[inspiration100]

Hello fellow Chem E's.  I just started taking a fluids class and I have something that has been bugging me greatly. 
I am reading about Fourier's law of heat conduction and keep running into a blockade in my mind about fluxes.  I don't know what it is, but I can't seem to get the picture in my head.
The book reads the following "The local rate of the heat flow per unit area (heat flux) in the positive y direction is designated by q(sub y)."

Simple enough, but if the heat flow is per unit area, how can it only be in 1 direction (y in this case)?  Can someone give me a better illustration on what this is trying to tell me?

Eternally greatful,
-inspiration100

[Borek]

Simple enough, but if the heat flow is per unit area, how can it only be in 1 direction (y in this case)?

Direction of the heat flow is perpendicular to the surface. There is only one direction that is perpendicular to the surface in a given point, isn't it?

[RealEngineer]

According to the zeroth law of thermodynamics, heat will flow along a temperature gradient - in other words from a high temperature region to a low temperature region. 

In most heat transfer problems given to undergraduates, the temperature gradient is in one plane only, as a result the heat flow (or heat flux) is in one direction.   This keeps things simple whilst still presenting the theory.  Of course, real life is not always so straight forward - although it is a useful simplification even for many problems encountered in industry.