Gradient estimates for a weighted nonlinear parabolic equation and applications

This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor

Current density and thermal propagation of electromagnetic CoFe2O4 and TiO2/C2H6O2 + H2O hybridized Casson nanofluids: A concentrated solar power maximization

The limited availability of fossil fuel, ecosystem consideration and economic factor stimulates interest in alternative energy provision and thermal energy enhancement. Utilization of solar radiation and nanofluids with solid tiny particle provides a platform to optimize renewable solar thermal system performance. Owing to its usages, this study examines thermal transfer and current density of electromagnetic gravity driven Casson hybridized nanofluid flow through partially filled porous media with Ohmic heating. A mixture of cobalt ferrite (CoFe2O4) and titanium dioxide (TiO2) is considered for the nanoparticles thermal propagation in base solvent ethylene-glycol+water (C2H6O2+H2O). A parabolic concentrated solar collector is used for the solar radiation absorption with a continuous energy supply. An invariant transformation of the partial derivative model is obtained using similarity variables. A semi-analytical shifted Chebyshev method coupled with the integrated collocation scheme has been adopted to provide theoretical solutions to the model. The study revealed that concentrated solar power current density is raised as the electric field factor and medium porosity is increased. The fluid velocity is damped while the temperature distribution is enhanced as the nanoparticle volume fraction is boosted. Thus, this investigation will improve the efficiency of thermal engineering products and enhance industrial performance