text: The non-dimensional energy equation for fluid flow in a boundary layer can simplify to the following, when heating from viscous dissipation and heat generation can be neglected:
  Where  and  are the velocities in the x and y directions respectively normalized by the free stream velocity,  and  are the x and y coordinates non-dimensionalized by a relevant length scale,  is the Reynolds number,  is the Prandtl number, and  is the non-dimensional temperature, which is defined by the local, minimum, and maximum temperatures:
  The non-dimensional species transport equation for fluid flow in a boundary layer can be given as the following, assuming no bulk species generation:
  Where  is the non-dimensional concentration, and  is the Schmidt number.
  Transport of heat is driven by temperature differences, while transport of species is due to concentration differences. They differ by the relative diffusion of their transport compared to the diffusion of momentum. For heat, the comparison is between viscous diffusivity () and thermal diffusion (), given by the Prandtl number. Meanwhile for mass transfer, the comparison is between viscous diffusivity () and mass Diffusivity (), given by the Schmidt number.
  In some cases direct analytic solutions can be found from these equations for the Nusselt and Sherwood numbers. In cases where experimental results are used, one can assume these equations underlie the observed transport.
  At an interface, the boundary conditions for both equations are also similar. For heat transfer at an interface, the no-slip condition allows us to equate conduction with convection, thus equating Fouriers law and Newtons law of cooling:
  Where q” is the heat flux,  is the thermal conductivity,  is the heat transfer coefficient, and the subscripts  and  compare the surface and bulk values respectively.
  For mass transfer at an interface, we can equate Ficks Law with Newtons law for convection, yielding:
  Where  is the mass flux [kg/s ],  is the diffusivity of species a in fluid b, and  is the mass transfer coefficient. As we can see,  and  are analogous,  and  are analogous, while  and  are analogous.