Impacts of Viscous Dissipation and Nanoparticle Flow in Pressure-Driven Hydrosphere and Atmosphere Interface on Climate Change: A Numerical Perspective

Abstract

The effects of natural convection heat transfer from the hydrosphere to the atmosphere are investigated numerically on the climate in current work under the assumptions that the hydrosphere phase is influenced by viscous dissipation and that there is an evaporation region at its surface where density is pressure dependent. Furthermore, the impacts of atmospheric nanoparticles are examined using Buongiorno's Model. This is carried out by constructing a two-dimensional mathematical model in the form of a spherical coordinate system that includes three regions: the hydrosphere, the evaporation and the atmosphere, connected through trans-boundaries. To better comprehend the physical importance of the proposed study, the system of governing equations is altered into a dimensionless system using a set of relevant variables and numerically answered using the finite difference approach via primitive variable formulation and the Gaussian elimination scheme. The consequences of numerous dimensionless variables, such as the viscous dissipation parameter in the hydrosphere, the density variation parameter in the evaporation region and the Brownian motion parameter and the thermophoresis parameter in the atmospheric region, are seen on climate patterns. The radial distribution of temperature across the hydrosphere, evaporation zone, and atmosphere is observed using concentric contour plots for Grashof number Gr = 8 and 20. The results indicate a distinct negative temperature gradient, with the highest thermal intensity at the hydrosphere and progressively lower values toward the outer atmospheric region, highlighting steady radial heat transfer through the evaporation zone.