Fundamentals of Heat Transfer

The following is a brief overview of some fundamental heat transfer concepts. To learn more, the reader is encouraged to review the source publications and cited websites.

The 1st Law of Thermodynamics involves the conservation of energy. It states that - within a closed system where no other energy material can enter or leave - energy can neither be created nor destroyed.^{1, 2} Although energy cannot be created or destroyed, it can be transferred to work as other forms of energy.

Transferring heat energy is subject to the 2nd Law of Thermodynamics.³ The 2nd Law (again applying to a closed system) says that - for a spontaneous process - there is a net increase in entropy⁴ (i.e., a measure of the disorder that exists in a system⁵).

Three alternate but equivalent ways to describe the 2nd Law are:

Heat flows spontaneously from a hot body to a cool one. (Example: A hot microprocessor or laser diode is cooled by flow of heat into heat sink or cold plate.)

It is impossible to convert heat completely into useful work. (Example: In a combustion engine, a certain heat component must always be exhausted without performing work.)

Every isolated system becomes disordered in time. (Example: In conduction when hot and cold bodies first contact each other, the system is somewhat ordered. Hotter molecules move faster than cooler molecules. But, once the entire system attains a uniform temperature, this order is lost.)

Expressed in mathematical terms, any of the above statements imply the other two.⁶

The 1st and 2nd Laws of Thermodynamics govern the various modes of heat transfer: conduction, convection and radiation.

In conduction, heat flows from a higher temperature region to regions of lower temperature. This occurs within solid, liquid, or gaseous mediums or between different mediums that make direct physical contact with each other.⁷ "The transfer of the energy of motion between adjacent molecules conducts the heat. In a gas, the 'hotter' molecules, have greater energy and motions, and impart energy to adjacent molecules at lower energy levels. This type of transfer occurs to some extent in all solids, gases or liquids in which a temperature gradient exists. In conduction, energy can also be transferred by "free" electrons, which is important in metallic solids."⁸ Examples of conduction are heat transfer through the surfaces of a cold plate or through the walls of a refrigerator.

In convection, the combined action of heat conduction, energy storage, and mixing motion serve to transport energy. "Convection is most important as the mechanism of energy transfer between a solid surface and a liquid or a gas."⁹ "In forced-convection heat transfer, a pump, fan, or other mechanism forces a fluid to flow past a solid surface. In natural or free convection, warmer or cooler fluid next to the solid surface causes a circulation because of density differences resulting from the temperature differences in the fluid."¹⁰ An example of free convection is the loss of heat into ambient air via the fins of a heat exchanger. If a fan is used to circulate the air over the heat exchanger fins, this becomes an example of forced convection.

In radiation, heat flows from a higher temperature body to a lower temperature body when the bodies are separated in space, even across a vacuum.¹¹ "The same laws that govern the transfer of light, also govern the transfer of heat. Solids and liquids tend to absorb the radiation being transferred through it, hence radiation is important mainly in transfer through space or gases."¹²

Examples of radiation include the transfer of heat from the sun to the earth, and from a quartz lamp to a cool object that requires warming.

"The basic relation for heat transfer by conduction, proposed by the French scientist J.B.J. Fourier in 1822, states:

The rate of heat flow by conduction in a material, qk , equals the product of the following three quantities:

• k - Thermal conductivity of the material
• A - Area of the section through which heat flows by conduction as measured perpendicularly to the direction of heat flow
• dT/dx - Temperature gradient at the section, i.e., the rate of change of temperature T with respect to the difference in the direction of the heat flow x.

Writing the heat conduction equation in mathematical form requires a sign convention; i.e., the direction of increasing distance x is the direction of positive heat flow. According to the second law of thermodynamics, heat will automatically flow from points of higher temperature to points of lower temperature. Thus, heat flow will be positive when the temperature gradient is negative. The basic equation for one-dimensional conduction in the steady state is: qk = -kA (dT/dx)"¹³.

Thermal conductivity is a measurement of the rate at which a given material will transfer heat.¹⁴ "The thermal conductivity of a substance is the quantity of heat in cal/sec passing through a body 1 cm thick with a cross section of 1 sq. cm when the temperature difference between the hot and cold sides of the body is 1 deg. C."¹⁵ This intrinsic property is independent of the materials size, shape, or orientation.

Thermal resistance is the inverse of thermal conductivity and indicates how a material inhibits the conduction of heat.¹⁶ Materials with a high thermal conductivity have a low thermal resistance and have poor heat insulation qualities (e.g., copper and aluminum). Conversely, materials with a low thermal conductivity have a high thermal resistance, and have good heat insulation qualities (e.g., fiberglass insulation and corkboard).¹⁷

1. https://www.chemistry.ohio-state.edu/~woodward/ch121/ch5_law.html.

2. https://theory.uwinnipeg.ca/mod_tech/node78.html.

3. ibid.

4. http://learn.chem.vt.edu/tutorials/entropy/2ndlaw.html.

5. Microsoft Encarta World English Dictionary, St. Martin's Press, 1999, Pp 596.

6. de Sorgo, Miksa, ibid.

7. de Sorgo, Miksa, "Understanding Phase Change Materials", ElectronicsCooling Magazine, May. 2002

8. http://learn.chem.vt.edu/tutorials/entropy/2ndlaw.html.

9. Kreith, Frank, Principles of Heat Transfer, 2nd Edition, University of Colorado, International Textbook Co., Chapter 1, Pp 6.

10. Transport Processes and Unit Operations, 3rd Edition, Christie Geankopolis, University of Minn. Prentice Hall, Chapter 4, Pp 215.

11. Kreith, Frank, Principles of Heat Transfer, 2nd Edition, University of Colorado, International Textbook Co., Page 8.

12. Transport Processes and Unit Operations, 3rd Edition, Christie Geankopolis, University of Minn. Prentice Hall, Chapter 4, Pp 216.

13. Kreith, Frank, Principles of Heat Transfer, 2nd Edition, University of Colorado, International Textbook Co., Pp 7.

14. Transport Processes and Unit Operations, 3rd Edition, Christie Geankopolis, University of Minn. Prentice Hall, Chapter 4, Pp 216.

15. Kreith, Frank, Principles of Heat Transfer, 2nd Edition, University of Colorado, International Textbook Co., Pp 9.

16. Transport Processes and Unit Operations, 3rd Edition, Christie Geankopolis, University of Minn. Prentice Hall, Chapter 4, Pp 216.

17. http://theory.uwinnipeg.ca/mod_tech/node75.html.

18. http://www.lib.umich.edu/dentlib/dental_tables/thermcond.html.

19. http://www.xrefer.com/entry/619844.

20. http://theory.uwinnipeg.ca/mod_tech/node75.html.