Abstract
The Casson model is a fascinating model, which is genuinely recommended for use with fluids of a non-Newtonian type. The conventional model is not capable to represent the Casson model with the suspension of foreign bodies (dust particles). Due to this, the two-phase model for the mixture of Casson model fluid and dust particles is formulated. This study examines the emerging role of dust particles in changing the behavior of Casson model. In particular, two-phase flow of dusty Casson model with modified magnetic field and buoyancy effect under Newtonian heating boundary condition along a vertically stretching sheet is considered. The equations that govern under Casson model, together with dust particles, are reduced to a system of nonlinear ordinary differential equations by employing the suitable similarity variables. These transformed equations are then solved numerically by implementing the Runge–Kutta–Fehlberg (RKF45) method. The numerical results of skin friction coefficient plus Nusselt number are displayed graphically. The results revealed the fluid’s velocity tends to deteriorate due to the existence of dust particles, whilst its temperature is increased. The two-phase flow is one of the mathematical modeling techniques for multiphase flow, where the relationship between the fluid and solid is examined more closely. It is expected that the present findings can contribute to the understanding of the theory of two-phase flow mathematically, which will continue to produce significant research in this field.
Highlights
The convection flow of fluid occurs due to the temperature difference and heat transference rate.In particular, the mechanism of convection can be classified into three types, which are free, forced and Crystals 2020, 10, 814; doi:10.3390/cryst10090814 www.mdpi.com/journal/crystalsCrystals 2020, 10, 814 mixed
The dusty Casson model on free convection flow, with the effect of an aligned magnetic field subjected to boundary conditions of Newtonian heating (NH), has been presented
It is worth noting that if β = N = 0 and α1 = π/2 is substituted into Equations (16)–(19), this present study replaces the free convection of the Casson model flow problem with a transverse magnetic field
Summary
The convection flow of fluid occurs due to the temperature difference and heat transference rate.In particular, the mechanism of convection can be classified into three types, which are free, forced and Crystals 2020, 10, 814; doi:10.3390/cryst10090814 www.mdpi.com/journal/crystalsCrystals 2020, 10, 814 mixed. The convection flow of fluid occurs due to the temperature difference and heat transference rate. Mixed convection occurs when those two convections occur simultaneously. Engineering fields contain many applications of free convection flow, for instance, automatic control system of electrical and electronic components [1]. It is found that the obtained findings from the stretching sheet flow of viscous fluid with free convection are significant for fabric, plastic and polymer industries [2,3]. Most of the available literature on the flow problem deals with free convection under certain circumstances, such as various types of surfaces, physical parameters, as well as types of fluid and boundary conditions. The boundary condition of Newtonian heating (NH) has been conducted by Merkin [4]. As a continuance to this pioneering study, Lesnic et al [5] and Chaudhary and Jain [6]
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