Soret and Dufour Effects on Unsteady Free Convection Fluid Flow in the Presence of Hall Current and Heat Flux

Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.

Importance of initial buoyancy field on evolution of mantle thermal structure:Implications of surface boundary conditions

Although there has been significant progress in the seismic imaging of mantle heterogeneity, the outstanding issue that remains to be resolved is the unknown distribution of mantle temperature anomalies in the distant geological past that give rise to the present-day anomalies inferred by global tomography models. To address this question, we present 3-D convection models in compressible and self-gravitating mantle initialised by different hypothetical temperature patterns. A notable feature of our forward convection modelling is the use of self-consistent coupling of the motion of surface tectonic plates to the underlying mantle flow, without imposing prescribed surface velocities （i.e., p/ate-like boundary condition）. As an approximation for the surface mechanical conditions before plate tectonics began to operate we employ the no-slip （rigid） boundary condition. A rigid boundary condition dem- onstrates that the initial thermally-dominated structure is preserved, and its geographical location is fixed during the evolution of mantle flow. Considering the impact of different assumed surface boundary conditions （rigid and plate-like） on the evolution of thermal heterogeneity in the mantle we suggest that the intrinsic buoyancy of seven superplumes is most-likely resolved in the tomographic images of present-day mantle thermal structure. Our convection simulations with a plate-like boundary condition reveal that the evolution of an initial cold anomaly beneath the Java-lndonesian trench system yields a long-term, stable pattern of thermal heterogeneity in the lowermost mantle that resembles the present- day Large Low Shear Velocity Provinces （LLSVPs）, especially below the Pacific. The evolution of sub- duction zones may be, however, influenced by the mantle-wide flow driven by deeply-rooted and long- lived superplumes since Archean times. These convection models also detect the intrinsic buoyancy of the Perm Anomaly that has been identified as a unique slow feature distinct from the two principal LLSVPs. We find there is no need for dense chemical ＇piles＇ in the lower mantle to generate a stable distribution of temperature anomalies that are correlated to the LLSVPs and the Perm Anomaly. Our tomography-based convection simulations also demonstrate that intraplate volcanism in the south-east Pacific may be interpreted in terms of shallow small-scale convection triggered by a superplume beneath the East Pacific Rise.

Convective Schrodinger Equation:Insights on the Potential Energy’s Role to Wave Particle Decay

In this paper, we coupled the Quantum Mechanics conventional Schrödinger’s equation, for the particles, with the Maxwell’s wave equation, in order to study the potential’s role on the conversion of the electromagnetic field energy to mass and vice versa. We show that the dissipation (“conductivity”) factor and the particle implicit proper frequency are both related to the potential energy. We have also derived a new expression for the Schrödinger’s Equation considering the potential energy into this equation not as an ad hoc term, but also as an operator (Hermitian), which has the scalar potential energy as a natural eigenvalue of this operator.