A simple method to estimate the density of biodiesel blend as simultaneous function of temperature and volume percent of biodiesel is proposed. Employing the Kay's mixing rule, we developed a model and investigated theoretically the density of different vegetable oil biodiesel blends as a simultaneous function of temperature and volume percent of biodiesel. Key advantage of the proposed model is that it requires only a single set of density values of components of biodiesel blends at any two different temperatures. We notice that the density of blend linearly decreases with increase in temperature and increases with increase in volume percent of the biodiesel. The lower values of standard estimate of error (SEE = 0.0003-0.0022) and absolute average deviation (AAD = 0.03-0.15 %) obtained using the proposed model indicate the predictive capability. The predicted values found good agreement with the recent available experimental data.

Anisotropic thermopower, S, in zigzag and armchair 2D phosphorene is investigated using Boltzmann transport formalism. Anisotropic behavior of thermopower shows that thermopower along armchair direction is higher than that of zigzag direction. The theoretical studies of S and its dependence on the temperature, T, carrier concentration, n s, and phonon mean free path, λ, bring out the features of anisotropic thermopower. The limitations of the often used Mott expression for the analysis of thermopower are brought out. For the range of carrier concentration, 1016 < n s < 1018 m−2, the anisotropic ratio of S varies from 3.1 to 2.3 at room temperature. The modification in the behavior of S from anisotropic to low anisotropic for higher carrier concentration and at lower temperature is noticed. These theoretical investigations are in good agreement with recent experimental results.

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