The heat flux q"_{x} (W/m^{2)} is the heat transfer rate in the x direction per unit area perpendicular to the direction of transfer, and it is proportional to the temperature gradient, dT/dx, in this direction. The proportionality constant k is a transport property known as the thermal conductivity (W/m · K) and is a characteristic of the wall material.
Note that this equation provides a heat flux, that is, the rate of heat transfer per unit area. The heat rate by conduction, q_{x} (W), through a plane wall of area A is then the product of the flux and the area, q_{x} = q"_{x} · A.

The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), there is also energy being transferred by bulk, or macroscopic, motion of the fluid. Such motion, in the presence of a temperature gradient, will give rise to heat transfer. Because the molecules in the aggregate retain their random motion, the total heat transfer is then due to a superposition of energy transport by the random motion of molecules and by the bulk motion of the fluid. It is customary to use the term convection when referring to this cumulative transport and the term advection when referring to transport due to bulk fluid motion.
Regardless of the particular nature of the convection heat transfer process, the appropriate rate equation is of the form

where q", the convection heat flux (W/m^{2}), is proportional to the difference between the surface and fluid temperatures, T_{s} and T_{∞}, respectively. This expression is known as Newton's law of cooling, and the proportionality constant h (W/m^{2} · K) is referred to as the convection heat transfer coefficient. It encompasses all the parameters that influence convection heat transfer. In particular, it depends on conditions in the boundary layer, which are influenced by surface geometry, the nature of the fluid motion, and an assortment of fluid thermodynamic and transport properties.
Excerpt 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.
