Different Areas to Use
Definitions
Interfacial Area
This refers to the total area of contact at the interface between fluid A and fluid B.
Surface Area
The surface area of an object measures the total area at the outermost border of the object; in other words, at the surface.
CrossSectional Area
This is the area that a flowing fluid would see
when passing through an object. For example, a fluid flowing horizontally through a cylinder would see
a circular path as it moves down, thus the crosssectional area here would be the area of a circle.
Equations
Cylinder
Surface Area:
(1) 
(Note: In most cases, the second term is almost always neglected as the fluid continuously flows, so the ends of the cylinder are not considered in calculations involving total surface area.)
Crosssectional Area:
(2) 
Sphere
Surface Area:
(3) 
Crosssectional Area:
(4) 
(Note: Think about why this area is equal to the corresponding area in cylinders.)
When to Use What
In some cases, texts will use different variables to denote different areas when discussing heat and mass transfer. For the most part, though, an area will most likely be symbolized by , making it important to be aware of which area an equation is referring to.
Heat Transfer

(5) 
Here, the on the righthandside of the equation corresponds to the convective heat transfer, and uses the surface area of the object the fluid is flowing through.
Mass Transfer

(6) 
Again, the area term on the righthandside corresponds to the surface area of the object through which the fluid is flowing.
Flow of an Object
When calculating the velocity of a moving object, the area used in the appropriate equations beforehand correspond to the crosssectional area of the object itself, as opposed to the area through which it is moving. As a baseline, calculations involving Reynold's number usually follow these guidelines.

(7) 
To calculate the above velocity , one might use the volumetric flow rate and area as follows,

(8) 
where
 is the crosssectional area of the object (usually a particle) moving through a fluid.