This paper consists of three parts. In the first part, we demonstrate the performance of the explicit algebraic (EA) subgrid-scale (SGS) stress model at Reτ = 934 and Reτ = 2003, based on friction velocity and channel half-width, for the case of large eddy simulation (LES) of turbulent channel flow. Performance of the EA model is compared to that of the dynamic Smagorinsky (DS) model for four different coarse resolutions and statistics are compared to the DNS of del Álamo & Jiménez (2003) and Hoyas & Jiménez (2008). Mean velocity profiles and Reynolds stresses are presented for the different cases. The EA model predictions are found to be reasonably close to the DNS profiles at all resolutions, while the DS model predictions are only in agreement at the finest resolution. The EA model predictions are found to be less resolution dependent than those with the DS model at both Reynolds numbers. In the second and third parts, we use Langevin stochastic differential equations to extend the EA model with stochastic contributions for SGS stresses and scalar fluxes. LES of turbulent channel flow at Reτ = 590, including a passive scalar, is carried out using the stochastic EA (SEA) models and the results are compared to the EA model predictions as well as DNS data. Investigations, show that the SEA model provides for a reasonable amount of backscatter of energy both for velocity and scalar, while the EA models do not provide for backscatter. The SEA model also improves the variance and length-scale of the SGS dissipation for velocity and scalar. However, the resolved statistics like the mean velocity, temperature, Reynolds stresses and scalar fluxes are hardly affected by the inclusion of the stochastic terms.