Transport phenomena
Transport Phenomena are irreversible processes that arise from the random continuous motion of molecules. The three types of transport phenomena are momentum, mass of a component in a multicomponent mixture, and thermal energy. A complete description of the transport phenomena is embodied in the following two relationships:
 Conservation laws
 Constitutive molecular flux laws
The conservation laws are continuity equations; these equations dictate that the accumulation of a quantity in a control volume equals the transport of into and out of the control volume plus any generation or consumption of in the control volume due to nonconservative mechanisms.
In other words,
The conservation laws can be formulated as either microscopic (differential) balances or as macroscopic (integral) balances.
Microscopic balance
In the microscopic description, the balance equation is formulated on a per volume basis. For instance, if is a transport quantity is on a per volume basis, the differential balance is

(1) 
where
 is the rate of accumulation of on a per volume basis. is the mass density.
 is the convective inflow and outflow of per unit volume due to both advective (bulk flow) and molecular (diffusive) mechanisms.
 is the generation or consumption of on a per volume basis due nonconservative mechanisms. This may be an external force in the momentum balance or a reaction in a mole balance.
Macroscopic balance
In the macroscopic description and there are three types mass, momentum and energy, , and the integral balance equation is

(2) 
where
 is the rate of accumulation of in the control volume.
 is the convective inflow and outflow of due to both advective (bulkflow) and molecular (diffusive) mechanisms.
 is the generation or consumption of per unit area at the control surface.
 is the generation or consumption of per unit volume at the control surface.
 is the unit normal that defines the surface of the the control volume.
Flux
Flux describes the movement of a property. For this class specifically, we will only be dealing with transport properties of Momentum, Energy and Mass. Flux is a vector that has both magnitude and direction and usually has units of the property per unit area per unit time.
For example,
 Mole Flux has units of moles per unit area per unit time.
 And Energy Flux has units of energy per unit area per unit time.
Different mechanisms allow for flux to occur.
 Bulk Flow or Advective Mechanism
 Molecular or Diffusive / Conductive Mechanism
Advective Flux
Advection is the bulk movement of a property due to a velocity field. That is, the advective movement occurs in the direction of the velocity field.
For example,
After perfume is sprayed in a room with the wind blowing, someone standing in the path of the wind will smell the perfume, because the wind carries the perfume particles along with it until the particles are evenly distributed. This all occurs due to the advective movement of the particles.
Convective Flux
Convective flux is the movement of a property due to both advective and molecular mechanisms. It has dimensions of "property per unit time per unit area" and has the general form

(3) 
where
 is the advective flux of due to a velocity field
 is the molecular flux of due to the gradient in .
Constitutive molecular flux laws
The constitutive equations describe how the flux of , or is related to a particular gradient (Cartesian, Cylindrical, Spherical). The three most common flux laws are
 Newton's law of viscosity in momentum transfer:
 Fourier's law of conduction in heat transfer :
 Fick's law of diffusion in mass transfer:
Diffusivity and the analogy between the three types of molecular transport
In the absence of external bulk flow and nonconservative mechanisms, the microscopic balance reduces to

(4) 
Substituting the constitutive molecular flux laws into the above equation for momentum, heat, and mass, each equation can be written explicitly as

(5) 
In each case, the coefficient before the Laplacian operator has dimensions of length^{2} per unit time and is known as the diffusivity. The diffusivities for the three cases are
 Momentum: Kinematic viscosity
 Thermal energy: Thermal diffusivity
 Mass: Diffusion coefficient
Hence, the diffusivities give the characteristic rates at which the velocity field, temperature field, and density field spreads in the absence of advective (bulk flow) mechanisms.
Summary of transport relationships
Momentum  Mass  Thermal Energy  

Transport quantity  (Internal energy) or (Enthalpy)  
Transport quantity per unit volume  or  
Solution of microscopic balance  Velocity field  Density or concentration field  Temperature field 
Flux law  
Diffusivity (Length^{2}/time)  
Convective transfer coefficient  
Convective boundary condition  
Dimensionless convection/diffusion ratio  Reynolds number  Sherwood number  Nusselt number 
Corresponding macroscopic balance  Mechanical energy balance  Component mass balance  Internal energy balance 
Key dimensionless numbers  Friction factor, Reynolds number  Sherwood number, Reynolds number, Schmidt number  Nusselt number, Reynolds number, Grashof number, Prandtl number 
Correlation relationship  (forced convection) or (natural convection)  
Other transport modes  Radiation 