Symbols and Formulas
Staff posted on October 23, 2006 |
Symbols and Formulas
A simple definition of heat transfer is energy in transit due to a temperature difference. If there is a temperature difference in a medium or between media, heat transfer must occur.

Commonly Used Symbols
The follow tables are a list of variables, their symbols, and the associative units commonly used in heat transfer expressions. All the equations present in the heat transfer section have the same quantity denoted by the symbols in the table.

Independent Parameters
 Quantity Symbol Object Units Temperature T scalar K Time t scalar s Thermal conductivity k scalar W/m · K Specific heat c scalar J/kg · K Convection heat transfer coefficient h scalar W/m2K Emissivity e scalar W/m2K Density r scalar kg/m3 Internal heat generation qqen scalar kg/m3

Dependent Parameters
 Quantity Symbol Object Units Heat flux q" vector W/m2 1-D heat flux q scalar W

Table of Dimensionless Parameters
 As is common with fluid mechanics analysis, a number of dimensionless parameters are employed to describe convective heat transfer. A summary of these variables is included in the following tables: General Convection (Forced and Free) Parameter Formula Interpretation Prandtl number Ratio of fluid velocity boundary layer thickness to the fluid temperature boundary layer thickness. Nusselt number Ratio of heat transferred from surface to heat conducted away by fluid.
 Forced Convection Only Parameter Formula Interpretation Reynold's number Ratio of fluid inertia stress to viscous stress (for flow over flat plates). Reynold's number (Reynold's number for pipe flow) Stanton number Free Convection Only Parameter Formula Interpretation Grashof number Ratio of fluid buoyancy stress to viscous stress. Rayleigh number Heat Transfer Coefficient

The heat transfer coefficient encompasses all of the parameters that influence convection heat transfer. It depends on conditions in the boundary layer, which are influenced by surface geometry, the nature of the fluid motion, and other fluid thermodynamic and transport properties. Convection heat transfer will frequently appear as a boundary condition in the solution of conduction problems. The table below is the typical values of the convection heat transfer coefficient.

Typical Values of Convection Heat Transfer Coefficient

 Process h (W/m2 · K) Free convection Gases 2–25 Liquids 50–1000 Forced convection Gases 25–250 Liquids 50–20,000 Convection with phase change Boiling or condensation 2500–100,000 Some material excerpted from: Incroprera, Frank and De Witt, David P. Introduction to Heat Transfer. Second Edition. New York: John Wiley & Sons, Inc. 1985, 1990. Copyright © 1985, 1990, by John Wiley & Sons, Inc. This material is used by permission of John Wiley & Sons, Inc.
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