1. Heat and Mass Transfer Review
Nam Sun Wang
Process Engineering Economics and Design II
Cortez Fisher · Megan Fretz · Sean Roth · Steven Acuna

2. Heat Transfer Introduction
Heat transfer (or heat) is thermal energy in transit due to a spatial temperature difference
Three types of heat transfer processes
Convection
Conduction
Radiation
Types of process heating systems
Steam
Fire Heaters
Sean
source : Bergman, Theodore L., et al. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.

3. Analogies between Fluids and Heat Transfer Mechanisms
Conduction is analogous to the classical fluids illustration of a layer by layer movement between a static plate and a moving plate
We can therefore think of conduction analogous to a frying pan where heat gets conducted from the heat source to the pan, to ultimately the food (i.e. layer by layer)
Sean
source : Bergman, Theodore L., et al. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.

4. Analogies between Fluids and Heat Transfer Mechanisms
Convection is more analogous to the classical fluids example of fluid being driven by a pressure gradient (where P1 > P2)
P1 P2
We can then think of convection as bulk movement by bulk flow
Sean
source : Bergman, Theodore L., et al. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.

5. Conduction
Conduction is the process in which heat is transferred directly through a substance when there is a difference in temperature
Example: The handle of a metal spoon becomes hot after sitting in hot coffee

6. Conduction Follows Fourier’s Law:
where Q is the amount of heat transfer, k is a thermal conductivity, A is area ΔT is the difference in temperature, and L is material thickness

7. Conduction This process occurs mainly in solid materials.
Materials with higher k values are more conductive, while materials with lower k values are more insulating.

8. Conduction
Temperature profile over two walls made of different materials
From this image, we see that Temperature 1 is higher than temperature 2 and heat is traveling from the left to the right. The two walls are made of two varying materials and we can see that k1 has a higher value than k2 due to the gradients across the two walls. The temperatures before and after Wall 2 have a greater difference because wall 2 is more insulating thus a lower k value.

9. Convection
Heat transfer that occurs between a surface and a moving fluid when the two mediums are at different temperatures
Energy Transfer Mechanisms
Random molecular motion (diffusion)
Macroscopic motion of fluid
Radiation
Types of Convection
Forced
Free/Natural
Examples
Hot plate to bring water to a boil
Hot air balloon
Sean
source : Bergman, Theodore L., et al. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.

10. Convection Examples

11. Convection Convection Rate Equation:
Q positive if heat is transferred from surface
h depends on conditions in boundary layer
Surface geometry
Nature of fluid motion
Fluid Transport Properties
Thermodynamic properties
Typical Convection Heat Transfer Coefficients:

12. Convection Boundary Layers

13. Convective Boundary Layer Equations

14. Radiation
Radiation is energy emitted from matter in the form of rays or waves.
Unlike conduction and convection it does not require the presence of a material medium.
Example: Heat emissions felt on one’s hands during a campfire.

15. Radiation
Radiation emitted by a surface is a function of the thermal energy of matter and the rate of energy released per unit surface area (W/m2). derived from the Stefan-Boltzmann Law
The upper limit of Emissive Power is coined as the ideal radiator or blackbody EB
TS is the absolute temperature of the surface (K)
EB=σTS σ is the Stefan-Boltzman constant (5.67x10-8 W/m2*K4)
Not all radiation is an ideal radiator and as such we add a limiting coefficient ε such that
E=εσTS4
ε is the emissivity coefficient from 0 to 1, and varies depends on material
source : Bergman, Theodore L., et al. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.

16. Radiation
The rate of irradiation (i.e. rate of radiation on the surface) can be designated as G
Absorption of radiation increases the thermal energy of the absorbing material
Not all radiation is absorbed, we thus include a limiting coefficient α such that
Gabs=αG
G is the rate of irradiation
Gabs is the irradiation absorbed
α is the absorptivity coefficient bounded from 0 to 1
It is important to know that α depends on the surface of the material and the source of radiation into such material

17. Radiation qrad’’= q/A=εBb(Ts)-αG = εα(TS4-TSur4)
The net rate of radiation heat transfer from the surface becomes;
qrad’’= q/A=εBb(Ts)-αG = εα(TS4-TSur4)
In real world situations we simultaneously put heat transfer along with radiation such that the total rate of heat transfer from the surface becomes:
q=qconv+qrad=hA(Ts-T∞)+εα(TS4-TSur4)
source : Bergman, Theodore L., et al. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.

18. Boundary Conditions Most Common Boundary Conditions:
Constant Surface Temperature
Constant Surface Heat Flux
Convective Surface Condition
One-Dimensional Steady State Heat
Conduction with no Heat Gen.

19. where k is constant Constant Surface Temperature Constant Surface Flux
Adiabatic = no heat flux
Convective Surface Condition
One-Dimensional Steady State Heat Conduction with no Heat Gen.
where k is constant S

20. We can use heat equations and boundary conditions to determine temperature profile
Case 1 (for conduction):
BC 1: x=0, T =Ts1
BC 2: x=L, T=Ts2
Based on , by BC 1
Based on BC 2
Hence,
Case 2 (for conduction):
BC 1: x=0, T =Ts
BC 2: x=L,
Based on , by BC 1
Based on BC 2
Therefore,

21. Heat Transfer among Varying Shapes
SA= 2(ab+ac+bc)
V=abc
SA=2πrh+2πr2
V= πr2h
SA= 4πr2
V=(4/3)πr3
By looking at the surface areas and volumes of various shapes, we can tell how shape affects heat transfer. The greater the surface area to volume ratio, the more heat is able to be transferred. Because a sphere has the lowest surface area to volume ratio, this is the best shape to use if heat transfer is undesireable. If heat transfer is desirable, then you would want to use a rectangular prism to transfer heat.

22. Conclusion As chemical engineers we are to understand the
fundamentals of heat transfer so that we can apply
them to engineering processes such as:
Heat Exchangers
Distillation Columns
Maintaining Desired Reactor Temperatures
Designing novelty Insulating Materials
Understanding these processes allows us to better
design and maximize the parameters of these applications
to ensure desired results.
The small white cubes are LI-900, a type of low-density surface insulation composed almost entirely of silica glass fibers. They are basically pure quartz sand that are 94% air by volume.

23. Works Cited
Bergman, Theodore L., et al. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011
Transport phenomena, R. B. Bird, W. E. Stewart, and E. N. Lightfoot, John Wiley and Sons, Inc., New York (1960).
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