Numerical simulation of unidimensional bubbly flow in linear and non-linear one parameter elastic liquid through a nozzles
Department of Mathematics and Statistics, Faculty of Basic and Applied Sciences, International Islamic University, 44000, Islamabad, Pakistan
2 Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia
Accepted: 10 January 2022
Published online: 20 January 2022
This paper studies one dimensional bubbly cavitating flow of elastic fluids through micro sized nozzles of different shapes. Cavitating flows are applicable in wide range of applications in medical and engineering sciences, such as, the cleansing of teeth, ultrasound and cancer treatment. They are also responsible for erosion on metallic surfaces, damages to machinery, pumps etc. The above make advances in the field important and useful in reducing possible destructive effects of such flows. In current study two types of elastic fluid models namely neo-Hookean and linear elastic are considered. The nonlinear dynamics of bubbly mixture is modeled by incorporating the Rayleigh–Plesset equation. The system is modelled by nonlinear system of ordinary differential equations, which are reduced to non-dimensional form via suitable similarity transformations. The Runge–Kutta numerical technique of 4th order is utilized to solve the set of flow equations. The influences of various emerging parameters on bubble radius, velocity profile and pressure of bubble are illustrated graphically and discussed in detail.
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