The laminar velocity profile of a power-law fluid is given by 
are power-law parameters,
is the distance between the parallel plates,
is the vertical coordinate and
is the horizontal pressure gradient.
The energy and mass conservation equations, assuming that all physical properties are constant and that viscous dissipation and axial heat conduction effects are negligible, are:
are the heat transfer coefficient, diffusivity and reaction pre-exponential factor, respectively;
is the activation energy;
is the fluid density; and
is the fluid heat capacity. We use these factors for convenience and solve these equations using the built-in Mathematica function NDSolve
The results show that the temperature and conversion profiles are parabolic and become progressively blunter as the value of
decreases below unity and sharper for
 R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena
, 2nd ed., New York: John Wiley & Sons, Inc., 2002.