Mixing length model of convection in stellar cores

The standard mixing length model of convection is ill behaved at the centre of a star since the pressure scale height H_p=P/(ρg)→∞ as r→0, and the convective flux remains non zero at r=0. We propose a modifcation of this model of convection that has the correct behaviour in the central regions of a star and smoothly changes to the standard MLT away from the centre.