1. Review & Theory of Heat Transfer
CHBE 446: Process Engineering Economics and Design II
Project 1 Presentation
Feb. 8th 2019
Team 5: Nathnael Asfaw, Sina Ataei, Michael Cohen, Albert Park, Shamim Rahman, Hartej Singh

2. History of Heat Transfer
Sir Isaac Newton
Sir Isaac Newton’s Law of Cooling (1701) provided the formal groundwork for the modern subject of heat transfer
This law was incorporated by French mathematician and physicist Joseph Fourier in 1822 to develop his mathematical theory of heat conduction, which included the convective boundary condition (Biot Number)
Application of the concepts of heat transfer coefficients took a major step forward with the publication of “Basic Law of Heat Transfer” by Wilhelm Nusselt in 1915
Hartej

3. Applications of Heat Transfer in Industry
The concept of Heat Transfer is encountered in our everyday lives, from when we make our hot cup of coffee in the morning, to when we wait for our car’s to heat up on a cold winter morning
In an engineering context, concepts of Heat Transfer are used in many industries to make important design decisions
Examples of Heat Transfer that a Chemical Engineer in industry may encounter include the effective implementation of Heat Exchangers, Cooling Towers, and Cooling Jackets for reactors
Hartej

4. Industrial-scale shell and tube heat exchanger
Heat Exchangers
Industrial-scale shell and tube heat exchanger
The objective is to transfer heat from one medium to another without the actual transfer of the fluid
Heat Exchangers are equipment that are vital in many engineering disciplines
Common household examples of Heat Exchangers include refrigerators and air conditioners
Co-current configuration
Counter-current configuration
Ponce, D. A. CHBE 437 Armfield Heat Exchanger - Lab Manual
Nati

5. Shell & Tube Heat Exchanger
Most common heat exchanger in industrial applications
Tubes are tightly packed parallel to the axis of the shell
One fluid flows through the tubes, another flows outside the tubes through the shell
Baffles are used to direct flow
Nati

6. Convection
Convection involves energy transfer between a surface and adjacent bulk fluid
Newton developed rate equation for convective heat transfer in 1701
Known as “Newton’s law of cooling”
q/A=hΔT
Two distinguishable types of convection
Forced convection: fluid is passed through solid surface by fan or pump
Free or “natural” convection: warmer or cooler fluid adjacent to solid boundary causes heat circulation due to density difference resulting from temperature gradient
Shamim
Image from

7. Correlations for Convective Transfer
Convective heat transfer coefficient or film coefficient h
Represents resistance to convective heat transfer
Some convective systems cannot be solved analytically
Various empirical correlations must be applied depending on system’s physical properties to determine h
Various correlations depend on:
Temperature of interest: bulk fluid or film
Turbulent or laminar flow determined by Reynold’s Number (ratio of inertial forces to viscous forces)
Geometry of system: sphere, conduit, cylinder, etc.
Shamim
Image from

8. Conduction Transfer of energy through molecular interaction
Occurs when two neighboring molecules have different energy levels
Fourier developed heat conduction equation in 1822
Known as “Fourier’s law of heat conduction”
q/A = -k dT/dx = -k▽T
q = Heat-transfer rate
A = Area
k = thermal conductivity
SIna

9. Conduction Applications
Steady State Conduction
Mostly dealt with one dimensional conduction
Few examples of two dimensional conduction, such as the air duct
Unsteady State Conduction
Real-life application and examples
Very hard to solve for analytically
Mostly used graphs to approximate final values

10. Dimensionless Numbers: Conductionh
Heat transfer in surrounding fluid
Biot
Conduction in object k
Fourier
Dimensionless time for heat penetrating an object
Michael

11. Dimensionless Numbers: Convection
Fluid property
Boundary layer size
Kinematic viscosity (momentum)
Prandtl
Thermal diffusivity
h, k
Convective heat transfer of fluid
Nusselt
Conductive heat transfer of fluid

12. Dimensionless Numbers: Convection
Bulk convection (in direction of flow)
Forced convection
Peclet
Conduction (in direction of flow)
Heat transfer
Stanton
Forced convection
Boundary layer correlations
Thermal capacity of fluid

13. Miscellaneous Unsteady Transport
Negligible Internal Resistance
Negligible Surface Resistance
Finite Internal + External Resistance
Semi-Infinite Wall
Albert

14. Squat Objects
Y= Ya* Yb
Y=Ya*Ycyl
Y= Ya*Yb*Yc

15. Negligible Internal Resistance
Biot Number → 0, functionally <.1
Well-Mixed
Lumped Parameter Method
Sensible Heat Balance, Newton’s Law of Cooling

16. Negligible Surface Resistance
Temperature varies in object T(x,t)
Graphical Solution Figure 18.3 using center line
Ts = T∞ ❄

17. Finite Internal/External Resistance
Intermediate Biot Number
Heisler Charts

18. Semi Infinite Wall
Intermediate Biot Number Ts

19. References
Philip Kosky, ... George Wise, in Exploring Engineering (Third Edition), 2013
ProfessorMajid Ghassemi, Dr.Azadeh Shahidian, in Nano and Bio Heat Transfer and Fluid Flow, 2017
Welty, J. R.; Wicks, C. E.; Wilson, R. E.; Rorrer, G. L. Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed.; Wiley: Hoboken, 2008.
Lee Ho Sung,
K. C. CHENG & T. FUJII (1998) heat in history Isaac Newton and Heat Transfer, Heat Transfer Engineering, 19:4, 9-21, DOI: / (

20. Questions?