Is the heat transfer equation inaccurate?

Hello all,

Heat transfer between two particles is calculated by fix heat/gran with the equation given on

http://www.cfdem.com/media/DEM/docu/fix_heat_gran_conduction.html

But the equation seems to have an extra factor of (pi)^0.5 (i.e, square root of pi). I checked the cited paper by Chaudhuri et al. (2006), and a former paper by Batchelor and O'Brien (1977). Both papers have the heat transfer equation with radius of contact and not area of contact, as given in the liggghts documentation