The present work aims at developing a full second order model for turbulent transport of a passive scalar. A turbulent Prandtl number formulation is obtained by reducing the second order modelling. A first order turbulence model is than proposed with an algebraic formulation of the turbulent scalar flux. The model is tested in homogeneous shear flow with an imposed mean scalar gradient. The Direct Numerical Simulation (DNS) data by Rogers et al were used in the validation of the first and second order modelling of the turbulent passive scalar transport. The comparison of the numerical results with DNS data shows good agreements.
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