qx hAT qx hA(Tw T )
heating
Metal wall Twh cold fluid Twc
Warm fluid
cooling
Tc
qx
k
h

A(Tw T )
• The reason for this is 1) Heat must transfer through the boundary layer by conduction. conductivity (k) 2) Most of the fluid have a low thermal 3) While in the turbulent core there are a rapid moving eddies, which they are equalizing the temperature.
• The closed-type exchanger is the most popular one. • One example of this type is the Double pipe exchanger.
• In this type, the hot and cold fluid streams do not come into direct contact with each other. They are separated by a tube wall or flat plate.
h h .C p Qh A.m .Th
c c .C p Qc A.m .Tc
0
ˆ ˆ .h .h m m
in out
•Control Volume
COLD
HOT
Cross Section Area
Thermal Boundary Layer
THERMAL BOUNDARY LAYER

qx hhot .Th Tiw .A
qx kcopper .2L r ln o ri
Th Tiw
qx hh .Ai

ro qx .ln ri To,wall Ti,wall kcopper .2L

qx hc To,wall Tc Ao

qx To,wall Tc hc .Ao
Th Tc
qx U.A.Th Tc

U 1 A.R
qx R1 R2 R3
ro ln r 1 1 i Th Tc qx hh .Ai kcopper .2L hc .Ao
Principle of Heat Exchanger
• First Law of Thermodynamic: “Energy is conserved.” 0 0 0 dE ˆ ˆ .hin m .hout q w s e generated m dt out in
Heat Exchangers prevent car engine overheating and increase efficiency Heat exchangers are used in Industry for heat transfer
Heat exchangers are used in AC and furnaces
T2 T1 T2 ln T 1
Log Mean Temperature evaluation h c ?p ?p ? h .C ? c .C m .T3 T6 m .T7 T10 T2 T1 TLn U T2 A.TLn A.TLn ln T 1
If this motion is associated with heat transfer mechanism only, then it is called Natural Convection
Forced Convection
If this motion is associated by mechanical means such as pumps, gravity or fans, the movement of the fluid is enforced. And in this case, we then speak of Forced convection.
Energy moves from hot fluid to a surface by convection, through the wall by conduction, and then by convection from the surface to the cold fluid.
Region III: Solid – Cold Liquid Convection
How is the heat transfer?
• Heat can transfer between the surface of a solid conductor and the surrounding medium whenever temperature gradient exists. Conduction Convection Natural convection Forced Convection
1 CON CURRENT FLOW 2
COUNTER CURRENT FLOW
U = The Overall Heat Transfer Coefficient [W/m.K]
Region I : Hot Liquid – Solid Convection Region II : Conduction Across Copper Wall Region III : Solid – Cold Liquid Convection
Region II : Conduction Across Copper Wall FOURIER’S LAW
dT dqx k . dr
• Velocity distribution and boundary layer When fluid flow through a circular tube of uniform crosssuction and fully developed, The velocity distribution depend on the type of the flow. In laminar flow the volumetric flowrate is a function of the radius.
1 1 d (T ) U .T .dA. m .C h m .C c c p h p

T2
T1
Th Tc A2 d (T ) U . . dA T qc A1 qh

T2
T1
1 d (T ) 1 U . m .C h m .C c T c p h p
Natural and forced Convection
Natural convection occurs whenever heat flows between a solid and fluid, or between fluid layers. As a result of heat exchange Change in density of effective fluid layers taken place, which causes upward flow of heated fluid.
Lesson 22 Heat Transfer
• • • •
• • • • •
How is the heat transfer? Mechanism of Convection Applications . Mean fluid Velocity and Boundary and their effect on the rate of heat transfer. Fundamental equation of heat transfer Logarithmic-mean temperature difference. Heat transfer Coefficients. Heat flux and Nusselt correlation Simulation program for Heat Exchanger
1
+
ro ro . ln r r 1 i U o hhot .ri kcopper .ri hcold
r
i
r
o
Calculating U using Log Mean Temperature
Hot Stream : Cold Stream:
Boundary layer
r
• Accordingly the temperature gradient is larger at the wall and through the viscous sub-layer, and small in the turbulent core.
Tube wall
Heat Exchangers
• A device whose primary purpose is the transfer of energy between two fluids is named a Heat Exchanger.
Applications of Heat Exchangers
dqx hc .Tow Tc .dA
Th Ti,wall
NEWTON’S LAW OF CCOLING

Region I : Hot LiquidSolid Convection NEWTON’S LAW OF CCOLING Q hot