The Combined Effect of Gravity Modulation and Throughflow on Thermal Instability in the Hele-Shaw Cell Filled with Oldroyd-B Nanofluid

This paper shows the combined effect of throughflow and gravity modulation on the stability of Oldroyd-B nanofluid filled in Hele-Shaw cell. Nanofluid compared to the base fluid has higher thermal conduction. The thermal conductivity of nanofluid increased and thus increases the amount of energy transferred. The Oldroyd-B fluid model is important because of its numerous applications such as production of plastic sheet and extrusion of polymers through a slit die in polymer industry, biological solution pant tars glues, etc. In linear stability analysis, we found the expression of the critical Hele-Shaw Rayleigh number by using the normal mode method. Two-term Fourier series method is used for non-linear stability analysis and is also considered the Brinkman model for flow of nanofluid in Hele-Shaw cell. In linear stability analysis, we observed that there is no effect of Oldroyd-B nanofluid, which means that Deborah number (λ1) and retardation parameter (λ2) do not affect the stability analysis. Oldroyd-B nanofluid is similar to ordinary nanofluid in linear analysis. In non-linear analysis, Deborah number, retardation parameter, throughflow, gravity modulation, and Hele-Shaw number play a major role in heat/mass transfer. Enhancement in both heat/mass transfer in the system while increasing throughflow and Deborah number. An increment in Hele-Shaw number (Hs), decreases heat/mass transfer in the system.