E! I Heat and Mass Transfer
2.3. GENERAL HEAT CONDUCTIOH EQUATION IN
CYLINDRICAL COORDINATES
While dealing with problems of conduction of heat through systems having cylindrical geometries
(8.3., rods and pipes) it is convenient to use cylindrical coordin

ME 333
Heat Transfer
Lecture 5
Spring 2015
The Temperature Distribution
The temperature distribution represents how temperature
varies with position in the medium.
If this distribution is known, it helps in determining
Conduction heat flux at any point

ME 333
Heat Transfer
Lecture 4
Spring 2015
Problem 1.60
During its manufacture, plate glass at 600C is cooled by
passing air over its surface such that the convection
heat transfer coefficient is h= 5W/m2 K. To prevent
cracking, it is known that the tempe

ME 333
Heat Transfer
Lecture 3
Spring 2015
Radiation
The changes in the electron configurations of the constituent
atoms or molecules results in the emission of electromagnetic
waves (photons).
Thermal radiations can be absorbed, reflected and transmitted

ME 333
Heat Transfer
Lecture 2
Spring 2015
Review of Thermodynamics
Thermodynamics is the science of energy.
Thermodynamics
Therme
(Heat)
Energy Conversion
Dynamics
(Power)
Work and Heat: Energy Interactions or Boundary Interactions
Thermodynamics is co

ME 333
Heat Transfer
Lecture 41
Spring 2015
Driving Force
2
Driving Force
3
Analogy Between Heat and Mass Transfer
4
Mass Transfer by Diffusion
A species is an identifiable molecule, such as CO2, that can be
transported by diffusion and advection and/or

ME 333
Heat Transfer
Lecture 42
Spring 2015
Mass Transfer in Non-stationary Media
Absolute Species Flux:
The total flux relative to a fixed coordinate system.
Consider species A in a binary mixture of A and B:
Absolute mass flux:
is the average velocity o

ME 333
Heat Transfer
Lecture 40
Spring 2015
Problem 12.42
A
large body of nonluminous gas at a temperature of 1200K has
emission bands between 2.5 and 3.5m and between 5 and 8 m.
The effective emissivity in the first band is 0.8 and in the second
0.6. Det

ME 333
Heat Transfer
Lecture 7
Spring 2015
Problem 2.24
The temperature distribution across a wall 0.3 m thick at a certain
instant of time is,
where T is in degrees Celsius and x is in meters, a=200C, b=200C/m, and c=30C/m2. The wall has a thermal conduc

ME 333
Heat Transfer
Lecture 8
Spring 2015
Temperature Distribution in Plane Wall
2
Thermal Resistance
Resistance is the ratio of a driving potential to the
corresponding transfer rate
3
The Composite Wall
Overall heat Transfer Coefficient:
4
The Composit

ME 333
Heat Transfer
Lecture 16
Spring 2015
Variation of and h along a flat plate
2
Problem 6.8
Air
at a free stream temperature of T20C is in parallel flow over a
flat plate of length L=5 m and temperature Ts=90C. However,
obstacles placed in the flow in

ME 333
Heat Transfer
Lecture 15
Spring 2015
The Convection Boundary Layers
Velocity Boundary Layer:
Thermal Boundary Layer:
2
Local and Average Convection Coefficients
Since;
Equating the two heat rates given above
3
Laminar and Turbulent Flow
4

ME 333
Heat Transfer
Lecture 14
Spring 2015
Fin Performance
Fins are used to increase the heat transfer from a
surface by increasing the effective surface area.
However, the fin itself represents a conduction
resistance to heat transfer from the origina

ME 333
Heat Transfer
Lecture 13
Spring 2015
Fins of Uniform Cross-sectional Area
2
Fins of Uniform Cross-sectional Area (2)
Boundary Conditions:
B.C (1):
B.C (2):
Case A:
3
Fins of Uniform Cross-sectional Area (3)
Case B: Fin tip is adiabatic (No Convecti

ME 333
Heat Transfer
Lecture 12
Spring 2015
Problem 3.95
2
1-D Conduction with Convection
Until now, we have considered heat transfer from the boundaries
of a solid to be in the same direction as heat.
In contrast, for an extended surface, the direction

ME 333
Heat Transfer
Lecture 11
Spring 2015
Temperature Distribution with Heat Generation
Plane Wall:
For 1-D, steady-state conditions
with heat generation,
General solution:
With generation the heat flux is no longer independent of x.
So, Thermal Resista

ME 333
Heat Transfer
Lecture 10
Spring 2015
Problem 3.9
The composite wall of an oven consists of three materials,
two of which are of known thermal conductivity, k A=20
W/m-K and kC=50 W/m-K, and known thickness, LA=0.30 m
and LC=0.15 m. The third materi

ME 333
Heat Transfer
Lecture 9
Spring 2015
Temperature Distribution in Radial Systems
For 1-D, steady-state conditions
with no heat generation,
General solution:
2
The Composite Cylindrical Wall
3
An Alternative Conduction Analysis
If A is uniform and k i

ME 333
Heat Transfer
Lecture 39
Spring 2015
Emission from Real Surfaces
Emissivity: The ratio of the radiation emitted by the surface to the
radiation emitted by a blackbody at the same temperature.
The spectral radiation emitted by a real surface differs

ME 333
Heat Transfer
Lecture 38
Spring 2015
Planks Distribution
Spectral Intensity:
Planks Constant:
Boltzmann Constant:
Speed of light in vacuum:
Spectral Emissive Power of Blackbody:
The 1st and 2nd
radiation constants
2
Blackbody Emissive Power Distrib

ME 333
Heat Transfer
Lecture 36
Spring 2015
Radiation Intensity: Mathematical Definitions
Plane Angle: For a circle of unit radius, the length
of an arc is equivalent in magnitude to the plane
angle it subtends.
Solid Angle: The area of a surface on a sph

ME 333
Heat Transfer
Lecture 25
Spring 2015
Internal Flow (Flow Conditions)
2
The Mean Velocity and the Velocity Profile
3
Friction Factor
4
Moody Diagram
5

ME 333
Heat Transfer
Lecture 24
Spring 2015
The Cylinder in Cross Flow
2
Effect of Reynolds No on Separation
3
Effect of Reynolds No on Drag Coefficient
4
Convection Heat Transfer Over Cylinders
5
Convection Heat Transfer Over Cylinders (2)
6

ME 333
Heat Transfer
Lecture 23
Spring 2015
Problem 7.24
Steel
(AISI 1010) plates of thickness 6 mm and length L=1 m on a
side are conveyed from a heat treatment process and are
concurrently cooled by atmospheric air of velocity u=10 m/s and
T = 20 C in p

ME 333
Heat Transfer
Lecture 22
Spring 2015
The Results of Blasius Solution
These results may be used to compute important laminar flow over
an isothermal flat plate parameters for 0 < x <xc.
2
The Results of Blasius Solution (2)
For fluids of small Pr i.

ME 333
Heat Transfer
Lecture 21
Spring 2015
The Empirical Method
For a fixed geometry;
2
The Empirical Method (2)
For Fluid 1: Pr1
S.No
For Fluid 3: Pr3
For Fluid 2: Pr2
ReL
S.No
ReL
S.No
1
1
1
2
2
2
3
3
ReL
3
Film Temperature:
3
The Analytical Method
Bla

ME 333
Heat Transfer
Lecture 20
Spring 2015
Reynolds Analogy
When
Pr1; the case for most gases
; The case of flat plate when u=U in the free stream
Reynolds Analogy
2
Modified Reynolds Analogy: Chilton-Colburn Analogy
jH : Colburn Factor for Heat Transfe

ME 333
Heat Transfer
Lecture 19
Spring 2015
Functional Forms of the Solutions
2
Functional Forms of the Solutions (2)
It provides a measure of the
convection heat transfer
occurring at the surface.
The Nusselt number is to the thermal boundary layer what