Symmetry Methods of Flow and Heat Transfer between Slowly Expanding or Contracting Walls

Magalakwe, Gabriel; Khalique, Chaudry Masood

doi:10.1155/2013/137930

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…The arrangement of consistently extending or contracting channel in a semi-infinite rectangular permeable channel was researched by Mohyud-Din et al (2010). A mathematical solution was explored by Magalakwe and Khalique (2013) for the flow and heat transfer between gradually expanding or contracting channel walls. Xinhui et al (Xinhui et al, 2014;Si et al, 2013) characterized the flow of non-Newtonian flow in a permeable channel with extending or contracting walls.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic flow of molybdenum disulfide nanofluid in a channel with shape effects

Raza

Mebarek‐Oudina

Chamkha

2019

MMMS

156

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Purpose The purpose of this paper is to examine the combined effects of thermal radiation and magnetic field of molybdenum disulfide nanofluid in a channel with changing walls. Water is considered as a Newtonian fluid and treated as a base fluid and MoS2 as nanoparticles with different shapes (spherical, cylindrical and laminar). The main structures of partial differential equations are taken in the form of continuity, momentum and energy equations. Design/methodology/approach The governing partial differential equations are converted into a set of nonlinear ordinary differential equations by applying a suitable similarity transformation and then solved numerically via a three-stage Lobatto III-A formula. Findings All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters. The validations of numerical results have been taken into account with other works reported in literature and are found to be in an excellent agreement. The study reveals that the Nusselt number increases by increasing the solid volume fraction for different shapes of nanoparticles, and an increase in the values of wall expansion ratio α increases the velocity profile f′(η) from lower wall to the center of the channel and decreases afterwards. Originality/value In this paper, a numerical method was utilized to investigate the influence of molybdenum disulfide (MoS2) nanoparticles shapes on MHD flow of nanofluid in a channel. The validity of the literature review cited above ensures that the current study has never been reported before and it is quite new; therefore, in case of validity of the results, a three-stage Lobattoo III-A formula is implemented in Matlab 15 by built in routine “bvp4c,” and it is found to be in an excellent agreement with the literature published before.

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Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic flow of molybdenum disulfide nanofluid in a channel with shape effects

Raza

Mebarek‐Oudina

Chamkha

2019

MMMS

156

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“…Series solution of uniformly expanding or contracting walls in a semi-infinite rectangular porous channel was investigated by Mohyud-din et al [10]. An analytical solution was investigated by Magalakwe and Khalique [11], for the flow and heat transfer between slowly expanding or contracting walls. Xinhui et al [12] and [13] analyzed the flow of non-newtonian fluid in a porous channel with expanding or contracting walls.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Flow of a Casson Fluid between Two Orthogonally Moving Porous Disks: A Numerical Investigation

Raza¹,

Rohni²,

Omar³

2017

Communications in Numerical Analysis

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The purpose of the present paper is to study the unsteady two dimensional laminar incompressible flow of non-Newtonian fluid between two orthogonally moving porous disks using the Casson fluid model that is used to characterize the non-Newtonian fluid behavior. Governing partial differential equations are reduced into nonlinear ordinary differential equations by using suitable similarity transformation and then solved numerically by Runge-Kutta-Fehlberg technique. The numerical results are found excellent agreement with the literature published before. Trusting to this validity, effects of different physical parameters are discussed. The study reveals that velocity of the fluid particles increases with an increase in the disk expanding ratio.

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Analysis of MHD Fluid Flow and Heat Transfer Inside an Inclined Deformable Filter Chamber: Lie Group Method

Lekoko,

Magalakwe,

Khalique

2023

Int. J. Appl. Comput. Math

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This paper investigates MHD fluid flow and distribution of heat inside a filter chamber during a process of filtering particles from the fluid. A flow model of MHD viscous incompressible fluid inside a filter is studied to seek semi-analytical solutions which are analysed to find flow and heat dynamics that lead to optimal outflow (maximum filtrates) during filtration. Lie group method is used to reduce a system of four partial differential equations describing fluid flow and temperature distribution inside the filter chamber to a system of two ordinary differential equations. The reduced system is then solved by perturbation process to obtain semi-analytical solutions for flow velocity and temperature variation inside the chamber. To understand the flow dynamics and heat distribution of the underlying case study better, the influence of different parameters during filtration resulting from the filter design, flow dynamics and heat effects are graphically presented and analysed in order to identify a combination of flow parameters that yields the best filtration process. The findings show that to maximise filtrates production, more fluid injection is required during filtration. Moreover, from the findings, it is evident that the temperature increase inside the chamber arising from the Joule heating effect is ideal since it increases internal work done and hence increases filtrates production.

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Symmetry Methods of Flow and Heat Transfer between Slowly Expanding or Contracting Walls

Cited by 3 publications

References 6 publications

Magnetohydrodynamic flow of molybdenum disulfide nanofluid in a channel with shape effects

Magnetohydrodynamic flow of molybdenum disulfide nanofluid in a channel with shape effects

Unsteady Flow of a Casson Fluid between Two Orthogonally Moving Porous Disks: A Numerical Investigation

Analysis of MHD Fluid Flow and Heat Transfer Inside an Inclined Deformable Filter Chamber: Lie Group Method

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