Study of Thermal-Instability in Nanoliquid (Walter-B Viscoelastic) within the Hele-Shaw Cell Under Thermal-Modulation Using Cubic Ginzburg-Landau (GBL) Equation

Abstract

This paper includes both linear and local nonlinear exploration to estimate the onset of instability and heat/mass transportation in nanoliquid (Walter-B viscoelastic) within the Hele-Shaw (HS) cell under the impact of thermalmodulation. The stability exploration uses Nusselt numbers based on the cubic Ginzburg-Landau (GBL) equation. We have considered three types of thermal-modulation viz symmetric thermal-modulation, asymmetric thermal-modulation, and lower-boundary thermal-modulation. In the sequel, the impact of the non-dimensional parameters is discussed graphically in detail. It is described that elastic-parameter (H), nanoliquid Prandtl number (Pr), and amplitude of the thermal-modulation (δ) destabilize the system, that is, the heat/mass transportation increases. On the other hand, HS-number (Hs), nanoliquid Lewis-number (Le), redefined diffusivity-ratio (NA), concentration Rayleigh-number (Rn), and modulating-frequency (Ω) stabilize the system. Moreover, it is found that in all three types of thermal-modulation, maximun heat/mass transportation can be observed in the case of asymmetric modulation. Walter-B nanoliquid can be used to enhance the heat/mass transportation as compared to a normal nanoliquid.