It was mentioned in Jonas larson paper ' Two -Equation Turbulence Models For Turbine Blade Heat Transfer Simulations' that Navier stokes solver with algebriac turbulence models will give good results for simple cases but for cases with seperated regions ,shocks and high turbulence levels Navier stokes solver with transport turbulence models is good since it account for history effects .so , i want to know what is this history effect .

History effects in this context means that the turbulence in one point is dependent on the turbulence upstream of that point, ie what happened to the turbulent fluid before it reached the point, ie the history of the turbulence.

Algebraic models are local in the sence that they prescribe the turbulence in a point as a direct function of the local average flow-field in that point. Two-equation models account for history effects in the sence that they convect and diffuce both turbulent energy and a turbulent dissipation. So if you had something upstream that generated a lot of turbulence (like a separation) a two-equation model can account for this, whereas an algebraic model usually can't.

Thanks Jonas the way of expressing is very precise and clear again thanking u for ur kind response ....regards bajjal