A note on some solutions of micropolar fluid in a channel with permeable walls

2018 ◽  
Vol 14 (1) ◽  
pp. 91-101 ◽  
Author(s):  
Jawad Raza ◽  
Azizah M. Rohni ◽  
Zurni Omar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Micropolar Fluid ◽  
Design Methodology ◽  
Shooting Method ◽  
Similarity Transformation ◽  
Physical Parameters ◽  
Content Type ◽  
Single Solution ◽  
Permeable Walls

Purpose The purpose of this paper is to investigate different branches of the solution of micropolar fluid in a channel with permeable walls. Moreover, the intention of the study is to examine the effect of different physical parameters on fluid flow. Design/methodology/approach The mathematical modeling is performed on the basis of law of conservation of mass, momentum and angular momentum. The governing partial differential equations were transformed into ordinary differential equations by applying suitable similarity transformation. Afterwards, the set of nonlinear ordinary differential equations was solved numerically by a shooting method. Findings The study reveals that various branches of the solution of the proposed problem exist only in the case of strong suction. Originality/value The investigation of new branches of the solution of non-Newtonian micropolar fluid is relatively difficult as far as the single solution is concern. This study explores the new branches of the solution of a micropolar fluid in a channel with suction/injection. Simultaneous effect of suction Reynolds number and vortex viscosity parameter on velocity and micro-rotation profile is examined for different branches of solution in order to make the analysis more interesting.

Unsteady separated stagnation-point flow and heat transfer past a stretching/shrinking sheet in a copper-water nanofluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2588-2605 ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stagnation Point ◽  
Design Methodology ◽  
Similarity Transformation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper (Cu)-water nanofluid using the mathematical nanofluid model proposed by Tiwari and Das. Design/methodology/approach A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary (similarity) differential equations which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Findings It is found that the solution is unique for stretching case; however, multiple (dual) solutions exist for the shrinking case. Originality/value The authors believe that all numerical results are new and original, and have not been published elsewhere.

Effect of temperature on the MHD stagnation-point flow past an isothermal plate for a Boussinesquian Newtonian and micropolar fluid

2018 ◽  
Vol 28 (6) ◽  
pp. 1315-1334 ◽  
Author(s):  
Alessandra Borrelli ◽  
Giulia Giantesio ◽  
Maria Cristina Patria
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Micropolar Fluid ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Environment Temperature ◽  
Uniform External Magnetic Field

Purpose This paper aims to analyze the steady two-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid when the obstacle is uniformly heated. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. Some analytical considerations about existence and uniqueness of the solution are obtained. The system is then solved numerically using the bvp4c function in MATLAB. Findings If the temperature of the obstacle Tw coincides with the environment temperature T0, then the motion reduces to the usual orthogonal stagnation-point flow; if Tw = T0, then it is necessary to include in the similarity function describing the velocity an oblique part due to the temperature. Also, the presence of a uniform external magnetic field orthogonal to the obstacle is examined. In all cases, the motion is reduced to a system of nonlinear ordinary differential equations with boundary conditions, whose solution is discussed numerically when the Prandtl and the Hartmann number varies. Originality/value The present results are original and new for the problem of magnetohydrodynamic mixed convection in the plane stagnation-point flow of a Newtonian or a micropolar fluid over a vertical flat plate. At infinity, the motion approaches the orthogonal stagnation-point flow of an inviscid fluid; the effect of an uniform external magnetic field is considered, and the obstacle has a uniform temperature.

A new similarity solution with stability analysis for the three-dimensional boundary layer of hybrid nanofluids

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Najiyah Safwa Khashi'ie ◽  
Norihan M. Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Similarity Transformation ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Dimensional Boundary

Purpose The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties. Design/methodology/approach The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed. Findings The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only. Originality/value The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

Influence of induced magnetic field and slip conditions on convective Prandtl fluid flow over a stretching surface with homogeneous and heterogeneous reactions

2020 ◽  
Vol 17 (1) ◽  
pp. 127-147 ◽  
Author(s):  
R. Meenakumari ◽  
P. Lakshminarayana ◽  
K. Vajravelu
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heterogeneous Reactions ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Content Type ◽  
Homogeneous And Heterogeneous Reactions ◽  
Moderate Magnetic Field

PurposeThe aim of the present paper is to investigate the homogeneous and heterogeneous reactions on Prandtl fluid flow at a stretching sheet with an induced magnetic field and slip boundary conditions.Design/methodology/approachThe governing equations include the continuity, induced magnetic field, momentum, energy and homogeneous–heterogeneous equations. Initially, with suitable similarity variables, the governing partial differential equations and converted into a system of ordinary differential equations. Then, the nonlinear ordinary differential equations are solved by a shooting technique with the help of the BVC5C Matlab package.FindingsThe results of the present investigation are presented through graphs for different values of the various parameters. The authors observed that the large values of the stretching ratio and the induced magnetic parameters are moderate magnetic field, velocity and temperature primarily. Also, the authors found the more velocity and temperatures by boosting the slip parameters.Originality/valueIn addition, the values of the skin friction and the rate of heat transfer for various values of physical parameters are tabulated and deliberated in detail.

Physicochemical and rheological properties of titania and carbon nanotubes in a channel with changing walls

2016 ◽  
Vol 12 (4) ◽  
pp. 619-634 ◽  
Author(s):  
Jawad Raza ◽  
Azizah M. Rohni ◽  
Zurni Omar ◽  
M. Awais ◽  
A.Q. Baig
Keyword(s):  
Carbon Nanotubes ◽  
Differential Equations ◽  
Rheological Properties ◽  
Multiple Solutions ◽  
Design Methodology ◽  
Physical Parameters ◽  
Shooting Technique ◽  
Content Type ◽  
Energy Profiles ◽  
Real World Problem

Purpose The purpose of this paper is to investigate some multiple solutions for carbon nanotubes (CNTs) in a porous channel with changing walls. Moreover, the intention of the study is to examine the physicochemical and rheological properties of titania and CNTs. Design/methodology/approach The mathematical modeling is performed for the laws of conservation of mass, momentum and energy profiles. Governing partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically with the help of shooting technique. Findings The effects of different physical parameters on the rheology of nanofluids are discussed graphically and numerically, in order to make the analysis more interesting. The present study revealed that multiple solutions of nanofluids in a channel with changing walls are obtained only for the case of suction. Originality/value Some new branches of the solution for nanofluids in a channel with changing walls are obtained in this research, which has never been reported before. Combined effects of physicochemical and rheology of titania and carbon nanotubes are investigated briefly. The effects of physical parameters on velocity and temperature profile are examined in detail which is more realistic than real-world problem.

Non-Newtonian Magneto-Hydrodynamic Fluid with Radiation by Stretching Cylinder

2020 ◽  
Vol 9 (2) ◽  
pp. 106-113
Author(s):  
Gamal M. Abdel-Rahman ◽  
Amal M. Al-Hanaya
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Physical Parameters ◽  
Temperature Profiles ◽  
Stretching Cylinder ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Energy Equations

The aim of the present paper is to study the numerical solutions of the steady magnetohydrodynamic and heat generation effects on anon-Newtonian fluid with radiation through a porous medium by a stretching cylinder. The governing continuity, momentum, and energy equations are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. Numerical results were presented for velocity and temperature profiles for different parameters of the problem are studied graphically. Finally, the effects of related physical parameters on skin friction and the rate of heat transfer are also studied.

A novel approach on micropolar fluid flow in a porous channel with high mass transfer via wavelet frames

2021 ◽  
Vol 10 (1) ◽  
pp. 39-45
Author(s):  
S. Kumbinarasaiah ◽  
K.R. Raghunatha
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
High Mass ◽  
Porous Channel ◽  
Physical Parameters ◽  
Wavelet Frames ◽  
Parseval Frame ◽  
Highly Nonlinear ◽  
Frame Method

Abstract In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed.

MHD flow, under the kinetic postulate, of fluids that are initially liquid under thermal radiation effects

2019 ◽  
Vol 97 (6) ◽  
pp. 579-587
Author(s):  
Azad Hussain ◽  
Zainia Muneer ◽  
M.Y. Malik ◽  
Saadia Ghafoor
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Radiation Effects ◽  
Shooting Method ◽  
Porous Plate ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Runge Kutta Method

The present study focuses on the non-Newtonian magnetohydrodynamic flow, under the kinetic postulate, of fluids that are initially liquid past a porous plate in the appearance of thermal radiation effects. Resemblance transfigurations are used to metamorphose the governing equations for temperature and velocity into a system of ordinary differential equations. We then solved these differential equations subject to convenient boundary conditions by using the shooting method along with the Runge–Kutta method. Heat transfer and characteristic flow results are acquired for different compositions of physical parameters. These results are extended graphically to demonstrate interesting attributes of the physics of the problem. Nusselt number and skin friction coefficients are also discussed via graphs and tables for different values of dimensionless parameters. Decline occurs in velocity profile due to escalating values of M. Temperature profile depicts growing behavior due to acceleration in the values of λ and M. Nusselt number and skin friction curves represent rising behavior according to their parameters.

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

2021 ◽  
Vol 87 (1) ◽  
pp. 30-40
Author(s):  
Anisah Dasman ◽  
Abdul Rahman Mohd Kasim ◽  
Iskandar Waini ◽  
Najiyah Safwa Khashi’ie
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Wall Temperature ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Particle Interaction ◽  
Dust Particles ◽  
Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

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