Page 34 - Modelling in Transport Phenomena A Conceptual Approach

Chapter 2

Molecular and Convective

Transport

The total flux of any quantity is the sum of the molecular and convective fluxes. The
fluxes arising from potential gradients or driving forces are called molecular fZuxes.
Molecular fluxes are expressed in the form of constitutive (or, phenomenological)
equations for momentum, energy, and mass transport. Momentum, energy, and
mass can also be transported by bulk fluid motion or bulk flow and the resulting
flux is called convective fZm. This chapter deals with the formulation of molecular
and convective fluxes in momentum, energy and mass transport.

2.1 MOLECULAR TRANSPORT

Substances may behave differently when subjected to the same gradients. Consti-
tutive equations identify the characteristics of a particular substance. For example,
if the gradient is momentum, then the viscosity is defined by the constitutive equa-
tion called Newton’s law of viscosity. If the gradient is energy, then the thermal
conductivity is defined by Fourier’s law of heat conduction. If the gradient is con-
centration, then the diffusion coefficient is defined by Fick’s first law of diffusion.
Viscosity, thermal conductivity and diffusion coefficient are called transport prop-
erties.

2.1.1 Newton’s Law of Viscosity

Consider a fluid contained between two large parallel plates of area A, separated
by a very small distance Y. The system is initially at rest but at time t = 0,
the lower plate is set in motion in the x-direction at a constant velocity V by
applying a force F in the x-direction while the upper plate is kept stationary.
The resulting velocity profiles are shown in Figure 2.1 for various times. At t = 0,

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