Support

Trouble Report

For immediate assistance browse through our support center. You can find answers to many questions in just a few minutes.

If still experiencing problems, send us a report.

required
Why the math question?

Online Simulation

And More

Top Tags

  1. radiation
  2. heat transfer
  3. carbon nanotubes
  4. microscale heat conduction
  5. molecular dynamics
  6. phonons
  7. heat conduction
  8. note
  9. boiling
  10. thermal radiation
  11. radiativeproperties
  12. index of refraction
  13. thermal transport
  14. nanotechnology
  15. optical thickness
  16. acetylene
  17. equation
  18. boiling flow regime
  19. thin films
  20. transport
  21. flow visualization
  22. infrared
  23. microchannels
  24. thermal circuit
  25. two-phase flow

Other

Heat Transfer Cheat Sheet

Table of Contents

Tags

This page provides an “equation sheet” that students like to use on tests. Developed by Vanderbilt University’s heat transfer class (ME 248, Fall)

Sign Convention

We are using Prof. Walker’s convention:

name quantity units alternative
heat tansfer q W Q or \dot{q}
heat flux q'' W / m2 q
generation q''' W / m3 G

Equivalent Resistance

Analogy of electricity to Fourier’s Law

Assumptions

  • No generation
  • Constant properties
  • Steady state
  • One-dimensional conduction

q=\frac{\nabla T}{R_{eq}}

where R_{eq}\, is the series and parallel combination of resistances as if they were resistors in units of K/W.


For Conduction:

Planar: R_{\rm planar}= \frac{L}{kA}

Cylindrical: R_{\rm cylindrical}= \frac{ln(r_{o}/r_{i})}{2 \pi l k}


Spherical: R_{\rm spherical}= \frac{\frac{1}{r_{i}}-\frac{1}{r_{o}}}{\pi 4 k}


For Convection:

Planar: R_{conv}= \frac{1}{hA}


Cylindrical: R_{conv}= \frac{1}{h 2 \pi r_{o}l}


Spherical: R_{conv}= \frac{1}{h 4 \pi r_{o}^2}


For Radiation:

R_{rad} = \frac{1}{\epsilon \sigma A (T+T_{surr})(T^2 + T_{surr}^2)}

Or if \frac{(\delta T/ T_{m})^2}{4}<<1 then R_{rad} = \frac{1}{A h_{rad}} where h_{rad}= 4 \sigma T_{m}^3 \epsilon and T_{m} = T\, at the middle of two know temperatures

For Contact Surfaces:

R_{contact}= \frac{1}{h_{c}A}

Basic definitions: Heat transfer- thermal energy in transit due to a spatial temperature difference. Conduction- heat transfer across a medium (solid or fluid). Convection- heat transfer between a surface and a moving fluid. Thermal Radiation- all surfaces of finite temperature emit energy in the form of electromagnetic waves.

Last modified on 06 Oct, 2008