Thermal instability on heat and mass transfer of Oldroyd-B nanofluid with several types of gravity modulation in various enclosures

Abstract

In this paper, the influence of three different types of gravity modulation on the stability of a layer of Oldroyd-B nanofluid in various enclosures is investigated. Gravity modulation using sine, square, and triangular waveforms can be significant. It has various applications, such as industrial processes, electronic cooling, and material science. The Oldroyd-B liquid model is significant because of its numerous applications, including the production of plastic sheets and polymer extrusion through a slit, dye in the polymer industry, biological solution of paint, tars, glues, and so on. We found the expression of the Rayleigh number by applying the normal mode technique in linear stability analysis. The results demonstrate that the porosity and porous parameters stabilize the system. The system becomes unstable due to the aspect ratio. This result implies that convection travels faster in a tall enclosure compared to a square enclosure and a shallow enclosure. In nonlinear analysis, we found the Nusselt and Sherwood numbers for heat and mass transportation. In heat and mass transfer, the Deborah number, retardation parameter, gravity modulation, porous parameter, porosity, and aspect ratio play essential roles. Porous parameter and porosity delayed the rate of heat and mass transportation. The value of the retardation parameter increases then the heat and mass transportation decreases. The system’s heat and mass transfer increases by increasing the Deborah number’s value. The aspect ratio increases the system’s heat and mass transfer. The heat and mass transfer in tall enclosure is much higher than in square and shallow enclosures.