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.

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.

Dynamical analysis of hydromagnetic Brownian and thermophoresis effects of squeezing Eyring–Powell nanofluid flow with variable thermal conductivity and chemical reaction

2019 ◽  
Vol 15 (6) ◽  
pp. 1100-1120 ◽  
Author(s):  
Hammed Abiodun Ogunseye ◽  
Sulyman Olakunle Salawu ◽  
Yusuf Olatunji Tijani ◽  
Mustapha Riliwan ◽  
Precious Sibanda
Keyword(s):  
Thermal Conductivity ◽  
Dynamical Behavior ◽  
Variable Thermal Conductivity ◽  
Linearization Method ◽  
Dynamical Analysis ◽  
Nanofluid Flow ◽  
Content Type ◽  
Time Variations ◽  
Flow Through ◽  
Linear Differential

Purpose The purpose of this paper is to investigate the dynamical behavior of heat and mass transfer of non-Newtonian nanofluid flow through parallel horizontal sheet with heat-dependent thermal conductivity and magnetic field. The effects of thermophoresis and Brownian motion on the Eyring‒Powell nanofluid heat and concentration are also considered. The flow fluid is propelled by squeezing force and constant pressure gradient. The hydromagnetic fluid is induced by periodic time variations. Design/methodology/approach The dimensionless momentum, energy and species balance equations are solved by the spectral local linearization method that is employed to numerically integrate the coupled non-linear differential equations. Findings The response of the fluid flow, temperature and concentration to variational increase in the values of the parameters is graphically presented and discussed accordingly. Originality/value The validity of the method used was checked by comparing it with previous related article.

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.

scholarly journals Finite difference computation of free magneto-convective Powell-Eyring nanofluid flow over a permeable cylinder with variable thermal conductivity

2020 ◽  
Vol 96 (2) ◽  
pp. 025222
Author(s):  
G Kumaran ◽  
R Sivaraj ◽  
V Ramachandra Prasad ◽  
O Anwar Beg ◽  
Ram Prakash Sharma
Keyword(s):  
Thermal Conductivity ◽  
Finite Difference ◽  
Variable Thermal Conductivity ◽  
Nanofluid Flow

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.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

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.

Numerical identification of temperature dependent thermal conductivity using least squares method

2019 ◽  
Vol 30 (6) ◽  
pp. 3083-3099
Author(s):  
Anna Ivanova ◽  
Stanislaw Migorski ◽  
Rafal Wyczolkowski ◽  
Dmitry Ivanov
Keyword(s):  
Thermal Conductivity ◽  
Finite Difference ◽  
Heat Equation ◽  
Difference Scheme ◽  
Least Squares ◽  
Finite Difference Scheme ◽  
Nonlinear Heat Equation ◽  
Temperature Dependent ◽  
Content Type ◽  
Temperature Dependent Thermal Conductivity

Purpose This paper aims to considered the problem of identification of temperature-dependent thermal conductivity in the nonstationary, nonlinear heat equation. To describe the heat transfer in the furnace charge occupied by a homogeneous porous material, the heat equation is formulated. The inverse problem consists in finding the heat conductivity parameter, which depends on the temperature, from the measurements of the temperature in fixed points of the material. Design/methodology/approach A numerical method based on the finite-difference scheme and the least squares approach for numerical solution of the direct and inverse problems has been recently developed. Findings The influence of different numerical scheme parameters on the accuracy of the identified conductivity coefficient is studied. The results of the experiment carried out on real measurements are presented. Their results confirm the ones obtained earlier by using other methods. Originality/value Novelty is in a new, easy way to identify thermal conductivity by known temperature measurements. This method is based on special finite-difference scheme, which gives a resolvable system of algebraic equations. The results sensitivity on changes in the method parameters was studies. The algorithms of identification in the case of a purely mathematical experiment and in the case of real measurements, their differences and the practical details are presented.

Non-similar solution of Casson nanofluid with variable viscosity and variable thermal conductivity

2019 ◽  
Vol 30 (8) ◽  
pp. 3919-3938 ◽  
Author(s):  
Ankita Bisht ◽  
Rajesh Sharma
Keyword(s):  
Thermal Conductivity ◽  
Stretching Sheet ◽  
Variable Viscosity ◽  
Variable Thermal Conductivity ◽  
Solar Thermal ◽  
Content Type ◽  
Casson Nanofluid ◽  
Solar Thermal Collectors ◽  
Variation Parameter ◽  
Nonlinear Stretching

Purpose The purpose of this study is to provide a numerical investigation of Casson nanofluid along a vertical nonlinear stretching sheet with variable thermal conductivity and viscosity. Design/methodology/approach The boundary-layer equations are presented in the dimensionless form using proper non-similar transformations. The subsequent non-dimensional nonlinear partial differential equations are solved using the implicit finite difference technique. To linearize the nonlinear terms present in these equations, the quasilinearization technique is used. Findings The investigation showed graphically the temperature, velocity and nanoparticle volume fraction for particular included physical parameters. It is observed that the velocity profile decreases with an increase in the values of Casson fluid parameter while increases with an increase in the viscosity variation parameter. The temperature profile enhances for large values of velocity variation parameter and thermal conductivity parameter while it reduces for large values of thermal buoyancy parameter. Further, the Nusselt number and skin-friction coefficient are introduced which are helpful in determining the physical aspects of Casson nanofluid flow. Practical implications The immediate control of heat transfer in the industrial system is crucial because of increasing energy prices. Recently, nanotechnology is proposed to control the heat transfer phenomenon. Ongoing research in complex nanofluid has been fruitful in various applications such as solar thermal collectors, nuclear reactors, electronic equipment and diesel–electric conductor. A reasonable amount of nanoparticle when added to the base fluid in solar thermal collectors serves to deeper absorption of incident radiation, and hence it upgrades the efficiency of the solar thermal collectors. Originality/value The non-similar solution of Casson nanofluid due to a vertical nonlinear stretching sheet with variable viscosity and thermal conductivity is discussed in this work.

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