The rate of heat transfer in forced convection depends on properties of both the fluid (density, heat capacity, etc.) and of the flow (geometry, turbulence, etc.). The calculation is generally complex, and may involve boundary layer theory and tricky mathematics, so we typically use empirical correlations based on masses of data. These enable us to determine heat transfer coefficients for use in calculations.
A heat transfer coefficient, h, is the proportionality factor between the heat flux and an overall temperature difference driving force:
The defining equation can be rearranged into "resistance form", relating heat flow to the temperature difference and a resistance:
Consider the case where heat is transferred from a fluid through a wall to another fluid. The heat first transfers from the bulk fluid to the inside of the wall. Transfer is primarily convective, and we usually assume that all of the resistance can be "lumped" into a "film" adjoining the wall:
Since is is a "no accumulation, no generation" case, the heat flow must be constant and continuous through each of the layers. Consequently, the problem becomes a system of three equations with three unknowns (qi=qw=qo, Twi, and Two).
If the resistance form is used, a single equation can be developed. To do this, recall from previous studies (in transport phenomena, electric circuits, etc.) that resistances combine according to the connection pattern:
The method of combining resistances suggests an "overall" approach might be useful. This produces the idea of an overall heat transfer coefficient
Real problems may not be as simple as three layers in series. It is usually wise to include resistances for scaling or fouling of the wall, contact resistances between two solid layers, etc.
The heat transfer coefficient depends on fluid properties (heat capacity, viscosity, thermal conductivity, density) and flow properties (pipe diameter, velocity). Dimensional analysis shows the relation between the variables:
Modified: 1/4/2002, 2/4/2003
Copyright 1999, 2002, 2003 by R.M. Price -- All Rights Reserved