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1

Conjugate mixed convection of a micropolar fluid over a vertical hollow circular cylinder

Ahmed Alliche Sid, Ayoub Bennia, Manal Bouaziz Amina, Najib Bouaziz Mohamed

International Journal of Applied Mechanics and Engineering

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2024

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Vol. 29, no. 1

1--18

EN

This work conducts a numerical examination into the influence of a magnetic field and viscosity dissipation on the movement of a micropolar fluid over the surface of a vertical, hollow circular cylinder via conjugate mixed convection. In this investigation, we obtained a numerical solution for a non-linear differential equations-based modeling system by employing MATLAB and the bvp4c solver, which operates on a two-equation model. We show graphically how micropolar materials, conjugate heat transfer, viscous energy dissipation, buoyancy factors and magnetic field affect the temperature at the interface, local skin friction and heat transfer. By contrasting the acquired results with those found in the published research, which exhibit a high degree of concordance, the validity of the methodology is proven.

2

Soret and dufour effects on mhd flow of a micropolar fluid past over a vertical Riga plate

Borah Keshab, Konch Jadav, Chakraborty Shyamanta

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 3

5-18

EN

The present study investigates heat and mass transport phenomena associated with the MHD flow of micropolar fluid over a vertically stretched Riga plate under the action of a uniform magnetic field applied parallel to the plate. The objective of the study is to analyze Soret and Dufour effects on this physical situation in the presence of chemical reaction. The governing partial differential equations are converted into ordinary differential equations using suitable similarity transformations. The equations are solved numerically by developing programming codes in MATLAB for the very efficient shooting method along with the fourth order Runge-Kutta scheme. The velocity, microrotation, temperature and species concentration distribution are presented graphically for various emerging physical parameters like Hartmann number, material parameter, Soret number, Dufour number and other dimensionless parameters. It is found that the species concentration distribution profiles increase with increasing Soret number, whereas the temperature distribution profile decreases with an increasing Soret number. This work also provides solutions for shear stress at plates, the rate of heat and mass transfer in addition to those for velocity, microrotation, temperature and species concentration. Comparisons with previous studies are carefully examined, and it is found that they are generally in agreement.

3

Exact solution for non-newtonian fluid flow beyond a contaminated fluid sphere

Kunche Vijaya Lakshmi, Meduri Phani Kumar

Engineering Transactions

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2022

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Vol. 70, iss. 3

287--299

EN

Stokes flow of non-Newtonian fluid beyond a partially contaminated non-Newtonian fluid sphere with interfacial slip condition is considered. An analytic solution for the flow fields indicated by the stream function and the drag force over the sphere was obtained. Special well-known cases are reduced. It was observed that with an increase in slip parameter values, there is a rise in drag coefficient values.

4

Parthiban R., Palani G.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 4

179--191

EN

The current study aims to explore stagnation spot flow of a micropolar fluid about a plain linear exponentially expanding penetrable surface in the incidence of radiation and in-house heat production/immersion. Through similarity mapping, the mathematical modeling statements are transformed to ODE's and numerical results are found by shooting techniques. The impact of varying physical constants on momentum, micro-rotation and temperature is demonstrated through graphs. The computed measures including shear, couple stress, mass transfer and the local surface heat flux with distinct measures of factors involved in this proposed problem are presented through a table.

5

Micropolar flow over a black isothermal plate in the presence thermal radiation

Raptis A.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 2

235--241

EN

This study numerically investigates the effects of thermal radiation on the flow over a black isothermal plate for an optically thin gray micropolar fluid. The flowing medium absorbs and emits radiation, but scattering is not included. The computational results are discussed graphically for several selected flow parameters.

6

A numerical approach to slip flow of a micropolar fluid above a flat permeable contracting surface

Parthiban R., Palani G., Tinker Seema, Sharma R. P.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 2

173--185

EN

A plain linear penetrable contracting sheet with slip over a micro-polar liquid with a stagnation-point flow is analyzed. Through similarity mapping, the mathematical modeling statements are transformed as ODE’s and numerical results are found by shooting techniques. The varying impacts of physical quantities on the momentum, micro-rotation, and temperature were demonstrated through graphs. The computed measures including shear and couple stress with distinct measures of factors involved in this proposed problem are presented through a table.

7

Vertical heat transport at infinite Prandtl number for micropolar fluid

Caggio M., Kalita P., Łukaszewicz G., Mizerski K. A.

Archives of Mechanics

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2020

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Vol. 72, nr 6

525--553

EN

We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh–Bénard convection problem at the infinite Prandtl number for a micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh number, with a logarithmic correction. The derived bound is compared with the optimal known one for the Newtonian fluid. It follows that the (optimal) upper bound for the micropolar fluid is less than the corresponding bound for the Newtonian fluid at the same Rayleigh number. Moreover, strong microrotational diffusion effects can entirely suppress the heat transfer. In the Newtonian limit our purely analytical findings fully agree with estimates and scaling laws obtained from previous theories significantly relying on phenomenology.

8

Drag force of a porous particle moving axisymmetrically in a closed cavity of micropolar fluid

Madasu Krishna Prasad

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 4

41--51

EN

The present paper deals with the problem of an incompressible axisymmetric creeping flow caused by a porous spherical particle in a spherical cavity filled with micropolar fluid. Depending on the kind of cell model, appropriate boundary conditions are used on the surface of sphere and spherical cavity. Drag force on the porous particle in the presence of a cavity is calculated to determine the correction factor to the Stokes law. A general expression for the hydrodynamic force acting on the porous sphere and, hence, for the wall correction factor of the sphere are obtained. The special cases of the porous sphere in viscous fluid, zero permeability solid sphere in micropolar fluid and viscous fluid are obtained in open and closed cavity respectively.

9

Unsteady MHD mixed convection flow of a micropolar fluid over a vertical wedge

Roy N. C., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 2

363--391

EN

An analysis is presented to investigate the unsteady magnetohydrodynamic (MHD) mixed convection boundary-layer flow of a micropolar fluid over a vertical wedge in the presence of thermal radiation and heat generation or absorption. The free-stream velocity and surface temperature are assumed to be oscillating in magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the finite difference method for the entire frequency range, and the series solution for low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions provide a good agreement with the series solutions. The amplitudes of skin friction and couple stress coefficients are found to be strongly dependent on the Richardson number and the vortex viscosity parameter. The Prandtl number, the conduction-radiation parameter, the surface temperature parameter and the pressure gradient parameter significantly affect the amplitudes of skin friction, couple stress and surface heat transfer rates. However, the amplitudes of skin friction coefficient are considerably affected by the magnetic field parameter, whereas the amplitudes of heat transfer rate are appreciably changed with the heat generation or absorption parameter. In addition, results are presented for the transient skin friction, couple stress and heat transfer rate with the variations of the Richardson number, the vortex viscosity parameter, the pressure gradient parameter and the magnetic field parameter.

10

Role of slip velocity in a magneto-micropolar fluid flow from a radiative surface with variable permeability: a numerical study

Sharma B. K., Tailor V., Goyal M.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 3

637--651

EN

An analysis is presented to describe the hydromagnetic mixed convection flow of an electrically conducting micropolar fluid past a vertical plate through a porous medium with radiation and slip flow regime. A uniform magnetic field has been considered in the study which absorbs the micropolar fluid with a varying suction velocity and acts perpendicular to the porous surface of the above plate. The governing non-linear partial differential equations have been transformed into linear partial differential equations, which are solved numerically by applying the explicit finite difference method. The numerical results are presented graphically in the form of velocity, micro-rotation, concentration and temperature profiles, the skin-friction coefficient, the couple stress coefficient, the rate of heat and mass transfers at the wall for different material parameters.

11

Squeeze flow modeling with the use of micropolar fluid theory

Kucaba-Piętal A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 6

927--933

EN

The aim of this paper is to study the applicability of micropolar fluid theory to modeling and to calculating tribological squeeze flow characteristics depending on the geometrical dimension of the flow field. Based on analytical solutions in the lubrication regime of squeeze flow between parallel plates, calculations of the load capacity and time required to squeeze the film are performed and compared – as a function of the distance between the plates – for both fluid models: the micropolar model and the Newtonian model. In particular, maximum distance between the plates for which the micropolar effects of the fluid become significant will be established. Values of rheological constants of the fluids, both those experimentally determined and predicted by means of using equilibrium molecular dynamics, have been used in the calculations. The same analysis was performed as a function of dimensionless microstructural parameters.

12

Numerical simulation of flow and heat transfer in hydromagnetic micropolar fluid between two stretchable disks with viscous dissipation effects

Ali K., Ahmad S., Ashraf M.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 2

633--643

EN

A study of magnetohydrodynamic (MHD) flow with viscous dissipation and heat transfer in an electrically conducting laminar steady viscous incompressible micropolar fluid between two infinite uniformly stretching disks is presented. The transformed self similar nonlinear ODEs are first linearized using a quasi linearization method and then solved by employing a combination of a direct and an iterative method. The study may be beneficial to flow and thermal control of polymeric processing.

13

Drag on a permeable sphere placed in a micropolar fluid with non-zero boundary condition for microrotations

Mishra V., Gupta B. R.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 3

97--109

EN

This paper concerns an analytical study of an infinite expanse of uniform flow of steady axisymmetric creeping flow of an incompressible micropolar fluid around the permeable sphere assuming a nonhomogeneous boundary condition for microrotation vector. It is assumed that microrotation vector is proportional to the rotation rate of velocity vector. The stream function solutions for the flow fields are obtained in the terms of modified Bessel’s functions and Gegenbauer functions. Continuity of normal velocity, no-slip condition, non-zero microrotation vector on the sphere, uniform velocity at infinity are the different boundary conditions used to determine the flow fields explicitly. The microrotation component, pressure field, bounds of permeability parameter and drag force experienced by the permeable sphere are calculated. Dependence of the drag force on different fluid parameters is presented graphically and discussed. It is found that drag force decreases with increasing spin parameter. Several cases of interest are deduced from the present analysis.

14

The concept of a quasi-micropolar fluid model

Szubartowski D., Ganczarski A.

Czasopismo Techniczne. Mechanika

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2016

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Y. 113, iss. 1-M

224--230

EN

This paper presents a micropolar fluid model that direct applies Cosserat’s continuum to hydrodynamics. The corresponding system of equations describing isotropic micropolar fluid is obtained by assuming lack of symmetry of the Cauchy stress tensor and taking into account the conservation of angular momentum. This turns out to be an extension of the NavierStokes fluid but containing turbulent effect built in.

PL

W artykule przedstawiono mikropolarny model cieczy stanowiący bezpośrednie zastosowanie kontinuum Cosseratów w hydromechanice. Zakładając brak symetrii tensora naprężenia Cauchy’ego oraz uwzględniając zasadę zachowania momentu pędu otrzymano układ równań opisujący izotropową ciecz mikropolarną. Układ równań jest uogólnieniem równań NavieraStokesa poprzez uwzględnienie efektu turbulentnego.

15

On axisymmetrical boundary problem of unsteady motion of micropolar fluid in the half-space

El-Sirafy I. H., Aboutahoun A. W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 1

51--62

EN

The aim of this paper is developing an exact solution for the problem of axisymmetrical flow of unsteady motion of micropolar fluid in the half-space when the shear stresses are given on the boundary. The Laplace-Hankel transform technique is used to solve this problem. Some physical quantities such as velocities, pressure and microrotations are obtained and illustrated numerically.

16

Heat transfer enhancement in natural convection in micropolar nanofluids

Rup K., Nering K.

Archives of Mechanics

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2016

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Vol. 68, nr 4

327--344

EN

In this work an analysis of momentum, angular momentum and heat transfer during unsteady natural convection in micropolar nanofluids is presented. Selected nanofluids treated as single phase fluids, contain small particles. In particular, two ethylene glycol-based nanofluids were analyzed. The volume fraction of these solutions was 6%, 3.5% and 0.6%. The first ethylene glycol solution contained Al2O3 nanoparticles (d = 38.4 nm), and the second ethylene glycol solution contained Cu nanoparticles (d = 10 nm).

17

Heat flow through a thin cooled pipe filled with a micropolar fluid

Beneš M., Pažanin I., Suárez-Grau F. J.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 3

569--579

EN

In this paper, a non-isothermal flow of a micropolar fluid in a thin pipe with circular cross- -section is considered. The fluid in the pipe is cooled by the exterior medium and the heat exchange on the lateral part of the boundary is described by Newton’s cooling condition. Assuming that the hydrodynamic part of the system is provided, we seek for the micropolar effects on the heat flow using the standard perturbation technique. Different asymptotic models are deduced depending on the magnitude of the Reynolds number with respect to the pipe thickness. The critical case is identified and the explicit approximation for the fluid temperature is built improving the known result for the classical Newtonian flow as well. The obtained results are illustrated by some numerical simulations.

18

Analytical solution to the MHD flow of micropolar fluid over a linear stretching sheet

Siddheshwar P. G.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 2

397--406

EN

The flow due to a linear tretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.

19

Unsteady natural convection in micropolar nanofluids

Rup K., Nering K.

Archives of Thermodynamics

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2014

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Vol. 35, no. 3

155--170

EN

This paper presents the analysis of momentum, angular momentum and heat transfer during unsteady natural convection in micropolar nanofluids. Selected nanofluids treated as single phase fluids contain small particles with diameter size 10-38.4 nm. In particular three water-based nanofluids were analyzed. Volume fraction of these solutions was 6%. The first of the analyzed nanofluids contained TiO2 nanoparticles, the second one contained Al2O3 nanoparticles, and the third one the Cu nanoparticles.

20

Effects of chemical reaction on magneto-micropolar fluid flow from a radiative surface with variable permeability

Sharma B. K., Singh A. P., Yadav K., Chaudhary R. C.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

833--851

EN

This paper presents a study of a hydromagnetic free convection flow of an electrically conducting micropolar fluid past a vertical plate through a porous medium with a heat source, taking into account the homogeneous chemical reaction of first order. A uniform magnetic field has also been considered in the study which acts perpendicular to the porous surface of the above plate. The analysis has been done by assuming varying permeability of the medium and the Rosseland approximation has been used to describe the radiative heat flux in the energy equation. Numerical results are presented graphically in the form of velocity, micro- rotation, concentration and temperature profiles, the skin-friction coefficient, the couple stress coefficient, the rate of heat and mass transfers at the wall for different material parameters. The study clearly demonstrates how a chemical reaction influences the above parameters under given conditions.