This document discusses various types of convection heat transfer including forced convection, natural convection, and heat exchangers. It provides the governing equations for laminar and turbulent flow over flat plates and cylinders for external forced convection. For internal forced convection, it describes how the reference temperature changes along the flow. Free or natural convection is described using equations involving the Grashof and Rayleigh numbers. Finally, it summarizes the LMTD and ε-NTU methods for analyzing heat exchangers.

1. Convection
By :-
140080125013 (kishan patel)
140080125014 (Ankit machhi)
140080125015 (Karan machhi)
140080125016 (Manthan panchal)
Guided by :- Dr.Manish Mehta

2. Viscous Flow
The Navier-Stokes Equations
Nonlinear, second order, partial differential equations.
Couette Flow, Poiseuill Flow.






∂
∂
+
∂
∂
+
∂
∂
++
∂
∂
−=





∂
∂
+
∂
∂
+
∂
∂
+
∂
∂






∂
∂
+
∂
∂
+
∂
∂
++
∂
∂
−=





∂
∂
+
∂
∂
+
∂
∂
+
∂
∂






∂
∂
+
∂
∂
+
∂
∂
++
∂
∂
−=





∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
z
w
y
w
x
w
g
z
p
z
w
w
y
w
v
x
w
u
t
w
z
v
y
v
x
v
g
y
p
z
v
w
y
v
v
x
v
u
t
v
z
u
y
u
x
u
g
x
p
z
u
w
y
u
v
x
u
u
t
u
z
y
x
µρρ
µρρ
µρρ
0=
∂
∂
+
∂
∂
+
∂
∂
z
w
y
v
x
u

3. Convection
• Basic heat transfer equation
Primary issue is in getting convective heat
transfer coefficient, h
h relates to the conduction into the fluid at
the wall
average heat transfer
coefficient
)( ∞−= TTAhq ss =h
∫=∫=
L
A
s
s
dxh
L
hdAh
A
h
s 0
1
:unit widthforor,
1
( )∞
=
−
∂
∂
=
TT
y
T
k
h
s
y
f
x
0
-

4. Convection Heat Transfer Correlations
Key is to fully understand the type of problem and
then make sure you apply the appropriate
convective heat transfer coefficient correlation
External Flow
For laminar flow over flat plate
y
0=
dx
dP
∞∞UT ,
sT
δ
3
1
2
1
x PrRe0.332=≡
k
xh
Nu x
x 3
1
2
1
x PrRe0.664=≡
k
xh
uN x
x






∫+∫=
L
xc
turb
xc
lamx dxhdxh
L
h
1
0

5. External Convection Flow
For flow over cylinder
Overall Average Nusselt number
Table 7.2 has constants C and m as f(Re)
For flow over sphere
For falling liquid drop
41
31
Pr
Pr
PrRe 





==
s
m
DD C
k
Dh
Nu
41
4.03221
Pr)Re0.06Re(0.42 





µ
µ
++==
s
DDD
k
Dh
Nu
3121
PrRe0.62 DDNu +=

6. Convection with Internal Flow
Main difference is the constrained boundary layer
Different entry length for laminar and turbulent flow
Compare external and internal flow:
 External flow:
Reference temperature: T∞ is constant
 Internal flow:
Reference temperature: Tm will change if heat transfer is occurring!
 Tm increases if heating occurs (Ts > Tm )
 Tm decreases if cooling occurs (Ts < Tm )
ro
δ
δ

7. Internal Flow (Cont’d)
For constant wall temperature
T
x
)(xTs
)(xTm
thermalfdx ,
LMsconv ThAq ∆=
in
p
conv
xm T
cm
q
T x, +⋅
′
=


8. Free (Natural)
Convection
• Grashof number in natural convection is analogous to
the Reynolds number in forced convection
Unstable,
Bulk fluid motion
Stable,
No fluid motion
( )
forcesViscous
forcesBuoyancy
2
3
=
−
= ∞
ν
β LTTg
Gr s
L

9. Free (Natural)
ConvectionRayleigh number: For relative magnitude of
buoyancy and viscous forces
Review the basic equations for different
potential cases, such as vertical plates,
vertical cylinders, horizontal plates
(heated and cooled)
For horizontal plates, discuss the equations
9.30-9.32. (P513)
Please refer to problem 9.34.
For vertical surface, transition to turbulence at Rax ≅ 109
Pr⋅= xx GrRa

10. Heat Exchangers
• Two basic methods discussed:
1. LMTD Method
2. ε-NTU Method
Example:
Shell and Tube:
Cross-counter Flow
outBT ,
side)(shell,inBT
side)(tube,inAT
outAT ,
LMTD
i
o
inout
TUA
T
T
TT
UAq ∆=
∆
∆
∆−∆
=
ln
( )icih TTCq
or
qq
,,min
max
:
−=
=
ε
ε
( )icih TTCqwhere
q
q
,,minmax
max
: −=
=ε
min
,
NTU
C
UA HXoverall
=
( )rCNTUf ,=ε
( )1CC r
max
min
r <=
C
C