An Analytical Solution To The Graetz Problem
With Viscous Dissipation For Non-Newtonian
Fluids
Author(s)
R. Chiba, M. Izumi & Y. Sugano
Abstract
Forced convection heat transfer in a non-Newtonian fluid flow between parallel
plates subjected to convective cooling on the external surfaces is investigated
analytically. Fully developed laminar velocity distributions obtained by a power
law fluid rheology model are used, and viscous dissipation is taken into account.
The effect of heat conduction in the direction of fluid flow is considered
negligible. The physical properties are assumed to be constant. We approximate
the smooth change in the velocity distribution between the plates as a piecewise
constant velocity. The theoretical analysis of the heat transfer is performed using
an integral transform technique—Vodicka’s method. An important feature of the
approach is that an arbitrary distribution of the temperatures of the surrounding
media in the direction of fluid flow and an arbitrary velocity distribution of the
fluid can be permitted. A comparison with the existing results provides a
verification of this technique. The effects of the Brinkman number, Biot number
and rheological properties on the distributions of the fluid temperature and the
local Nusselt number are illustrated. Moreover, the effects of these parameters on
the length of the freeze-free zone are discussed in the case where the
temperatures of the surrounding media are below the solidification temperature
of the fluid.
Keywords: heat transfer, forced convection, non-Newtonian fluid, analytical
solution, viscous dissipation, Graetz problem, channel flow.
Keywords
heat transfer, forced convection, non-Newtonian fluid, analytical
solution, viscous dissipation, Graetz problem, channel flow.
Related Book
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