Review & Theory of Heat Transfer

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

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

4. 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 Counter-current configuration Co-current configuration

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

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 Image from https://energyeducation.ca/encyclopedia/Convection

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. Image from https://medium.com/hardbound-co/venture-convection-b8a9c264a095

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

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: Conduction h Heat transfer in surrounding fluid Conduction in object Biot k Dimensionless time for heat penetrating an object Fourier

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

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

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

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,http://www.mae.wmich.edu/faculty/Lee/me431/ch05_supp_heisler.pdf K. C. CHENG & T. FUJII (1998) heat in history Isaac Newton and Heat Transfer, Heat Transfer Engineering, 19:4, 9-21, DOI: 10.1080/01457639808939932 (https://www.tandfonline.com/doi/abs/10.1080/01457639808939932)

20. Questions?