1. Heat Transfer
Ana Galvao, Julie Kessler, Luke O’Malley, Matteo Ricci & Jessica Young
“L JJAM” aka “Dream Team” aka Team 3
CHBE446 02/02/18
Aka “Haha. A great shot. Priceless. Yes, you do whatever you want”

2. HOT HOT HOT! Background Theory Conduction Convection Heat Exchangers
Photo Cred: Meghan

3. Heat Transfer
The physical process in which thermal energy is transferred from one object to another as a result of a temperature difference
Thermodynamics vs Heat Transfer
Thermodynamics:
How much heat is transferred
How much work is done
State of the system
Heat Transfer:
How heat is transferred
Rate at which heat is transferred
Temperature distribution within an object

4. How heat is transferred
Conduction
Heat transfer due to molecular interactions.
Convection
Heat transfer due to the bulk movement of particles in a fluid.
Radiation
Energy emitted from matter through changes in electron configurations
**Cover: main equations in Heat Transfer (i.e.: Fick's law, …)

5. Common Heat Transfer Parameters
Quantity
Meaning
Symbol
Units
Thermal Energy
Internal energy present within a system due to its temperature
U = Cv( T - Tref)
J or J/kg
Temperature
Intensity of heat present in a object T
C, F, R, K
Heat Transfer
Total thermal energy transport caused by a temperature gradient Q J
Heat Rate
Thermal energy transport per unit time q
J/s or W
Heat Flux
Thermal energy transport per unit time and surface area
q``
W/m2

6. Basic Equations Fourier's Law of Thermal Conduction
Q = -kA(ΔT)
Q - Heat Rate (J/s or W)
k - Thermal Conductivity (W/(m⋅K))
A - Area (m2)
Newton’s Law of Cooling (Convection)
Q = hA(T - Ts)
h - Heat transfer coefficient (W/(m2 K))
T - Temperature of object
Ts - Temperature of Surroundings
Stefan-Boltzmann Law (Radiation)
Q = eσA(T4 - Ts4)
Q - Radiation rate (J/s or W)
e - Thermal emissivity
σ - Boltzmann constant ( (W/m2K4))
T - Temperature of object
Ts - Temperature of Surroundings

7. Conduction: Shell Balances and BCs
General Procedure:
Visualize system
Draw shell
Energy balance over shell
Apply Fourier’s Law
Solve for heat flux and temp gradient
Types of BCs:
Constant temperature
Insulated
Newton’s Law of Cooling
**Cover: boundary conditions, composite wall

8. Conduction: Differential Eqns
General Equation
Conduction Only
Nonconstant k
Thermal Diffusivity
No Source
Steady State and No Source
**Cover: boundary conditions, composite wall

9. Conduction: Unsteady
Negligible internal resistance (large k, Bi < .1) also called “lumped parameter”
Negligible surface/ internal resistance (Bi > 100)
Finite surface/ internal resistance ( .1 < Bi < 100 )
**Cover: boundary conditions, composite wall

10. Conduction: Quasi Steady
General Procedure
Develop SS model for barrier
Define
Write sensible heat balance
Barrier
T(t)
**Cover: boundary conditions, composite wall

11. Convection Heat transfer due to bulk flow of fluid
Much more difficult than conduction to calculate heat transfer analytically
Correlation used depends on several factors
Convective heat flow is where there is bulk flow of a fluid flowing over some surface typically a parallel plate or a pipe. The cases we generally look at have the surface temperature being constant. This space heater shows the hot air rising as it comes into contact with the surface, falling as it cools, and repeating. The temperature change in the fluid is much more difficult to calculate analytically than conduction, so several correlations have been found empirically for many different scenarios. The correlation depends on several factors such as whether the fluid is turbulent or laminar, if it’s flowing over a flat plate or through a pipe, if it’s gas or liquid, if there’s a phase change, and other factors.

12. Convective Correlations
Boundary Layer- Laminar Flow
Reynold’s Analogy- Laminar Flow through Pipe
Colburn Analogy- Turbulent Flow through Pipe
Dittus Boelter Equation- Turbulent Flow through pipe
n=0.4 for fluid being heated, 0.3 for fluid being cooled
Here are some of the convective correlations. There are several more but these are some of the more common ones we used in Heat and Mass Transfer.

13. Convective Correlations
Overall goal to solve for the Stanton number
Use the Stanton number to solve for the values of temperature in third equation
The point of these correlations is to calculate the Stanton number. Which, as you can see here, can be related by several of the factors and variables shown in the previous slide. The Stanton number is more importantly related to the relationship between the inlet, outlet, and wall temperature. There are several ways to calculate the Stanton number, which means in some cases iterations must be used to solve for the outlet temperature. In these cases the outlet temperature is guessed based on inlet and wall temp. This temperature is used to solve for the dimensionless variables, which are used to solve for the stanton number. This temperature is again used to solve for the “Y” value in the equations above which is used to again find the stanton number. This process is iterated until the stanton values are the same.

14. Characteristics of HXs
# of passes
Single Vs. Multiple
Configuration of HX
Double Pipe, Shell and Tube, Compact
Direction of relative flow
Parallel/Cocurrent Flow (same direction)
Counter/Countercurrent Flow (opposite direction)
Cross Flow (opposite direction, more complicated)
**Cover: Types of HXs, types of flows (cocurrent vs countercurrent),

15. Characteristics of HXs
# of passes
Single Vs. Multiple
Configuration of HX
Double Pipe, Shell and Tube, Compact
Direction of relative flow
Parallel/Cocurrent Flow (same direction)
Counter/Countercurrent Flow (opposite direction)*
Cross Flow (opposite direction, more complicated)
**Cover: Types of HXs, types of flows (cocurrent vs countercurrent),

16. Characteristics of HXs
# of passes
Single Vs. Multiple
Configuration of HX
Double Pipe, Shell and Tube, Compact
Direction of relative flow
Parallel/Cocurrent Flow (same direction)
Counter/Countercurrent Flow (opposite direction)
Cross Flow (opposite direction, more complicated)
**Cover: Types of HXs, types of flows (cocurrent vs countercurrent),

17. You may solve for various HX parameters using analytical methods and correlations.
Calculations:
Temp in & out
Tcin, Tcout, Thin, Thout
Efficiency
Area of heat transfer A
Overall heat transfer coefficient U
Methods:
Analytically
Single, Double, Non-Cross Flow
Correlations
All Else
Characteristics:
# of passes
Configuration
Direction of relative flow
**Cover: Types of HXs, types of flows (cocurrent vs countercurrent),

18. You may solve for various HX parameters using analytical methods and correlations.
Calculations:
Temp in & out
Tcin, Tcout, Thin, Thout
Efficiency
Area of heat transfer A
Overall heat transfer coefficient U
Methods:
Analytically
Single, Double, Non-Cross Flow
Correlations
All Else
Characteristics:
# of passes
Configuration
Direction of relative flow
**Cover: Types of HXs, types of flows (cocurrent vs countercurrent),

19. You may solve for various HX parameters using analytical methods and correlations.
Calculations:
Temp in & out
Tcin, Tcout, Thin, Thout
Efficiency
Area of heat transfer A
Overall heat transfer coefficient U
Methods:
Analytically
Single, Double, Non-Cross Flow
Correlations
All Else
Characteristics:
# of passes
Configuration
Direction of relative flow
**Cover: Types of HXs, types of flows (cocurrent vs countercurrent),

20. Heat Exchangers
Log Mean Temperature Difference (LMTD) Number of Transfer Units (NTU)
They are equivalent methods, since NTU is derived from LMTD without introducing any assumptions
LMTD: more appropriate for sizing, easy when all temps are known, only directly used for single pass HXs, (otherwise figures are required)
NTU: better if there are unknown temps, good for calculating rate of heat transferred, (no need for iterations), good for all types of hxs as long as effect. Is known,

21. Heat Exchangers
Example: Calculating Heat-Transfer Area - Oil & Water in HX
LMTD Method:
Examples on pages: & 382
Applying LMTD and NTU on counterflow, single pass HX.
LMTD:
1st: determine outlet temp of water using q(water)=q(oil)=mcT
2nd: find LMTD for specific configuration
3rd: Find area from given formula
NTU:
1st: find both Cs and determine C(min)
2nd: Find effectiveness
3rd: Use charts to find NTU
4th: Calculate area

22. Heat Exchangers
Example: Calculating Heat-Transfer Area - Oil & Water in HX
NTU Method
Examples on pages: & 382
Applying LMTD and NTU on counterflow, single pass HX.
LMTD:
1st: determine outlet temp of water using q(water)=q(oil)=mcT
2nd: find LMTD for specific configuration
3rd: Find area from given formula
NTU:
1st: find both Cs and determine C(min)
2nd: Find effectiveness (e)
3rd: Use charts to find NTU from e
4th: Calculate area

23. Questions?
Ask the expert!