Two parameter scaling group for unsteady convective magnetohydrodynamic flow

Uddin, Md. Jashim; Khan, Waqar A.; Ismail, Ahmad Izani Md.

doi:10.1016/j.aej.2016.02.004

Cited by 6 publications

(4 citation statements)

References 34 publications

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“…To convert PDEs to ODEs, two-parameter scaling transformations are used here. Both independent and dependent variables are scaled according to the group theoretic method as follows 40 , 41 where A, B, ξi, χi(i=1,2,3,4,5) are arbitrary constants. The PDEs (21)–(23) with BCs (24)–(25) are solved by using two-parameter scaling transformations (equation (26)).…”

Section: Two-parameter Lie Scaling Transformationsmentioning

confidence: 99%

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Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences

Tufail

Saleem

Chaudhry

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The model encountered an unsteady laminar and two-dimensional convective flow of Casson fluid passing through an inclined permeable vertical stretching sheet. The momentum, thermal and concentrated boundary layers (BLs) are used to analyze the unsteady effects of magnetohydrodynamics (MHD) (neglecting induced magnetic field), viscous dissipation, Joule heating and chemical reactions. The governed partial differential equations (PDEs) of the model are reduced to the ordinary differential equations (ODEs). The ξ and χ are selected as the two parameters of the scaling transformations. By using bvp4c with MATLAB, the ODEs are solved numerically and represent their results through the graphs and tables. After the non-dimensionalizing of the equations system, we get the emerging dimensionless parameters. The concentration process was enhanced by the Casson fluid parameter but it reduced the fluid flow and thermal transfer that can be found through the graphical results. The effect of Buoyancy is highlighted as it reduced the velocity profile function, but it is a growing function of the thermal and concentrated profiles. The physical quantities are integrated through the table and graphical analysis. In the center of the wall, the number Shx versus Sc decreases, but at the end it increases.

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Section: Two-parameter Lie Scaling Transformationsmentioning

confidence: 99%

“…By following literature, 40 , 41 we get the linear combination of the ξ i and χi as: and from the BCs, we get the final values as: …”

Section: Two-parameter Lie Scaling Transformationsmentioning

confidence: 99%

Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences

Tufail

Saleem

Chaudhry

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Yilmazer and Kocar [16] solved analytically heat conduction equation for an eccentric spherical annulus. Some efforts have been made to solve differential equations in fluid flow and heat conduction problems [17][18][19][20][21][22]. Tian [23] presented a symmetry analysis of non-linear heat conduction equations.…”

Section: Introductionmentioning

confidence: 99%

Heat conduction in rectangular solids with internal heat generation

Duan

2021

THERM SCI

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A representative steady-state heat conduction problem in rectangular solids with uniformly distributed heat generation has been investigated analytically. An analytical solution is provided by solving a nonhomogeneous partial differential equation. A simple and accurate model is proposed to predict the dimensionless shape factor parameter for the first time. The dimensionless shape factor is obtained in the light of the solution of Poisson equation with constant wall temperature boundary conditions. The area-mean temperature is found by integration on the rectangular cross-section. The model is very concise and nice for quick real world approximations, and it provides acceptable accuracy for engineering practice.

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“…The hydromagnetic unsteady mixed convection flow past porous plate sop in porous media was studied by Sharma et al [16]. Uddin et al [26] analysed unsteady MHD convective flow of heat and mass transfer past a vertical surface. Unsteady hydromagnetic mixed convection flow of heat and mass transfer in the stagnation region with a complex wall condition were studied by Chamka et al [2].…”

Section: Introductionmentioning

confidence: 99%

MHD mixed flow of unsteady convection with radiation over a vertical porous plate: Lie group symmetry analysis

Rajput

Patil

Jadhav

2017

ACM

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In this paper, we study the magnetohydrodynamic (MHD) mixed unsteady flow over a vertical porous plate. The system of non-linear partial differential equations governing the physical model is transformed into a system of non-linear ordinary differential equations via Lie group analysis. Using the Runge-Kutta fourth order method along with shooting technique the numerical analysis is carried out to study the effect of associated parameters on the velocity, temperature and concentration distribution. Computed results for the velocity, temperature and concentration distribution are discussed graphically.

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Two parameter scaling group for unsteady convective magnetohydrodynamic flow

Cited by 6 publications

References 34 publications

Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences

Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences

Heat conduction in rectangular solids with internal heat generation

MHD mixed flow of unsteady convection with radiation over a vertical porous plate: Lie group symmetry analysis

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