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.

Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1073-1083
Author(s):  
Muhammad Sohail ◽  
Umar Nazir ◽  
Yu-Ming Chu ◽  
Hussam Alrabaiah ◽  
Wael Al-Kouz ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Variable Temperature ◽  
Variable Thermal Conductivity ◽  
Skin Friction Coefficient ◽  
Temperature Dependent ◽  
Similarity Transformations ◽  
Rate Dependent ◽  
And Diffusion ◽  
Temperature Dependent Thermal Conductivity

Abstract This article addresses the effects of thermal radiation, stratification, and Joule heating for the flow of magnetohydrodynamics Sutterby nanofluid past over a stretching cylinder. The transport phenomenon of heat and mass are modeled under temperature-dependent thermal conductivity and diffusion coefficients, respectively. Moreover, traditional Fourier and Fick’s laws have been implemented in thermal and mass transport expressions. The governing model that consists of a set of coupled partial differential equations is converted into system of nonlinear coupled ordinary differential equations via suitable similarity transformations. The resulting set of expressions is analytically treated through an optimal homotopy scheme. The effects of different dimensionless flow parameters on the velocity, temperature, and concentration fields are illustrated through graphs. The patterns of skin friction coefficient, local Nusselt, and Sherwood numbers are examined via bar charts. The major outcome of the proposed study is that variable thermal conductivity decays the temperature and radiation raises the temperature of the system. Stratification parameters show the reverse behavior for temperature and concentration boundary layers. Shear rate-dependent rheology in view of Sutterby liquid has the ability to reduce the flow of fluid. Therefore, the ability of flow in rheology of Sutterby liquid becomes reduced. Consequently, layer of momentum boundary has increased with respect to parameter of Sutterby liquid.

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.

scholarly journals Thermo diffusion aspects in Jeffrey nanofluid over periodically moving surface with time dependent thermal conductivity

2019 ◽  
pp. 312-312 ◽  
Author(s):  
Khan Ullah ◽  
Shehzad Ali ◽  
Abbasi Munir ◽  
Arshad Hussain
Keyword(s):  
Thermal Conductivity ◽  
Nonlinear Differential Equations ◽  
Heated Surface ◽  
Lewis Number ◽  
Double Diffusion ◽  
Variable Thermal Conductivity ◽  
Deborah Number ◽  
Time Dependent ◽  
Jeffrey Fluid ◽  
Homotopy Analysis

Double diffusion flow of Jeffrey fluid in presence of nanoparticles is studied theoretically under time dependent thermal conductivity. The considered nanoparticles are evaporated over convectively heated surface which moves periodically in its own plane. The appropriate dimensionless variables are employed to obtain the dimensionless forms of governing equations. We computed the analytical solution of nonlinear differential equations by utilizing homotopy analysis method. The present investigation reveals the features of various emerging parameters like Deborah number, combined parameter, oscillation frequency to stretching rate ratio, Prandtl number, Lewis number, thermophoresis parameter, Brownian motion parameter, nano Lewis number, modified Dufour parameter and Dufour solutal Lewis number. A useful enhancement in movement of nanoparticles is observed by utilizing the combined magnetic and porosity effects. Unlike traditional studies, present analysis is confined with the unsteady transportation phenomenon from periodically moving surfaces. Such computation may be attributable in flow results from tensional vibrations due to stretching and elastic surfaces. The simulation presented here can be attractable significance in the bioengineered nanoparticles manufacturing. It is observed that the heat transportation of nanoparticles may efficiently enhance through the utilization of variable thermal conductivity. The solutal concentration decreases with increasing Deborah number and Lewis number. It is further noted that the nano Lewis number causes reduction of nanoparticles concentration.

Instability of Variable Thermal Conductivity Magnetohydrodynamic Nanofluid Flow in a Vertical Porous Channel of Varying Width

2017 ◽  
Vol 378 ◽  
pp. 85-101
Author(s):  
Md. Sarwar Alam ◽  
Oluwole Daniel Makinde ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Porous Wall ◽  
Variable Thermal Conductivity ◽  
Physical Parameters

A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al2O3-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

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.

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.

Radiative Flow with Variable Thermal Conductivity in Porous Medium

2012 ◽  
Vol 67 (3-4) ◽  
pp. 153-159 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
A. Alsaedi
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Differential Equations ◽  
Radiation Effect ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Homotopy Analysis

This article considers the radiation effect on the flow of a Jeffery fluid with variable thermal conductivity. Similarity transformations are employed to convert the partial differential equations into ordinary differential equations. The resulting equations have been computed by the homotopy analysis method (HAM). The numerical values of the local Nusselt numbers are also computed. The comparison with the numerical solutions of qƟ'(0) is presented. The obtained results are displayed and physical aspects have been examined in detail

scholarly journals Computation of non-similar solution for magnetic pseudoplastic nanofluid flow over a circular cylinder with variable thermophysical properties and radiative flux

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Thameem Basha Hayath ◽  
Sivaraj Ramachandran ◽  
Ramachandra Prasad Vallampati ◽  
O. Anwar Bég
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Circular Cylinder ◽  
Variable Viscosity ◽  
Variable Thermal Conductivity ◽  
Weissenberg Number ◽  
Soret And Dufour Effects ◽  
Content Type ◽  
Layer Flow

Purpose Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field. Design/methodology/approach The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included. Findings The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables. Research limitations/implications Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration. Practical implications The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment. Social implications This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream. Originality/value The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

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.

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