Exploration of variable fluid properties in a pressure gradient driven generalized vortex flow dynamics using numerical approach

Motivation: Vortex flow, which refers to the movement of fluid around an axis called a vortex line, finds applications in designing aircraft wings, mixing processes in chemical, and pharmaceutical processes, and understanding flows around tornadoes and cyclones. Background: Previous research on variable properties has demonstrated they are crucial in scenarios with significant temperature gradients. Methodology: This paper looks at the boundary layer developments under a generalized vortex flow considering temperature-dependent fluid properties. The generalized vortex represents the far-field tangential velocity in a power-law format and can be simplified to two specific cases: (i) rigid-body rotation and (ii) potential vortex. For mathematical analysis, two distinct variable viscosity models are employed, where a correlation between viscosity and temperature is inversely linear, while the other one is on the exponential temperature dependency model. Numerical Method: A highly robust and convenient built-in tool of MATLAB known as bvp5c is implemented to present exact similarity analyses of the models. Main Findings: The study concludes that velocity profiles obtained under variable physical properties are lower than those calculated with constant properties. Moreover, when liquid properties are considered, the solution curves from the two variable viscosity models show a close resemblance. Thicker thermal diffusion layers and reduced boundary heat flux are associated with increased values of the power law parameter.