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Article
Publication date: 1 August 2016

Ali Alhelfi and Bengt Ake Sunden

The purpose of this paper is to present numerical investigation of the gas/vapor bubble dynamics under the influence of an ultrasonic field to give a more comprehensive…

173

Abstract

Purpose

The purpose of this paper is to present numerical investigation of the gas/vapor bubble dynamics under the influence of an ultrasonic field to give a more comprehensive understanding of the phenomenon and present new results

Design/methodology/approach

In order to formulate the mathematical model, a set of governing equations for the gas inside the bubble and the liquid surrounding it are used. All hydrodynamics forces acting on the bubble are considered in the typical solution. The systems of equations required to be solved consist of ordinary and partial differential equations, which are both nonlinear and time dependent equations. A fourth order Runge-Kutta method is applied to solve the ordinary differential equations. On the other hand, the finite difference method is employed to solve the partial differential equations and a time-marching technique is applied.

Findings

The numerical model which is developed in the current study permits a correct prediction of the bubble behavior and its characteristics in an acoustic field generated at this occasion.

Originality/value

Previous studies considering numerical simulations of an acoustic bubble were performed based on the polytropic approximation or pressure uniformity models of the contents inside the bubble. In this study, an enhanced numerical model is developed to study the acoustic cavitation phenomenon and the enhancement concerns taking into account both the pressure and temperature gradients inside the bubble as well as heat transfer through the bubble surface into account which is very important to obtain the temperature of the liquid surrounding the bubble surface.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 2 November 2022

Muhammad Nadeem and Zitian Li

This study aims to purpose the idea of a new hybrid approach to examine the approximate solution of the fourth-order partial differential equations (PDEs) with time fractional…

46

Abstract

Purpose

This study aims to purpose the idea of a new hybrid approach to examine the approximate solution of the fourth-order partial differential equations (PDEs) with time fractional derivative that governs the behaviour of a vibrating beam. The authors have also demonstrated the physical representations of the problem in different fractional order.

Design/methodology/approach

Mohand transform is a new technique that the authors use to reduce the order of fractional problems, and then the homotopy perturbation method can be used to handle the further series solution in the form of convergence. The formulation of Mohand transform and the homotopy perturbation method is known as Mohand homotopy perturbation transform (MHPT). The fractional order in this paper is considered in the Caputo sense.

Findings

The results are formulated in the shape of iterative series and predict the solution close to the exact solution. This successive iteration demonstrates the authenticity and reliability of this scheme.

Research limitations/implications

This paper presents the significance of MHPT such that, firstly, Mohand transform is coupled with homotopy perturbation method and, secondly, the fractional order a is used to show the physical behaviour of the graphical solution.

Practical implications

This study presents the consistency and authenticity of the graphical solution with the exact solutions.

Social implications

This study demonstrates that Mohand transform is capable to handle the fractional order problem without any constraints and assumptions.

Originality/value

A new integral transform has been introduced without any restriction of variables that produces the results in a series form and confirms the validity of the proposed algorithm by graphical illustrations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 3
Type: Research Article
ISSN: 0961-5539

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