(i) Considering a two-dimensional turbulent flow, the instantaneous time-averaged equation governing the conservation of a scalar property can be written as: -2 (p)+ (p)+5, D +S " a(po) a (pud) a(pv) _ - + + t x by Applying the Reynolds averaging rule such as =; a+=+; a=a; a=a + a''; and derive the Reynolds-Averaged Navier-Stokes (RANS) form of the above equation (7): s s (ii) If the mean property can be defined as form of the above equation (7): (7) = [8 Marks] derive the Favre-Averaged Navier-Stokes (FANS) [8 Marks] (iii) Now, provided that is given as cpT, D is given as k, s, is given as and the specific heat at constant pressure is assumed to be a non-fluctuating fluid property, write down the RANS and FANS equations for temperature. [4 Marks]