Magnetohydrodynamic flow of nano Williamson fluid generated by stretching plate with multiple slips

2019 ◽  
Vol 15 (5) ◽  
pp. 871-894 ◽  
Author(s):  
Jawad Raza ◽  
Fateh Mebarek-Oudina ◽  
B. Mahanthesh
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Regression Line ◽  
Skin Friction Coefficient ◽  
Content Type ◽  
Williamson Fluid ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Stretching Plate ◽  
Multiple Slips

Purpose The purpose of this paper is to present an exploration of multiple slips and temperature dependent thermal conductivity effects on the flow of nano Williamson fluid over a slendering stretching plate in the presence of Joule and viscous heating aspects. The effectiveness of nanoparticles is deliberated by considering Brownian moment and thermophoresis slip mechanisms. The effects of magnetism and radiative heat are also deployed. Design/methodology/approach The governing partial differential equations are non-dimensionalized and reduced to multi-degree ordinary differential equations via suitable similarity variables. The subsequent non-linear problem treated for numerical results. To measure the amount of increase/decrease in skin friction coefficient, Nusselt number and Sherwood number, the slope of linear regression line through the data points are calculated. Statistical approach is implemented to analyze the heat transfer rate. Findings The results show that temperature distribution across the flow decreases with thermal conductivity parameter. The maximum friction factor is ascertained at stronger magnetic field. Originality/value In the current paper, the magneto-nano Williamson fluid flow inspired by a stretching sheet of variable thickness is examined numerically. The rationale of the present study is to generalize the studies of Mebarek-Oudina and Makinde (2018) and Williamson (1929).

Flow and Heat Transfer of Powell–Eyring Fluid due to an Exponential Stretching Sheet with Heat Flux and Variable Thermal Conductivity

2015 ◽  
Vol 70 (3) ◽  
pp. 163-169 ◽  
Author(s):  
Ahmed M. Megahed
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Differential Equations ◽  
Variable Thermal Conductivity ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter

AbstractAn analysis was carried out to describe the problem of flow and heat transfer of Powell–Eyring fluid in boundary layers on an exponentially stretching continuous permeable surface with an exponential temperature distribution in the presence of heat flux and variable thermal conductivity. The governing partial differential equations describing the problem were transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the shooting method over the entire range of physical parameters. The effects of various parameters like the thermal conductivity parameter, suction parameter, dimensionless Powell–Eyring parameters and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. In this work, special attention was given to investigate the effect of the thermal conductivity parameter on the velocity and temperature fields above the sheet in the presence of heat flux. The numerical results were also validated with results from a previously published work on various special cases of the problem, and good agreements were seen.

scholarly journals Electrically Conducting Flow through Exponential Power Law Fluid with Variable Thermal Conductivity

2019 ◽  
Vol 24 (3) ◽  
pp. 539-548
Author(s):  
M. Ferdows ◽  
M.Z.I. Bangalee ◽  
D. Liu
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Thermal Conductivity ◽  
Variable Thermal Conductivity ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Electrically Conducting ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Exponential Power

Abstract The problem of exponential law of steady, incompressible fluid flow in boundary layer and heat transfer are studied in an electrically conducting fluid over a semi-infinite vertical plate assuming the variable thermal conductivity in the presence of a uniform magnetic field. The governing system of equations including the continuity equation, momentum equation and energy equation have been transformed into nonlinear coupled ordinary differential equations using appropriate similarity variables. All the numerical and graphical solutions are obtained through the use of Maple software. The solutions are found to be dependent on three dimensionless parameters including the magnetic field parameter M, thermal conductivity parameter β and Prandtl number Pr. Representative velocity and temperature profiles are presented at various values of the governing parameters. The skin-friction coefficient and the rate of heat transfer are also calculated for different values of the parameters.

Numerical simulation for transient flow of Williamson fluid with multiple slip model in the presence of chemically reacting species

2019 ◽  
Vol 29 (11) ◽  
pp. 4445-4461
Author(s):  
Aamir Hamid ◽  
Masood Khan ◽  
Metib Alghamdi
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Transient Flow ◽  
Mathematical Formulation ◽  
Variable Thermal Conductivity ◽  
Integration Scheme ◽  
Fluid Temperature ◽  
Content Type ◽  
Williamson Fluid ◽  
Chemically Reacting

Purpose The purpose of this paper is to analyze a mathematical model for the time-dependent flow of non-Newtonian Williamson liquid because of a stretching surface. The mathematical formulation of the current model is accomplished from the momentum, energy and concentration balances by assuming a laminar, two-dimensional and incompressible flow subjected to a variable magnetic field. The study further aimed at discovering the possible effects of temperature-dependent thermal conductivity on the heat transfer characteristics. Design/methodology/approach In addition, a first-order chemical reaction is considered between the fluid and chemically reacting species. The governing transport model for Williamson fluid has been altered to ordinary differential equations via appropriate dimensionless parameters. These basic non-dimensional partially coupled differential equations of fluid motion are solved by an efficient Runge–Kutta–Fehlberg integration scheme along with the Nachtsheim–Swigert shooting technique. Findings It is found that the velocity slip parameter has a reducing impact on the skin friction coefficient. Moreover, we noticed that the Hartmann number and variable thermal conductivity parameters show prominent impacts on the velocity and temperature fields. It is also perceived that the fluid temperature shows an increasing trend with uplifting values of variable thermal conductivity. Originality/value No such work is yet published in the literature.

Variable viscosity and thermal conductivity effects on Williamson fluid flow over a slendering stretching sheet

2020 ◽  
Vol 17 (3) ◽  
pp. 357-371
Author(s):  
Moses Sunday Dada ◽  
Cletus Onwubuoya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Analysis Method ◽  
Content Type ◽  
Williamson Fluid ◽  
Homotopy Analysis

Purpose The purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in the presence of radiation and chemical reaction. All pertinent flow parameters are discussed and their influence on the hydrodynamics, thermal and concentration boundary layer are presented with the aid of the diagram. Design/methodology/approach The governing partial differential equations are reduced into a system of ordinary differential equations with the help of suitable similarity variables. A discrete version of the homotopy analysis method (HAM) called the spectral homotopy analysis method (SHAM) was used to solve the transformed equations. SHAM is efficient, and it converges faster than the HAM. The SHAM provides flexibility when solving linear ordinary differential equations with the use of the Chebyshev spectral collocation method. Findings The findings revealed that an increase in the variable thermal conductivity hike the temperature and the thermal boundary layer thickness, whereas the reverse is the case for velocity close to the wall. Originality/value The uniqueness of this paper is the exploration of combined effects of heat and mass transfer on MHD Williamson fluid flow over a slendering stretching sheet. The Williamson fluid term in the momentum equation is expressed as a linear function and the viscosity and thermal conductivity are considered to vary in the boundary layer.

Heat transfer enhancement of hybrid nanofluids over porous cone

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Umar Farooq ◽  
Hassan Waqas ◽  
Taseer Muhammad ◽  
Shan Ali Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Base Fluid ◽  
Volume Fraction ◽  
Flow Parameters ◽  
Heat Efficiency ◽  
Thermal Conductivity Parameter ◽  
Nanoparticles Volume Fraction ◽  
Conductivity Parameter

Abstract The nanofluid is most advantageous to enhance the heat efficiency of base fluid by submerging solid nanoparticles in it. The metals, oxides, and carbides are helpful to improve the heat transfer rate. In the present analysis, the role of the slip phenomenon in the radiative flow of hybrid nanoliquid containing SiO2 silicon dioxide and CNTs over in the porous cone is scrutinized. The behavior of the magnetic field, thermal conductivity, and thermal radiation are examined. Here the base fluid ethylene glycol water (C2H6O2−H2O) is used. Accepting similarity transformation converts the controlling partial differential equations (PDEs) into ordinary differential equations (ODEs). The numerical solution is obtained by utilizing the Lobatto-IIIa method. The significant physical flow parameters are discussed by utilizing tables and graphs. Final remarks are demonstrating the velocity profile is declined via higher magnetic parameter while boosted up for nanoparticles volume fraction. Furthermore, the thermal profile is enriching via thermal conductivity parameter, radiation parameter, and nanoparticles volume fraction.

Theoretical analysis of MHD Carreau liquid over a heated rotating disk under Von-Karman transformations

2019 ◽  
Vol 16 (2) ◽  
pp. 390-408 ◽  
Author(s):  
Memoona Bibi ◽  
Muhammad Sohail ◽  
Rahila Naz
Keyword(s):  
Differential Equations ◽  
Coupled System ◽  
Rotating Disk ◽  
Analytical Approximation ◽  
Skin Friction Coefficient ◽  
Governing Equations ◽  
Content Type ◽  
Highly Nonlinear ◽  
Contour Plots ◽  
Optimal Homotopy Asymptotic Method

Purpose The purpose of this paper is to perform an analytical approximation for the flow of magnetohydrodynamic Carreau fluid with the association of nanoparticles over a rotating disk. The disk is moving with a constant uniform speed. Governing equations are obtained by using these assumptions in the form of partial differential equations with boundary conditions. These coupled, highly nonlinear equations are transformed into a coupled system of ordinary differential equations by engaging similarity transformation in the rotating frame of reference. Design/methodology/approach An efficient and reliable scheme, namely optimal homotopy asymptotic method, is used to obtain the solutions of the arising physical problem, which is further analyzed graphically. After computing the solutions of the arising problem, plots of velocities, temperature and concentration are discussed briefly. Findings It has been observed that dimensionless velocity reduced due to magnetic effect between the boundary layer and escalating values of the magnetic parameter upsurges the temperature and concentration profiles. Contour plots and numerical results are given for local numbers like skin friction coefficient, Nusselt number and Sherwood number. Originality/value The work presented in this manuscript is neither published nor submitted anywhere for the consideration/publications. It is a novel work.

MHD slip flow and convective heat transfer due to a moving plate with effects of variable viscosity and thermal conductivity

2020 ◽  
Vol 16 (5) ◽  
pp. 991-1018
Author(s):  
Mahantesh M. Nandeppanavar ◽  
M.C. Kemparaju ◽  
R. Madhusudhan ◽  
S. Vaishali
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Differential Equations ◽  
Radiation Effects ◽  
Variable Viscosity ◽  
Heat Transfer Analysis ◽  
Concentration Profiles ◽  
Moving Plate ◽  
Content Type

PurposeThe steady two-dimensional laminar boundary layer flow, heat and mass transfer over a flat plate with convective surface heat flux was considered. The governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations and then solved numerically by Runge–Kutta method with the most efficient shooting technique. Then, the effect of variable viscosity and variable thermal conductivity on the fluid flow with thermal radiation effects and viscous dissipation was studied. Velocity, temperature and concentration profiles respectively were plotted for various values of pertinent parameters. It was found that the momentum slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the momentum slip.Design/methodology/approachNumerical Solution is applied to find the solution of the boundary value problem.FindingsVelocity, heat transfer analysis is done with comparing earlier results for some standard cases.Originality/value100

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.

Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid

2016 ◽  
Vol 26 (5) ◽  
pp. 1460-1485 ◽  
Author(s):  
B Mahanthesh ◽  
B J Gireesha ◽  
R S R Gorla
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Mixed Convection ◽  
Three Dimensional ◽  
Vertical Channel ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow ◽  
Rotating Channel

Purpose – The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid. Design/methodology/approach – Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed. Findings – Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer. Originality/value – Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated.

Entropy generation analysis for peristalsis of magneto Jeffrey materials

2021 ◽  
pp. 095440892110412
Author(s):  
Tasawar Hayat ◽  
Farhat Bibi ◽  
Ambreen Afsar Khan ◽  
Akbar Zaman ◽  
Ahmed Alsaedi
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Entropy Generation ◽  
Thermal Conductivity Coefficient ◽  
Temperature Dependent ◽  
Thermal Fields ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Temperature Dependent Thermal Conductivity ◽  
Heat Transfer Parameter

This article communicates peristalsis of Jeffrey material in curved geometry. Here, material has temperature-dependent thermal conductivity and viscosity. Mathematical modeling of an inclined magnetic field in curved configuration has been presented in this article. Irreversibility effects have been analyzed through entropy generation. Slip conditions are entertained both for velocity and thermal fields. Problem is first reduced in wave frame and then lubrication approach has been utilized. Numerical solution of dimensionless problem is obtained and important parameters of curiosity are examined. It is noticed that velocity enhances for higher viscosity whereas temperature decreases for higher thermal conductivity coefficient. Velocity of the flow is maximum for inclination of magnetic field to be zero and it is minimum for [Formula: see text] Heat transfer parameter enhances both for thermal conductivity parameter and Hartmann number. Temperature is high for curved configuration when compared with straight channel. It is observed that entropy remains unchanged in center of the channel and it is maximum near the channel walls. Entropy generation decays near the channel walls by higher viscosity and thermal conductivity parameters. However, entropy is more for higher inclination of magnetic field.

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