Explicit algebraic scalar-flux models that are valid for three-dimensional turbulent flows are derived from a hierarchy of second-order moment closures. The mathematical procedure is based on the Cayley-Hamilton theorem and is an extension of the scheme developed by Taulbee. Several closures for the pressure-scalar gradient correlations are considered and explicit algebraic relations are provided for the velocity-scalar correlations in both nonreacting and reacting flows. In the latter, the role of the Damkohler number is exhibited in isothermal turbulent flows with nonpremixed reactants. The relationship between these closures and traditional models based on the linear gradient-diffusion approximation is theoretically established. The results of model predictions are assessed by comparison with available laboratory data in turbulent jet flows.