INTRODUCTION TO HEAT TRANSFER

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INTRODUCTION TO HEAT TRANSFER (ME 411) Summer
2003 Lecture Number IX(Summary) Ali R.
Mazaheri Course webpage www.clarkson.edu/mazahe
ar/MAIN/ME411 Department of Mechanical and
Aeronautical Engineering Clarkson University
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Fouriers Law of Conduction
where
k Thermal Conductivity (Heat
conduction coefficient)
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3-D Conduction Heat Transfer in Cartesian
Coordinate Systems
For constant thermal conductivity, i.e.
kcte.
we have
where
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Cylindrical Coordinate System
For Constant k
Spherical Coordinate System
For Constant k
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Steady State 1-D Conduction Heat Transfer
The plane wall
q
Fouriers Law
q
T1
T2
T2
q
T1
Thermal resistance
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Resistance in Cartesian/Cyl./Sphe. Coordinate Sys.
Cartesian
Radial
Spherical
Convection B.Cs.
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Heat Source Systems
1. 1D Conduction with heat generation
The temperature distribution is
2. Cylinder with Heat Source
3. Hollow Cylinder with Heat Source
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Heat Source with Convection
1D Convection with heat generation
Find temperature at the center of the wire, T0.
d3mm
Tw
r
I200A
L1m
, h4000 W/m2 oC
where
Tw215 oC
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We know that
Where
T0231.6 oC
Temperature at the center of the wire..
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Conduction-Convection Systems (Fins)
Heat transfer from the finned surfaces
Total heat transfer
Consider following definitions
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Overall surface efficiency
Heat transfer from the original surface
Fin efficiency
Total heat transfer from the surface with fins
Assume

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Newtons Law of Cooling
Free stream
wall
q
Convection heat transfer coefficient W/m2 oC
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Lumped Heat Capacity System
The lumped capacity method is only valid when
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Multi-Dimensional Systems
Semi-Infinite rectangular bar
Semi-infinite Plate
Infinite rectangular bar
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Short Cylinder
Rectangular parallelepiped
Semi-Infinite Cylinder
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Heat Transfer In Multi-Dimensional Systems
Intersection of Two bodies
Intersection of Three bodies (Semi-infinite
rectangular bar rectangular parallelepiped)
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CONVECTION HEAT TRANSFER

• Definition superposition of energy transport by
  the random motion of molecule and the bulk motion
  of the fluid.

Type I Free Convection
Type II Forced Convection
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Convection Energy Balanceon a Flow Channel
q
Ti
Te
Enthalpy
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Convection Heat Transfer
Thermal Boundary Layer
Uinf.
Tw
x0
Heated
where
and
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Constant Heat Flux
Constant wall temperature
The average temperature difference along the
plate
Properties should be evaluated _at_ the film
temperature
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Fluid Friction and Heat Transfer Correlation
Wall shear stress
Velocity profile over a flat plate
Boundary layer thickness
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Reynolds-Colburn Analogy
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Heat TransferIn Laminar Tube Flow
For Calculation Purposes we use the following
formula
All properties are evaluated at the Bulk
Temperature
Bulk Temperature
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Forced Convection Heat Transfer
Empirical Relations for Pipe Flow
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Flow Across Tube Banks
In-line arrangement
Staggered arrangement
C and n are given in Table 6-4.
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Heat Exchangers
Th1
Tc2
Th2
F Correction factor
Tc1
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NTU Method
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Radiation Heat Transfer

• Conduction and Convection require the presence of
  a material while Radiation does not!

Stefan-Boltzmann Law of Thermal Radiation
Ideal Radiator or Blackbody
Stefan-Boltzmann constant 5.669e-8 W/m2 K4
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The net radiant exchange between two Blackbodies
Gray Bodies
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I
View factor
Emissivity