
where x is the distance from the leading edge of the plate and Rex = pV„x / p.
The averaged friction coefficient and the Nusselt number over the entire isothermal 
plate for laminar regime are:
h _ L 
k
1.32B
r4 ;
Nu= — = 0.664Rej Pr P r> 0 6
Taking the critical Reynolds number to be 5 xl 05, the length of the plate xcr 
over which the flow is laminar can be determined from
V X
=5 ; 10: =
V
Turbulent Flow
• The local friction coefficient and the Nusselt number at location x for 
turbulent flow over a flat isothermal plate are:
Page 4


Free and Forced Convection 
Convection is the mechanism of heat transfer through a fluid in the presence of 
bulk fluid motion. Convection is classified as natural (or free) and forced 
convection depending on how the fluid motion is initiated.
In natural convection, any fluid motion is caused by natural means such as the 
buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in 
forced convection, the fluid is forced to flow over a surface or in a tube by external 
means such as a pump or fan.
Forced Convection
• The rate of convection heat transfer is expressed by Newton’s law of cooling:
q;^ = h iz - T j ( ft/»j 2)
Q 'cm=hA(Ts- T j (W) •
• 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 
(laminar or turbulent).
' Zero velocity 
at the surface.
• It is assumed that the velocity of the fluid is zero at the wall, this assumption 
is called no-slip condition. 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,
ST
4 c o m Q c o n d * f.u d
cy
q ^ = h \ T ; - T j
- k
J:-Q
¦ — > h - -
cT
cv
T. ~ T
[w hn2 .K)
• The convection heat transfer coefficient, 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.
Thermal Boundary Layer
• Similar to velocity boundary layer, a thermal boundary layer develops when a 
fluid at specific temperature flows over a surface which is at different 
temperature.
U» T*
a
Pr = 1
Pr < 1 
ft < 6 ,
ft = fix
The thickness of the thermal boundary layer 5t is defined as the distance at which:
--------^ = 0.99
• The relative thickness of the velocity and the thermal boundary layers is 
described by the Prandtl number.
• For low Prandtl number fluids, i.e. liquid metals, heat diffuses much faster 
than momentum flow (remember Pr = v /a « 1 ) and the velocity boundary
layer is fully contained within the thermal boundary layer.
• For high Prandtl number fluids, i.e. oils, heat diffuses much slower than the 
momentum and the thermal boundary layer is contained within the velocity 
boundary layer.
Flow Over Flat Plate
• The friction and heat transfer coefficient for a flat plate can be determined by 
solving the conservation of mass, momentum, and energy equations (either 
approximately or
numerically). They can also be measured experimentally. It is found that the N 
usselt number can be expressed as:
Nu = — = CRe* P rr ‘ 
k
where C, m, and n are constants and L is the length of the flat plate. The properties 
of the fluid are usually evaluated at the film temperature defined as:
T, =
T;~TS
2
Laminar Flow
• The local friction coefficient and the Nusselt number at the location x for 
laminar flow over a flat plate are
Nuz = — = 0.332 Re* 2 P r1 ; Pr > 0.6 
1 k
0.664
^ ~ R e1 :'2
where x is the distance from the leading edge of the plate and Rex = pV„x / p.
The averaged friction coefficient and the Nusselt number over the entire isothermal 
plate for laminar regime are:
h _ L 
k
1.32B
r4 ;
Nu= — = 0.664Rej Pr P r> 0 6
Taking the critical Reynolds number to be 5 xl 05, the length of the plate xcr 
over which the flow is laminar can be determined from
V X
=5 ; 10: =
V
Turbulent Flow
• The local friction coefficient and the Nusselt number at location x for 
turbulent flow over a flat isothermal plate are:
N u = — = 0.0296 Re* 5 Pr* 3 
k
0.6 < Pr < 60 5x10s < Re, <10*
5x10- < R er <10
• The averaged friction coefficient and Nusselt number over the isothermal 
plate in turbulent region are:
hi
N u = — = 0.037Re* 5 Pr1 3 0 6 < P r < 6 0 5x10s < ReL < 10'
Natural Convection
In natural convection, the fluid motion occurs by natural means such as buoyancy. 
Since the fluid velocity associated with natural convection is relatively low, the heat 
transfer coefficient encountered in natural convection is also low.
Grashof Number
Grashof number is a dimensionless group. It represents the ratio of the buoyancy f 
orce to the viscous force acting on the fluid:
g buoyancy forces gAp\' g/JATV 
viscous forces pl'~ p v
It is also expressed as
• The role played by Reynolds number in forced convection is played by the 
Grashof number in natural convection.
• The critical Grashof number is observed to be about 109 for vertical plates.
• Thus, the flow regime on a vertical plate becomes turbulent at Grashof 
number greater than 109.
• The heat transfer rate in natural convection is expressed by 
Newton’s law of cooling as: Q’conv = h A (Ts - T°°)
k
• where g = gravitational acceleration, m/s2
• P = coefficient of volume expansion, 1/K
• 5 = characteristic length of the geometry, m
• v = kinematics viscosity of the fluid, m2/s
Note:
Page 5


Free and Forced Convection 
Convection is the mechanism of heat transfer through a fluid in the presence of 
bulk fluid motion. Convection is classified as natural (or free) and forced 
convection depending on how the fluid motion is initiated.
In natural convection, any fluid motion is caused by natural means such as the 
buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in 
forced convection, the fluid is forced to flow over a surface or in a tube by external 
means such as a pump or fan.
Forced Convection
• The rate of convection heat transfer is expressed by Newton’s law of cooling:
q;^ = h iz - T j ( ft/»j 2)
Q 'cm=hA(Ts- T j (W) •
• 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 
(laminar or turbulent).
' Zero velocity 
at the surface.
• It is assumed that the velocity of the fluid is zero at the wall, this assumption 
is called no-slip condition. 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,
ST
4 c o m Q c o n d * f.u d
cy
q ^ = h \ T ; - T j
- k
J:-Q
¦ — > h - -
cT
cv
T. ~ T
[w hn2 .K)
• The convection heat transfer coefficient, 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.
Thermal Boundary Layer
• Similar to velocity boundary layer, a thermal boundary layer develops when a 
fluid at specific temperature flows over a surface which is at different 
temperature.
U» T*
a
Pr = 1
Pr < 1 
ft < 6 ,
ft = fix
The thickness of the thermal boundary layer 5t is defined as the distance at which:
--------^ = 0.99
• The relative thickness of the velocity and the thermal boundary layers is 
described by the Prandtl number.
• For low Prandtl number fluids, i.e. liquid metals, heat diffuses much faster 
than momentum flow (remember Pr = v /a « 1 ) and the velocity boundary
layer is fully contained within the thermal boundary layer.
• For high Prandtl number fluids, i.e. oils, heat diffuses much slower than the 
momentum and the thermal boundary layer is contained within the velocity 
boundary layer.
Flow Over Flat Plate
• The friction and heat transfer coefficient for a flat plate can be determined by 
solving the conservation of mass, momentum, and energy equations (either 
approximately or
numerically). They can also be measured experimentally. It is found that the N 
usselt number can be expressed as:
Nu = — = CRe* P rr ‘ 
k
where C, m, and n are constants and L is the length of the flat plate. The properties 
of the fluid are usually evaluated at the film temperature defined as:
T, =
T;~TS
2
Laminar Flow
• The local friction coefficient and the Nusselt number at the location x for 
laminar flow over a flat plate are
Nuz = — = 0.332 Re* 2 P r1 ; Pr > 0.6 
1 k
0.664
^ ~ R e1 :'2
where x is the distance from the leading edge of the plate and Rex = pV„x / p.
The averaged friction coefficient and the Nusselt number over the entire isothermal 
plate for laminar regime are:
h _ L 
k
1.32B
r4 ;
Nu= — = 0.664Rej Pr P r> 0 6
Taking the critical Reynolds number to be 5 xl 05, the length of the plate xcr 
over which the flow is laminar can be determined from
V X
=5 ; 10: =
V
Turbulent Flow
• The local friction coefficient and the Nusselt number at location x for 
turbulent flow over a flat isothermal plate are:
N u = — = 0.0296 Re* 5 Pr* 3 
k
0.6 < Pr < 60 5x10s < Re, <10*
5x10- < R er <10
• The averaged friction coefficient and Nusselt number over the isothermal 
plate in turbulent region are:
hi
N u = — = 0.037Re* 5 Pr1 3 0 6 < P r < 6 0 5x10s < ReL < 10'
Natural Convection
In natural convection, the fluid motion occurs by natural means such as buoyancy. 
Since the fluid velocity associated with natural convection is relatively low, the heat 
transfer coefficient encountered in natural convection is also low.
Grashof Number
Grashof number is a dimensionless group. It represents the ratio of the buoyancy f 
orce to the viscous force acting on the fluid:
g buoyancy forces gAp\' g/JATV 
viscous forces pl'~ p v
It is also expressed as
• The role played by Reynolds number in forced convection is played by the 
Grashof number in natural convection.
• The critical Grashof number is observed to be about 109 for vertical plates.
• Thus, the flow regime on a vertical plate becomes turbulent at Grashof 
number greater than 109.
• The heat transfer rate in natural convection is expressed by 
Newton’s law of cooling as: Q’conv = h A (Ts - T°°)
k
• where g = gravitational acceleration, m/s2
• P = coefficient of volume expansion, 1/K
• 5 = characteristic length of the geometry, m
• v = kinematics viscosity of the fluid, m2/s
Note:
Natural Convection Correlations
• The complexities of the fluid flow make it very difficult to obtain simple 
analytical relations for natural convection. Thus, most of the relationships in 
natural convection are based on experimental correlations. The Rayleigh 
number is defined as the product of the Grashof and Prandtl numbers:
^a = GrPr =
sp(T2- T ^
Pr
• The Nusselt number in natural convection is in the following form:
hS
Nu = — = CRa
k
J i
where the constants C and n depend on the geometry of the surface and the 
flow.These relationships are for isothermal surfaces but could be used 
approximately for the case of non-isothermal surfaces by assuming surface 
temperature to be constant at some average value.
Isothermal Vertical Plate
• For a vertical plate, the characteristic length is L,
fo.59.foz14 104 < ^ < 1 0 9
lO.Lfoz1 '3 10* < Ra < 101 3
• Note that for ideal gases, (3 = 1 / T„
Isothermal Horizontal Plate
The characteristics length is A/p where the surface area is A, and the perimeter is 
P -
Upper surface of a hot plate
Nu =
0.54 Ra' 10+ <Ra <10
0.15foz1 ,3 10? < Ra < 101 1
• Lower surface of a hot plate
1/4
Nu = 0.27 Ra 105 <ito<10u