scholarly journals Stability Analysis on Magnetohydrodynamic Flow of Casson Fluid over a Shrinking Sheet with Homogeneous-Heterogeneous Reactions

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 652 ◽  
Author(s):  
Rusya Yahaya ◽  
Norihan Md Arifin ◽  
Siti Mohamed Isa
Keyword(s):  
Stability Analysis ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Heterogeneous Reactions ◽  
Shrinking Sheet ◽  
Local Skin

Two-dimensional magnetohydrodynamic (MHD) stagnation point flow of incompressible Casson fluid over a shrinking sheet is studied. In the present study, homogeneous-heterogeneous reactions, suction and slip effects are considered. Similarity variables are introduced to transform the governing partial differential equations into non-linear ordinary differential equations. The transformed equations and boundary conditions are then solved using the bvp4c solver in MATLAB. The local skin friction coefficient is tabulated for different values of suction and shrinking parameters. The profiles for fluid velocity and concentration for various parameters are illustrated. It was found that two solutions were obtained at certain ranges of parameters. Then, the bvp4c solver was used to perform stability analysis on the dual solutions. Based on the results, the first solution was more stable and physically meaningful than the other solution. The skin friction coefficient increased when suction increased, but decreased when the magnitude of shrinking parameter increased. Meanwhile, the velocity and concentration profile increased in the presence of a magnetic field. It is also noted that the higher the strength of the homogeneous-heterogeneous reactions, the lower the concentration of reactants.

scholarly journals Stagnation-point flow past a shrinking sheet in a nanofluid

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Roslinda Nazar ◽  
Mihaela Jaradat ◽  
Norihan Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Nonlinear System ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

AbstractIn this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

scholarly journals Unsteady MHD Bionanofluid Flow in a Porous Medium with Thermal Radiation near a Stretching/Shrinking Sheet

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
M. Irfan ◽  
M. Asif Farooq ◽  
A. Mushtaq ◽  
Z. H. Shamsi
Keyword(s):  
Porous Medium ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Internal Heat ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
The Impact

This research aims at providing the theoretical effects of the unsteady MHD stagnation point flow of heat and mass transfer across a stretching and shrinking surface in a porous medium including internal heat generation/absorption, thermal radiation, and chemical reaction. The fundamental principles of the similarity transformations are applied to the governing partial differential equations (PDEs) that lead to ordinary differential equations (ODEs). The transformed ODEs are numerically solved by the shooting algorithm implemented in MATLAB, and verification is done from MATLAB built-in solver bvp4c. The numerical data produced for the skin friction coefficient, the local Nusselt number, and the local Sherwood number are compared with the available result and found to be in a close agreement. The impact of involved physical parameters on velocity, temperature, concentration, and density of motile microorganisms profiles is scrutinized through graphs. It is analyzed that the skin friction coefficient enhances with increasing values of an unsteady parameter A , magnetic parameter M , and porosity parameter Kp . In addition, we observe that the density of a motile microorganisms profile enhances larger values of the bioconvection Lewis number Lb and Peclet number Pe and decreases with the increasing values of an unsteady parameter A .

Radiative hybrid nanofluid flow past a rotating permeable stretching/shrinking sheet

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Differential Equations ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Current Work ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Local Skin ◽  
Content Type

Purpose This paper aims to discuss a stability analysis on Cu-Al2O3/water nanofluid having a radiation and suction impacts over a rotating stretching/shrinking sheet. Design/methodology/approach The partial differential equations are converted into nonlinear ordinary differential equations using similarity transformation and then being solved numerically using built in function in Matlab software (bvp4c). The effects of pertinent parameters on the temperature and velocity profiles together with local Nusselt number and skin friction are reported. Findings Compared to previously published studies, the current work is noticed to be in good deal. The analysis further shows that the non-unique solutions exist for certain shrinking parameter values. Hence, a stability analysis is executed using a linear temporal stability analysis and concluded that the second solution is unstable, while the first solution is stable. The effect of suction parameter is observed to be significant in obtaining the solutions. The improvement of the local skin friction and the decrease of the local Nusselt number on the shrinking surface are observed with the increment of the copper nanoparticle volume fractions. Originality/value The originality of current work is the numerical solutions and stability analysis of hybrid nanofluid in rotating flow. This work has also resulted in producing the non-unique solutions for the shrinking sheet, and a stability analysis has also been executed for this flow showing that the second solution is unstable, while the first solution is stable. This paper is therefore valuable for engineers and scientist to get acquainted with the properties of the flow, its behavior and the way to predict it. The authors admit that all the findings are original and were not published anywhere else.

scholarly journals Unsteady Hydromagnetic Flow of Radiating Fluid Past a Convectively Heated Vertical Plate with the Navier Slip

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
O. D. Makinde ◽  
M. S. Tshehla
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Newtonian Heating ◽  
Local Skin ◽  
Navier Slip

This paper investigates the unsteady hydromagnetic-free convection of an incompressible electrical conducting Boussinesq’s radiating fluid past a moving vertical plate in an optically thin environment with the Navier slip, viscous dissipation, and Ohmic and Newtonian heating. The nonlinear partial differential equations governing the transient problem are obtained and tackled numerically using a semidiscretization finite difference method coupled with Runge-Kutta Fehlberg integration technique. Numerical data for the local skin friction coefficient and the Nusselt number have been tabulated for various values of parametric conditions. Graphical results for the fluid velocity, temperature, skin friction, and the Nusselt number are presented and discussed. The results indicate that the skin friction coefficient decreases while the heat transfer rate at the plate surface increases as the slip parameter and Newtonian heating increase.

scholarly journals MHD heat transfer flow of Casson fluid past a stretching wedge subject to suction and injection

2017 ◽  
Vol 13 (4) ◽  
pp. 637-641 ◽  
Author(s):  
Imran Ullah ◽  
Sharidan Shafie ◽  
Ilyas Khan
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Wedge Angle ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Suction Parameter ◽  
Keller Box Method

The steady two dimensional incompressible hydromagnetic boundary layer flow caused by stretching wedge immersed in Casson fluid with heat transfer and suction/injection is investigated numerically. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. Numerical results for local skin friction coefficient are compared with the existing literature and observed in closed agreement with those results. The effects of pertinent parameters on flow fields are displayed graphically and discussed. It is found that velocity decreases with increase of Casson parameter and wedge angle parameter when the wedge is stretching faster than free stream. It is also observed that rate of heat transfer at surface increases with the increase of Prandtl number and Casson fluid parameter. Moreover, with increase of suction parameter the fluid velocity decreases and rate of shear stress increases.

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Golam Mortuja Sarkar ◽  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Hiemenz Flow ◽  
Self Similar ◽  
The Stability

Purpose This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet. Design/methodology/approach The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable. Findings It is observed that the self-similar equations exhibit dual solutions within the range [λc, −1] of shrinking parameter λ, where λc is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain. Originality/value This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

Measurement of the Wall Shear Stress With Sublayer Thin Plate of Thermochromic Liquid Crystal

2015 ◽  
Author(s):  
Takashi Kodama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Liquid Crystal ◽  
Friction Coefficient ◽  
Wall Shear Stress ◽  
Skin Friction ◽  
Channel Flow ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Local Skin Friction ◽  
Wall Shear

New optical method for measurement of the local wall shear stress has been developed by using thermo-chromic liquid crystal temperature measurement based on hue [1], [2] of the camera view. The flow field is the fully developed turbulent channel flow. Thin film made of thermo-chromic liquid crystal is placed on the wall. A rectangular shaped obstacle is glued on the film. The obstacle is within a region of buffer layer with height from the wall. Temperature of the film and the obstacle are slightly raised by a heater below the wall. The air flow makes non-uniform temperature distribution and non-uniform color distribution appears on the surface of the film. Relations between hue and local skin friction coefficient were examined in a turbulent air channel flow. It is indicated that a certain hue of a point is varying linearly against the corresponding local skin friction coefficient.

Entropy generation analysis in flow of thixotropic nanofluid

2019 ◽  
Vol 29 (12) ◽  
pp. 4507-4530 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Salman Ahmad ◽  
Tasawar Hayat ◽  
M. Waleed Ahmad Khan ◽  
Ahmed Alsaedi
Keyword(s):  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Content Type ◽  
Flow Variables

Purpose The purpose of this paper is to address entropy generation in flow of thixotropic nonlinear radiative nanoliquid over a variable stretching surface with impacts of inclined magnetic field, Joule heating, viscous dissipation, heat source/sink and chemical reaction. Characteristics of nanofluid are described by Brownian motion and thermophoresis effect. At surface of the sheet zero mass flux and convective boundary condition are considered. Design/methodology/approach Considered flow problem is mathematically modeled and the governing system of partial differential equations is transformed into ordinary ones by using suitable transformation. The transformed ordinary differential equations system is figure out by homotopy algorithm. Outcomes of pertinent flow variables on entropy generation, skin friction, concentration, temperature, velocity, Bejan, Sherwood and Nusselts numbers are examined in graphs. Major outcomes are concluded in final section. Findings Velocity profile increased versus higher estimation of material and wall thickness parameter while it decays through larger Hartmann number. Furthermore, skin friction coefficient upsurges subject to higher values of Hartmann number and magnitude of skin friction coefficient decays via materials parameters. Thermal field is an increasing function of Hartmann number, radiation parameter, thermophoresis parameter and Eckert number. Originality/value The authors have discussed entropy generation in flow of thixotropic nanofluid over a variable thicked surface. No such consideration is yet published in the literature.

scholarly journals Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

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