TABLE OF CONTENTS Heat diffuses much like mass and is governed by similar equations. The temperature analog of Equation (8.12) is
| (8.52) |  |
where 
is the thermal diffusivity and 
follows the summation convention of Equation (5.17). The units on thermal diffusivity are the same as those on molecular diffusivity, m 2/s, but 
will be several orders of magnitude larger than 
. The reason for this is that mass diffusion requires the actual displacement of molecules but heat can be transferred by vibrations between more-orless stationary molecules or even between parts of a molecule as in a polymer chain. Note that 
, where ? is the thermal conductivity. Equation (8.52) assumes constant 
and ?. The assumption of constant density ignores expansion effects that can be significant in gases that are undergoing large pressure changes. Also ignored is viscous dissipation, which can be important in very high-viscosity fluids such as polymer melts. Standard texts on transport phenomena give the necessary embellishments of Equation (8.52).
The inlet and centerline boundary conditions associated with Equation (8.52) are similar to those used for mass transfer:
| (8.53) |  |
| (8.54) |  |
The usual wall boundary condition is
| (8.55) |  |
but the case of an insulated wall,
is occasionally used.
Equation (8.52) has the same form as Equation (8.12), and the solution techniques are essentially identical. Replace a with T, 
with 
, and 
with 
, and proceed as in Section 8.3.
The equations governing the convective diffusion of heat and...
