Abuzar Ghaffari - Academia.edu (original) (raw)

Papers by Abuzar Ghaffari

Pramana

The advanced thermal characteristics of nanomaterials allow better heat transfer efficiency in en... more The advanced thermal characteristics of nanomaterials allow better heat transfer efficiency in engineering, industrial and technological processes. In this report, the outcome of a comparative analysis between the dynamics of blood carrying Cu nanoparticles and blood carrying single-walled carbon nanotubes (SWCNTs) due to the stretching and rotation of two disks at various levels of rotation, stretching, power-law index and heat source/sink is presented. By using appropriate similarity variables, the leading partial differential equations (PDEs) are altered into one-dimensional equations (ODEs). The resulting ODEs are handled using the shooting method. The impact of governing parameters on the boundary layer profiles is analysed graphically. Fluid velocity gets enhanced in three dimensions during the rotation of the disk, but they predict different behaviours for the stretching parameters of the upper and lower disks. The temperature decays for power-law index, rotation and stretching parameters. Also, the rates of heat transfer are more extensive for shear-thinning. Finally, the effects of the Cu–blood(blood) nanofluid are dominant over the base fluid (blood) and SWCNTs–blood nanofluid.

Inventions, 2021

The current article incorporates the numerical investigation of heat exchange rate and skin frict... more The current article incorporates the numerical investigation of heat exchange rate and skin friction carried out through nanofluid saturated with thermally balanced porous medium over a rough horizontal surface that follows the sinusoidal waves. The effects of the external magnetic field are discussed by managing the magnetic field strength applied normally to the flow pattern. The occurring partial differential governing equations are grasped through a strong numerical scheme of the Keller box method (KBM) against the various parameters. The findings are elaborated through tables and diagrams of velocity, temperature, skin friction, Nusselt number, streamlines, and heat lines. The percentage increase in Nusselt number and coefficient of skin friction over the flat and wavy surface is calculated which leads to the conclusion that the copper (Cu) nanoparticles are better selected as compared to the silver (Ag) for heat transfer enhancement. It is also evident from sketches that the c...

Mathematical Problems in Engineering, 2021

In this paper, we have extended the operational matrix method for approximating the solution of t... more In this paper, we have extended the operational matrix method for approximating the solution of the fractional-order two-dimensional elliptic partial differential equations (FPDEs) under nonlocal boundary conditions. We use a general Legendre polynomials basis and construct some new operational matrices of fractional order operations. These matrices are used to convert a sample nonlocal heat conduction phenomenon of fractional order to a structure of easily solvable algebraic equations. The solution of the algebraic structure is then used to approximate a solution of the heat conduction phenomena. The proposed method is applied to some test problems. The obtained results are compared with the available data in the literature and are found in good agreement.Dedicated to my father Mr. Sher Mumtaz, (1955-2021), who gave me the basic knowledege of mathematics.

Journal of Non-Equilibrium Thermodynamics, 2020

In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical... more In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical wavy surface saturated in a porous medium is investigated. Ferrofluid is made by incorporating magnetic particles, in this case cobalt, at the nanoscale level into a base fluid. For the study of porous medium two well-known models, namely, Darcy and non-Darcy, are used. The mathematical model in terms of governing partial differential equations which are based on conservation laws in mechanics according to the assumption is developed, and this model is converted into a dimensionless form by suitable transformations. Due to the complex non-linear partial differential equations, the numerical solution is calculated by using an implicit finite difference scheme. The impact of involved parameters, namely, magnetic parameter, nanoparticle volume fraction parameter, the amplitude of the wavy surface, and the Grashof number, on Nusselt and average Nusselt numbers are studied through graphs and...

Case Studies in Thermal Engineering, 2021

A theoretical entropy generation analysis is conducted by applying the MHD and nonlinear thermal ... more A theoretical entropy generation analysis is conducted by applying the MHD and nonlinear thermal radiation effects contained in porous material for a steady three-dimensional power-law nanofluid flow near the stagnation point region. With the assistance of a thermally radiated nonuniform heat source /sink subject to convective boundary conditions, the heat transformation phenomenon is explored within the boundary layer over the stretchable rotatory disk. Multi-wall carbon nanotubes (MWCNTs) are incorporated in the ethylene glycol (C 2 H 6 O 2) as a base fluid. The proposed problem of fluid flow is mathematically modeled. The governing nonlinear partial differential equations (PDEs) are lessened to highly mixed nonlinear ordinary differential equations (ODEs) after the utilization of appropriate transformations. The effects of several classes of relevant parameters upon total entropy generation and Bejan number profiles are investigated by numerically addressing the ODEs with the purpose of a well-known Keller Box method. Furthermore, the skin friction coefficients and local Nusselt number are calculated for shearthinning and shear-thickening behaviors of the power-law fluid. Also, the total entropy generation increases for the Brinkman number and the permeability parameter but decreases for the material parameter, whereas the Bejan number has different behavior from entropy generation.

Case Studies in Thermal Engineering, 2021

Abstract The heat transfer phenomenon is beneficial and applicable in engineering, industries, an... more Abstract The heat transfer phenomenon is beneficial and applicable in engineering, industries, and technological processes. The production of energy with the help of some cheap resources plays a pivotal and renewable role in the industrial development of the countries. Owing to such a significant performance of heat transfer, the steady slip flow and heat transfer of tangent hyperbolic fluid over a lubricating surface of the stretchable rotatory disk is investigated. The effects of MHD, nonlinear radiation, and non-uniform heat source/sink subject to nonlinear boundary conditions are included in motion and energy equations. Because of the lubrication, a thin layer of the power-law fluid is produced at the surface of the disk. Since the lubricating layer is thin, the interfacial conditions are applied at the surface between the fluid and lubricant. The governing nonlinear partial differential equations (PDEs) have been converted into ordinary differential equations (ODEs), which are solved numerically using the Keller-box method. The upshots of pertinent parameters upon the dimensionless distributions of velocity and temperature are deliberated. The surface drag forces and heat transfer rates are computed, and the effects of governing parameters on them are examined. With the enhancement in the slip at the interface and Weissenberg number, the radial and azimuthal velocities enhances close to the disk, whereas they observe two diverse trends for the power-law index. Also, temperature escalates for radiation parameter, and this escalation is prominent for nonlinear radiation.

Physica Scripta, 2021

The non-Newtonian Sutterby fluid model can be implied to characterize the significant characteris... more The non-Newtonian Sutterby fluid model can be implied to characterize the significant characteristics of shear-thinning and shear-thickening for various ranges of the power-law index. The Sutterby fluid has a vast number of applications in engineering processes and industrial fluid mechanics. The steady two-dimensional stagnant flow of Sutterby nanofluid inside the boundary layer over a stretching wedge placed in a porous medium is investigated. The viscous incompressible fluid is electrically conducting, and a uniform magnetic field is imposed perpendicularly. The heat and mass transfer phenomenon is analyzed by incorporating the effects of nonlinear radiation, viscous dissipation, Joule heating, heat source/sink, and activation energy subject to convective-Nield boundary conditions. The physically modeled partial differential equations (PDEs) are lessened into ordinary differential equations (ODEs) with precise similarity variables. The numerical solution is obtained through the s...

Results in Physics, 2020

The ferrofluid are useful nanofluid and can be prepared by mixing magnetic types of nanoparticles... more The ferrofluid are useful nanofluid and can be prepared by mixing magnetic types of nanoparticles in base fluid. The mathematical modelling of ferrofluid under induced magnetic field through a vertical stretching surface is formulated in the current theoretical study. The study is performed for ferrofluid by considering magnetite Fe 3 O 4 magnetic nanoparticles in base fluid. In ferrofluid, the appropriate mixture of magnetic nanoparticles can lead to desire heat transfer phenomena. This theoretical study indicates that both Nusselt number and skin friction coefficient for Fe 3 O 4-water ferrofluid increase by improving the effects of magnetic parameterβ. Velocity and magnetic boundary layer thicknesses increase/decrease for assisting/opposing flow by strengthening magnetic effects and in the presence of magnetic type Fe 3 O 4 nanoparticle boundary layer thickness further enhances for pure water as compared to Fe 3 O 4 type of ferrofluid. Temperature profile and thermal boundary layer thickness increase for both assisting/opposing flow with enhancing the concentration of Fe 3 O 4 magnetic nanoparticle, however, thermal distribution reduces/upsurges in case of assisting/opposing flow with the increase of magnetic strength and thermal boundary layer thickness is greater for Fe 3 O 4 − water based ferrofluid as compared to regular fluid. The bvp4c built-in code in MATLAB software is employed for solution purposes. Results are displayed for the selection of effective parameters in data and graphical forms for both assisting and opposing flows.

Thermal Science, 2020

In this article, the impact of water-based hybrid nanofluid on heat transfer characteristics alon... more In this article, the impact of water-based hybrid nanofluid on heat transfer characteristics along the wavy frustum of the cone is examined. We considered hybrid nanofluid containing Cu and TiO2 nanoparticles. Non-similar form of the constitutive equations is obtained by using an appropriate set of transformations and results are achieved by employing transformed into compact non-similar form and are solved by the famous numerically implicit finite difference scheme known as Keller-box technique. The influence of the hybrid nanoparticles? volume fraction, frustum of cone half-angle, and the wavy texture parameters on the Nusselt number and skin friction are scrutinized and comparison is made between the wavy frustum of the cone and flat frustum of the cone through numerical data. It is observed that the rise in the truncated cone half-angle leads to an increase in skin friction and Nusselt number. The TiO2-water nanofluid has lower heat transfer rates as compared to Cu-TiO2 hybrid n...

Physica Scripta, 2020

The current research study investigates the steady three-dimensional flow and heat transfer of a ... more The current research study investigates the steady three-dimensional flow and heat transfer of a power-law nanofluid in the presence of the uniformly applied magnetic field and nonlinear thermal radiation over the stretchable rotating disk filled with gyrotactic microorganisms. The physically modeled partial differential equations (PDEs) are lessened to combined nonlinear ordinary differential equations (ODEs) with appropriate transformation. The influence of several types of pertinent parameters upon the dimensionless distributions of velocity, temperature, the concentration of nanoparticles, and microorganisms are analyzed graphically by solving the ODEs with a well-known shooting method. The tabular comparison is provided for the verification between the present results with those in the literature. Also, the physical quantities of interest are calculated, and the effects are scrutinized. Furthermore, it is noticed that the emerging parameters have produced a significant influenc...

Heat Transfer, 2020

The transfer of heat is an important phenomenon in the several areas due to its numerous applicat... more The transfer of heat is an important phenomenon in the several areas due to its numerous applications in industries. Several fluids like water, ethylene glycol and oil, and so on have very-low thermal conductivities due to which the transfer of heat in these fluids become very low. To enhance heat transfer rate, carbon nanotubes (CNTs) including single-walled CNTs and multi-walled CNTs are suspended into base fluids, this mixture is known as nanofluid. The aim of this study is to examine the heat transfer rate of nanofluid in the presence of CNTs over a stretchable rotating disk. The mathematical model, developed by Tiwari and Das, is used and solved numerically by using the shooting method. The impacts of governing constraints on the dimensionless velocities, temperature, skin friction, and Nusselt number are investigated. It is noted that heat transfer rate increases by enhancing the concentration of CNTs into base fluids. The numerical results show that the solid volume fraction of the CNTs augment heat transfer rate more in ethylene glycol as compared with water.

Computer Methods and Programs in Biomedicine, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Fluid Dynamics Research, 2020

Thermal Science, 2018

In this study, natural convection flow along a vertical wavy surface has been investigated with v... more In this study, natural convection flow along a vertical wavy surface has been investigated with variable heat flux. The governing equations are transformed into dimensionless PDE by using the non-dimensional variables and then solved numerically by using an implicit finite difference scheme known as Keller Box method. The effects of the parameters amplitude of the wavy surface, ?, exponent of the variable heat flux, m, and Prandtl number on the local skin friction coefficient and local Nusselt number are shown graphically. It is found that for the negative value of exponent of the variable heat flux, m, the local skin friction coefficient increases and Nusselt number decreases but the opposite behavior is observed for the positive values of m. The comparison of limiting case with the previous study is shown through table and it is found that the solution obtained is in excellent agreement with the previous studies.

Revista Mexicana de Física, 2018

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have b... more Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged...

Scientia Iranica, 2019

A study based on the theoretical investigation of Thermophoresis and Brownian motion effects on r... more A study based on the theoretical investigation of Thermophoresis and Brownian motion effects on radiative heat transfer in the neighborhood of stagnation point. Thermophoresis and Brownian motion play an important role in thermal and mass concentration analyses. These analyses help to comprehend the core ideas to carry out in the discipline of science and technology. An electrically conducting nanofluid is considered which is described by the Buongiorno transport model. The power-law form of the stretching wall velocity allows the similarity solution, the transformed system of the ordinary differential equations is computed numerically with the efficient rapid convergent spectral scheme. The obtained results for velocity, temperature, concentration, shear strain, mass and heat transfer rates are presented graphically for various values of the pertinent parameters. The outcomes divulge that with the increase of power-law exponent, mass and heat transfer rates enhance. The information for the volume and hightemperature transfer rate is provided in the form of Tables. The obtained results are matched with the existing results and are shown to be a good agreement.

Scientia Iranica, 2019

In this problem, a theoretical study is presented for the slip effects on the twodimensional flow... more In this problem, a theoretical study is presented for the slip effects on the twodimensional flow of a nano liquid in a semi-porous channel designed by two long rectangular plates having porous media. One of the channel walls is porous and other is rigid as well as slippery. A transverse magnetic field of homogenous strength is also applied to direction of flow. Magnetic nanoparticles   34 Fe O and non-magnetic nanoparticles   23 Al O are considered with ethylene glycol (EG) and water as base fluids (BFs). Least Square method (LSM) and Galerkin method (GM) are adopted to solve the equations, transformed from partial differential equations (DEs) to ordinary ones by Berman's similarity transformations. The obtained results from the two analytical methods are compared with the results obtained by fourth order Runge-Kutta numerical method (NM). By comparing the results of GM and LSM it is observed that variation in velocity profiles is minimal however the accuracy of GM is higher than LSM. The contributions of various flow parameters are presented through graphs. Results show a decrement in the fluid velocity with an increase in the slip and porosity parameter. The fluid boundary layer decreases with an increase in the Reynolds number. Flow field is less for the case of magnetic nanoparticles as compared to nonmagnetic particles.

Physica A: Statistical Mechanics and its Applications, 2019

In some cases, most of the boundary value problems contain multiple solutions in which one of the... more In some cases, most of the boundary value problems contain multiple solutions in which one of the solution is stable or physical reliable and other solutions are unstable. In this study, the problem of hydromagnetic flow due to shrinking sheet is considered and calculated dual solutions against velocity ratio parameter in case of shrinking sheet. A stability analysis is performed for the checking, which solution is stable. The main materials and methods used: Initially, due to more than one independent variable, the flow is governed by partial differential equations (PDEs). For simplicity the conversion of these PDEs were made in form of ODEs (ordinary differential equations) and solved analytically by using weighted residual method named as least square method. The resulting nonlinear system of equations is linearized by using Newton method (Burden and Faires, 1991). For the accuracy of this method, a comparison is made with the previous published work (Wang, 2008). The algorithm of least square method is constructed in Mathematica software and is very easy to apply as compare to analytical method namely: homotopy analysis method. In case of shrinking sheet there exists more than one solution. To check which solution is physical reliable or stable and unstable, a present problem is converted into time dependent problem and then stability analysis is performed and BVP4c method is used for calculating the eigenvalues. The main results obtained: In case of shrinking sheet there exists dual solutions and dual solutions are calculated for some values of velocity ratio parameter λand magnetic parameter M by using least square method. The range of dual solutions is shown by plotting the graphs of skin friction coefficient and local Nusselt number. After performing the stability analysis, the smallest eigenvalues are calculated for various values of λ and M. The main conclusions of the work: It is observed that positive eigenvalue corresponds to stable solution or physical reliable i.e. the disturbance in the solution decay initially and negative eigenvalue corresponds to unstable solution i.e. it produces initial growth of disturbance. It is also observed that eigenvalues become higher in the presence of Lorentz force.

Pramana

The advanced thermal characteristics of nanomaterials allow better heat transfer efficiency in en... more The advanced thermal characteristics of nanomaterials allow better heat transfer efficiency in engineering, industrial and technological processes. In this report, the outcome of a comparative analysis between the dynamics of blood carrying Cu nanoparticles and blood carrying single-walled carbon nanotubes (SWCNTs) due to the stretching and rotation of two disks at various levels of rotation, stretching, power-law index and heat source/sink is presented. By using appropriate similarity variables, the leading partial differential equations (PDEs) are altered into one-dimensional equations (ODEs). The resulting ODEs are handled using the shooting method. The impact of governing parameters on the boundary layer profiles is analysed graphically. Fluid velocity gets enhanced in three dimensions during the rotation of the disk, but they predict different behaviours for the stretching parameters of the upper and lower disks. The temperature decays for power-law index, rotation and stretching parameters. Also, the rates of heat transfer are more extensive for shear-thinning. Finally, the effects of the Cu–blood(blood) nanofluid are dominant over the base fluid (blood) and SWCNTs–blood nanofluid.

Inventions, 2021

The current article incorporates the numerical investigation of heat exchange rate and skin frict... more The current article incorporates the numerical investigation of heat exchange rate and skin friction carried out through nanofluid saturated with thermally balanced porous medium over a rough horizontal surface that follows the sinusoidal waves. The effects of the external magnetic field are discussed by managing the magnetic field strength applied normally to the flow pattern. The occurring partial differential governing equations are grasped through a strong numerical scheme of the Keller box method (KBM) against the various parameters. The findings are elaborated through tables and diagrams of velocity, temperature, skin friction, Nusselt number, streamlines, and heat lines. The percentage increase in Nusselt number and coefficient of skin friction over the flat and wavy surface is calculated which leads to the conclusion that the copper (Cu) nanoparticles are better selected as compared to the silver (Ag) for heat transfer enhancement. It is also evident from sketches that the c...

Mathematical Problems in Engineering, 2021

In this paper, we have extended the operational matrix method for approximating the solution of t... more In this paper, we have extended the operational matrix method for approximating the solution of the fractional-order two-dimensional elliptic partial differential equations (FPDEs) under nonlocal boundary conditions. We use a general Legendre polynomials basis and construct some new operational matrices of fractional order operations. These matrices are used to convert a sample nonlocal heat conduction phenomenon of fractional order to a structure of easily solvable algebraic equations. The solution of the algebraic structure is then used to approximate a solution of the heat conduction phenomena. The proposed method is applied to some test problems. The obtained results are compared with the available data in the literature and are found in good agreement.Dedicated to my father Mr. Sher Mumtaz, (1955-2021), who gave me the basic knowledege of mathematics.

Journal of Non-Equilibrium Thermodynamics, 2020

In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical... more In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical wavy surface saturated in a porous medium is investigated. Ferrofluid is made by incorporating magnetic particles, in this case cobalt, at the nanoscale level into a base fluid. For the study of porous medium two well-known models, namely, Darcy and non-Darcy, are used. The mathematical model in terms of governing partial differential equations which are based on conservation laws in mechanics according to the assumption is developed, and this model is converted into a dimensionless form by suitable transformations. Due to the complex non-linear partial differential equations, the numerical solution is calculated by using an implicit finite difference scheme. The impact of involved parameters, namely, magnetic parameter, nanoparticle volume fraction parameter, the amplitude of the wavy surface, and the Grashof number, on Nusselt and average Nusselt numbers are studied through graphs and...

Case Studies in Thermal Engineering, 2021

A theoretical entropy generation analysis is conducted by applying the MHD and nonlinear thermal ... more A theoretical entropy generation analysis is conducted by applying the MHD and nonlinear thermal radiation effects contained in porous material for a steady three-dimensional power-law nanofluid flow near the stagnation point region. With the assistance of a thermally radiated nonuniform heat source /sink subject to convective boundary conditions, the heat transformation phenomenon is explored within the boundary layer over the stretchable rotatory disk. Multi-wall carbon nanotubes (MWCNTs) are incorporated in the ethylene glycol (C 2 H 6 O 2) as a base fluid. The proposed problem of fluid flow is mathematically modeled. The governing nonlinear partial differential equations (PDEs) are lessened to highly mixed nonlinear ordinary differential equations (ODEs) after the utilization of appropriate transformations. The effects of several classes of relevant parameters upon total entropy generation and Bejan number profiles are investigated by numerically addressing the ODEs with the purpose of a well-known Keller Box method. Furthermore, the skin friction coefficients and local Nusselt number are calculated for shearthinning and shear-thickening behaviors of the power-law fluid. Also, the total entropy generation increases for the Brinkman number and the permeability parameter but decreases for the material parameter, whereas the Bejan number has different behavior from entropy generation.

Case Studies in Thermal Engineering, 2021

Abstract The heat transfer phenomenon is beneficial and applicable in engineering, industries, an... more Abstract The heat transfer phenomenon is beneficial and applicable in engineering, industries, and technological processes. The production of energy with the help of some cheap resources plays a pivotal and renewable role in the industrial development of the countries. Owing to such a significant performance of heat transfer, the steady slip flow and heat transfer of tangent hyperbolic fluid over a lubricating surface of the stretchable rotatory disk is investigated. The effects of MHD, nonlinear radiation, and non-uniform heat source/sink subject to nonlinear boundary conditions are included in motion and energy equations. Because of the lubrication, a thin layer of the power-law fluid is produced at the surface of the disk. Since the lubricating layer is thin, the interfacial conditions are applied at the surface between the fluid and lubricant. The governing nonlinear partial differential equations (PDEs) have been converted into ordinary differential equations (ODEs), which are solved numerically using the Keller-box method. The upshots of pertinent parameters upon the dimensionless distributions of velocity and temperature are deliberated. The surface drag forces and heat transfer rates are computed, and the effects of governing parameters on them are examined. With the enhancement in the slip at the interface and Weissenberg number, the radial and azimuthal velocities enhances close to the disk, whereas they observe two diverse trends for the power-law index. Also, temperature escalates for radiation parameter, and this escalation is prominent for nonlinear radiation.

Physica Scripta, 2021

The non-Newtonian Sutterby fluid model can be implied to characterize the significant characteris... more The non-Newtonian Sutterby fluid model can be implied to characterize the significant characteristics of shear-thinning and shear-thickening for various ranges of the power-law index. The Sutterby fluid has a vast number of applications in engineering processes and industrial fluid mechanics. The steady two-dimensional stagnant flow of Sutterby nanofluid inside the boundary layer over a stretching wedge placed in a porous medium is investigated. The viscous incompressible fluid is electrically conducting, and a uniform magnetic field is imposed perpendicularly. The heat and mass transfer phenomenon is analyzed by incorporating the effects of nonlinear radiation, viscous dissipation, Joule heating, heat source/sink, and activation energy subject to convective-Nield boundary conditions. The physically modeled partial differential equations (PDEs) are lessened into ordinary differential equations (ODEs) with precise similarity variables. The numerical solution is obtained through the s...

Results in Physics, 2020

The ferrofluid are useful nanofluid and can be prepared by mixing magnetic types of nanoparticles... more The ferrofluid are useful nanofluid and can be prepared by mixing magnetic types of nanoparticles in base fluid. The mathematical modelling of ferrofluid under induced magnetic field through a vertical stretching surface is formulated in the current theoretical study. The study is performed for ferrofluid by considering magnetite Fe 3 O 4 magnetic nanoparticles in base fluid. In ferrofluid, the appropriate mixture of magnetic nanoparticles can lead to desire heat transfer phenomena. This theoretical study indicates that both Nusselt number and skin friction coefficient for Fe 3 O 4-water ferrofluid increase by improving the effects of magnetic parameterβ. Velocity and magnetic boundary layer thicknesses increase/decrease for assisting/opposing flow by strengthening magnetic effects and in the presence of magnetic type Fe 3 O 4 nanoparticle boundary layer thickness further enhances for pure water as compared to Fe 3 O 4 type of ferrofluid. Temperature profile and thermal boundary layer thickness increase for both assisting/opposing flow with enhancing the concentration of Fe 3 O 4 magnetic nanoparticle, however, thermal distribution reduces/upsurges in case of assisting/opposing flow with the increase of magnetic strength and thermal boundary layer thickness is greater for Fe 3 O 4 − water based ferrofluid as compared to regular fluid. The bvp4c built-in code in MATLAB software is employed for solution purposes. Results are displayed for the selection of effective parameters in data and graphical forms for both assisting and opposing flows.

Thermal Science, 2020

In this article, the impact of water-based hybrid nanofluid on heat transfer characteristics alon... more In this article, the impact of water-based hybrid nanofluid on heat transfer characteristics along the wavy frustum of the cone is examined. We considered hybrid nanofluid containing Cu and TiO2 nanoparticles. Non-similar form of the constitutive equations is obtained by using an appropriate set of transformations and results are achieved by employing transformed into compact non-similar form and are solved by the famous numerically implicit finite difference scheme known as Keller-box technique. The influence of the hybrid nanoparticles? volume fraction, frustum of cone half-angle, and the wavy texture parameters on the Nusselt number and skin friction are scrutinized and comparison is made between the wavy frustum of the cone and flat frustum of the cone through numerical data. It is observed that the rise in the truncated cone half-angle leads to an increase in skin friction and Nusselt number. The TiO2-water nanofluid has lower heat transfer rates as compared to Cu-TiO2 hybrid n...

Physica Scripta, 2020

The current research study investigates the steady three-dimensional flow and heat transfer of a ... more The current research study investigates the steady three-dimensional flow and heat transfer of a power-law nanofluid in the presence of the uniformly applied magnetic field and nonlinear thermal radiation over the stretchable rotating disk filled with gyrotactic microorganisms. The physically modeled partial differential equations (PDEs) are lessened to combined nonlinear ordinary differential equations (ODEs) with appropriate transformation. The influence of several types of pertinent parameters upon the dimensionless distributions of velocity, temperature, the concentration of nanoparticles, and microorganisms are analyzed graphically by solving the ODEs with a well-known shooting method. The tabular comparison is provided for the verification between the present results with those in the literature. Also, the physical quantities of interest are calculated, and the effects are scrutinized. Furthermore, it is noticed that the emerging parameters have produced a significant influenc...

Heat Transfer, 2020

The transfer of heat is an important phenomenon in the several areas due to its numerous applicat... more The transfer of heat is an important phenomenon in the several areas due to its numerous applications in industries. Several fluids like water, ethylene glycol and oil, and so on have very-low thermal conductivities due to which the transfer of heat in these fluids become very low. To enhance heat transfer rate, carbon nanotubes (CNTs) including single-walled CNTs and multi-walled CNTs are suspended into base fluids, this mixture is known as nanofluid. The aim of this study is to examine the heat transfer rate of nanofluid in the presence of CNTs over a stretchable rotating disk. The mathematical model, developed by Tiwari and Das, is used and solved numerically by using the shooting method. The impacts of governing constraints on the dimensionless velocities, temperature, skin friction, and Nusselt number are investigated. It is noted that heat transfer rate increases by enhancing the concentration of CNTs into base fluids. The numerical results show that the solid volume fraction of the CNTs augment heat transfer rate more in ethylene glycol as compared with water.

Computer Methods and Programs in Biomedicine, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Fluid Dynamics Research, 2020

Thermal Science, 2018

In this study, natural convection flow along a vertical wavy surface has been investigated with v... more In this study, natural convection flow along a vertical wavy surface has been investigated with variable heat flux. The governing equations are transformed into dimensionless PDE by using the non-dimensional variables and then solved numerically by using an implicit finite difference scheme known as Keller Box method. The effects of the parameters amplitude of the wavy surface, ?, exponent of the variable heat flux, m, and Prandtl number on the local skin friction coefficient and local Nusselt number are shown graphically. It is found that for the negative value of exponent of the variable heat flux, m, the local skin friction coefficient increases and Nusselt number decreases but the opposite behavior is observed for the positive values of m. The comparison of limiting case with the previous study is shown through table and it is found that the solution obtained is in excellent agreement with the previous studies.

Revista Mexicana de Física, 2018

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have b... more Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged...

Scientia Iranica, 2019

A study based on the theoretical investigation of Thermophoresis and Brownian motion effects on r... more A study based on the theoretical investigation of Thermophoresis and Brownian motion effects on radiative heat transfer in the neighborhood of stagnation point. Thermophoresis and Brownian motion play an important role in thermal and mass concentration analyses. These analyses help to comprehend the core ideas to carry out in the discipline of science and technology. An electrically conducting nanofluid is considered which is described by the Buongiorno transport model. The power-law form of the stretching wall velocity allows the similarity solution, the transformed system of the ordinary differential equations is computed numerically with the efficient rapid convergent spectral scheme. The obtained results for velocity, temperature, concentration, shear strain, mass and heat transfer rates are presented graphically for various values of the pertinent parameters. The outcomes divulge that with the increase of power-law exponent, mass and heat transfer rates enhance. The information for the volume and hightemperature transfer rate is provided in the form of Tables. The obtained results are matched with the existing results and are shown to be a good agreement.

Scientia Iranica, 2019

In this problem, a theoretical study is presented for the slip effects on the twodimensional flow... more In this problem, a theoretical study is presented for the slip effects on the twodimensional flow of a nano liquid in a semi-porous channel designed by two long rectangular plates having porous media. One of the channel walls is porous and other is rigid as well as slippery. A transverse magnetic field of homogenous strength is also applied to direction of flow. Magnetic nanoparticles   34 Fe O and non-magnetic nanoparticles   23 Al O are considered with ethylene glycol (EG) and water as base fluids (BFs). Least Square method (LSM) and Galerkin method (GM) are adopted to solve the equations, transformed from partial differential equations (DEs) to ordinary ones by Berman's similarity transformations. The obtained results from the two analytical methods are compared with the results obtained by fourth order Runge-Kutta numerical method (NM). By comparing the results of GM and LSM it is observed that variation in velocity profiles is minimal however the accuracy of GM is higher than LSM. The contributions of various flow parameters are presented through graphs. Results show a decrement in the fluid velocity with an increase in the slip and porosity parameter. The fluid boundary layer decreases with an increase in the Reynolds number. Flow field is less for the case of magnetic nanoparticles as compared to nonmagnetic particles.

Physica A: Statistical Mechanics and its Applications, 2019

In some cases, most of the boundary value problems contain multiple solutions in which one of the... more In some cases, most of the boundary value problems contain multiple solutions in which one of the solution is stable or physical reliable and other solutions are unstable. In this study, the problem of hydromagnetic flow due to shrinking sheet is considered and calculated dual solutions against velocity ratio parameter in case of shrinking sheet. A stability analysis is performed for the checking, which solution is stable. The main materials and methods used: Initially, due to more than one independent variable, the flow is governed by partial differential equations (PDEs). For simplicity the conversion of these PDEs were made in form of ODEs (ordinary differential equations) and solved analytically by using weighted residual method named as least square method. The resulting nonlinear system of equations is linearized by using Newton method (Burden and Faires, 1991). For the accuracy of this method, a comparison is made with the previous published work (Wang, 2008). The algorithm of least square method is constructed in Mathematica software and is very easy to apply as compare to analytical method namely: homotopy analysis method. In case of shrinking sheet there exists more than one solution. To check which solution is physical reliable or stable and unstable, a present problem is converted into time dependent problem and then stability analysis is performed and BVP4c method is used for calculating the eigenvalues. The main results obtained: In case of shrinking sheet there exists dual solutions and dual solutions are calculated for some values of velocity ratio parameter λand magnetic parameter M by using least square method. The range of dual solutions is shown by plotting the graphs of skin friction coefficient and local Nusselt number. After performing the stability analysis, the smallest eigenvalues are calculated for various values of λ and M. The main conclusions of the work: It is observed that positive eigenvalue corresponds to stable solution or physical reliable i.e. the disturbance in the solution decay initially and negative eigenvalue corresponds to unstable solution i.e. it produces initial growth of disturbance. It is also observed that eigenvalues become higher in the presence of Lorentz force.