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.

MHD three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink

2014 ◽  
Vol 24 (5) ◽  
pp. 1073-1085 ◽  
Author(s):  
T. Hayat ◽  
S.A. Shehzad ◽  
A. Alsaedi
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Heat Source ◽  
Three Dimensional ◽  
Maxwell Fluid ◽  
Variable Thermal Conductivity ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow ◽  
Source Sink

Purpose – The purpose of this paper is to investigate the three-dimensional flow of Maxwell fluid with variable thermal conductivity in presence of heat source/sink. Design/methodology/approach – Similarity transformations are utilized to reduce the nonlinear partial differential equations into ordinary differential equations. The governing nonlinear problems are solved by homotopy analysis method. Findings – The paper found that the velocities decrease while temperature increases for higher Hartman number. It is also seen that the thermal boundary layer thickness and temperature are increased with an increase in variable thermal conductivity parameter and heat source/sink parameter. Practical implications – Heat transfer analysis with heat source/sink has pivotal role in many industrial applications like cooling of an infinite metallic plate in a cooling bath, drawing of plastic films, nuclear plants, gas turbines, various propulsion devices for missiles, space vehicles and processes occurring at high temperatures. Originality/value – This study discusses the magnetohydrodynamic three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink. No such analysis exists in the literature yet.

Non-similar solution of Sisko nanofluid flow with variable thermal conductivity: a finite difference approach

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ankita Bisht ◽  
Rajesh Sharma
Keyword(s):  
Thermal Conductivity ◽  
Finite Difference ◽  
Differential Equations ◽  
Velocity Ratio ◽  
Variable Thermal Conductivity ◽  
Brownian Diffusion ◽  
Control Parameters ◽  
Nanofluid Flow ◽  
Content Type ◽  
Thermal Buoyancy

Purpose The main purpose of this study is to present a non-similar analysis of two-dimensional boundary layer flow of non-Newtonian nanofluid over a vertical stretching sheet with variable thermal conductivity. The Sisko fluid model is used for non-Newtonian fluid with an exponent (n* > 1), that is, shear thickening fluid. Buongiorno model for nanofluid accounting Brownian diffusion and thermophoresis effects is used to model the governing differential equations. Design/methodology/approach The governing boundary layer equations are converted into nondimensional coupled nonlinear partial differential equations using appropriate transformations. The resultant differential equations are solved numerically using implicit finite difference scheme in association with the quasilinearization technique. Findings This analysis shows that the temperature raises for thermal conductivity parameter and velocity ratio parameter while decreases for the thermal buoyancy parameter. The thermophoresis and Brownian diffusion parameter that characterizes the nanofluid flow enhances the temperature and reduces the heat transfer rate. Skin friction drag can be effectively reduced by proper control of the values of thermal buoyancy and velocity ratio parameter. Practical implications The wall heating and cooling investigation result in the analysis of the control parameters that are related to the designing and manufacturing of thermal systems for cooling applications and energy harvesting. These control parameters have practical significance in the designing of heat exchangers and solar thermal collectors, in glass and polymer industries, in the extrusion of plastic sheets, the process of cooling of the metallic plate, etc. Originality/value To the best of authors’ knowledge, it is found from the literature survey that no similar work has been published which investigates the non-similar solution of Sisko nanofluid with variable thermal conductivity using finite difference method and quasilinearization technique.

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).

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.

scholarly journals Effect of magnetized variable thermal conductivity on flow and heat transfer characteristics of unsteady Williamson fluid

2020 ◽  
Vol 9 (1) ◽  
pp. 338-351
Author(s):  
Usha Shankar ◽  
N. B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Fluid Flow ◽  
Velocity Profile ◽  
Variable Thermal Conductivity ◽  
Flow Index ◽  
Williamson Fluid ◽  
Flow Equations ◽  
Velocity Parameter ◽  
Squeezed Flow

AbstractA two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with variable thermal conductivity and exterior squeezing with viscous dissipation effect is investigated, numerically. Present flow model is developed based on the considered flow geometry. Effect of Lorentz forces on flow behaviour is described in terms of magnetic field and which is accounted in momentum equation. Influence of variable thermal conductivity on heat transfer is considered in the energy equation. Present investigated problem gives the highly complicated nonlinear, unsteady governing flow equations and which are coupled in nature. Owing to the failure of analytical/direct techniques, the considered physical problem is solved by using Runge-Kutta scheme (RK-4) via similarity transformations approach. Graphs and tables are presented to describe the physical behaviour of various control parameters on flow phenomenon. Temperature boundary layer thickens for the amplifying value of Weissenberg parameter and permeable velocity parameter. Velocity profile decreased for the increasing squeezed flow index and permeable velocity parameter. Increasing magnetic number increases the velocity profile. Magnifying squeezed flow index magnifies the magnitude of Nusselt number. Also, RK-4 efficiently solves the highly complicated nonlinear complex equations that are arising in the fluid flow problems. The present results in this article are significantly matching with the published results in the literature.

scholarly journals Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 684
Author(s):  
Saeed Islam ◽  
Haroon Ur Rasheed ◽  
Kottakkaran Sooppy Nisar ◽  
Nawal A. Alshehri ◽  
Mohammed Zakarya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Variable Thickness ◽  
Heat Mass Transfer ◽  
Mathematical Formulation ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
The Impact

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

Effects of variable thermal conductivity and electrical conductivity on flow of williamson nanofluid between two parallel disks

2021 ◽  
Author(s):  
Mazmul Hussain ◽  
Nargis Khan
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Electric Conductivity ◽  
Variable Temperature ◽  
Lewis Number ◽  
Variable Thermal Conductivity ◽  
Industrial Applications ◽  
Weissenberg Number ◽  
Modeling And Analysis ◽  
Variable Nature

The variable nature of the thermal conductivity of nanofluid with respect to temperature plays an important role in many engineering and industrial applications including solar collectors and thermoelectricity. Thus, the foremost motivation of this article is to investigate the effects of thermal conductivity and electric conductivity due to variable temperature on the flow of Williamson nanofluid. The flow is considered between two stretchable rotating disks. The mathematical modeling and analysis have been made in the presence of magnetohydrodynamic and thermal radiation. The governing differential equations of the problem are transformed into non-dimensional differential equations by using similarity transformations. The transformed differential equations are thus solved by a finite difference method. The behaviors of velocity, temperature and concentration profiles due to various parameters are discussed. For magnetic parameter, the radial and tangential velocities have showed decreasing behavior, while converse behavior is observed for axial velocity. The temperature profile shows increasing behavior due to an increase in the Weissenberg number, heat generation parameter and Eckert number, while it declines by increasing electric conductivity parameter. The nanoparticle concentration profile declines due to an increase in the Lewis number and Reynolds number.

scholarly journals Implicit Finite Difference Simulation of Prandtl-Eyring Nanofluid over a Flat Plate with Variable Thermal Conductivity: A Tiwari and Das Model

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3153
Author(s):  
Nidal H. Abu-Hamdeh ◽  
Abdulmalik A. Aljinaidi ◽  
Mohamed A. Eltaher ◽  
Khalid H. Almitani ◽  
Khaled A. Alnefaie ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Difference ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Thermal Conductivity ◽  
Solid Particles ◽  
Engine Oil ◽  
Working Fluid ◽  
Implicit Finite Difference

The current article presents the entropy formation and heat transfer of the steady Prandtl-Eyring nanofluids (P-ENF). Heat transfer and flow of P-ENF are analyzed when nanofluid is passed to the hot and slippery surface. The study also investigates the effects of radiative heat flux, variable thermal conductivity, the material’s porosity, and the morphologies of nano-solid particles. Flow equations are defined utilizing partial differential equations (PDEs). Necessary transformations are employed to convert the formulae into ordinary differential equations. The implicit finite difference method (I-FDM) is used to find approximate solutions to ordinary differential equations. Two types of nano-solid particles, aluminium oxide (Al2O3) and copper (Cu), are examined using engine oil (EO) as working fluid. Graphical plots are used to depict the crucial outcomes regarding drag force, entropy measurement, temperature, Nusselt number, and flow. According to the study, there is a solid and aggressive increase in the heat transfer rate of P-ENF Cu-EO than Al2O3-EO. An increment in the size of nanoparticles resulted in enhancing the entropy of the model. The Prandtl-Eyring parameter and modified radiative flow show the same impact on the radiative field.

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