Showing papers on "Homotopy analysis method published in 2020"

Analysis of the model of HIV-1 infection of CD4+$CD4^{+}$ T-cell with a new approach of fractional derivative

Abstract: By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.

A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

Abstract: We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.

Irreversibility Analysis and Heat Transport in Squeezing Nanoliquid Flow of Non-Newtonian (Second-Grade) Fluid Between Infinite Plates with Activation Energy

Abstract: The main theme of this communication is to scrutinize the chemically reactive flow of second-grade nanoliquid between two infinite plates. The MHD fluid is considered. Both plates approach symmetrically to each other, generating squeezing flow. The Buongiorno model is utilized for the modeling. Viscous dissipation and Ohmic heating effects are further considered. The total irreversibility rate is achieved via thermodynamics second law. To transform the reactants into products, a concept of activation energy is used. The nonlinear PDEs are altered into ordinary ones through similarity transformations and solved through homotopy analysis method. The impact of sundry parameters on flow, temperature and concentration fields is studied with the help of graphic illustrations. Velocity and temperature gradients are discussed numerically through Tables 2 and 3. The velocity of fluid particles increases versus squeezing parameter, while temperature field decreases. The entropy rate and Bejan number demonstrate the contrast influence against Brinkman number.

Heat and mass transfer together with hybrid nanofluid flow over a rotating disk

Abstract: This article explores an incompressible hybrid nanofluid flow over an infinite impermeable rotating disk. The influence of a magnetic field has been added to better examine the fine point of nanoliquid flow. The main purpose of this work is to enhance our understanding of the exhaustion of energy in industrial and engineering fields. This study is mainly concerned with the von Karman traditional flow of a rotating disk, involving carbon nanotubes (CNTs) and magnetic ferrite nanoparticles together with a carrier fluid such as water. The nonlinear system of differential equations is transformed to the dimensionless ordinary differential equation by using an appropriate similarity framework, which is further treated with the “homotopy analysis method” for the analytic solution. A mathematical calculation is provided to prove and illustrate why the hybrid nanofluids are advantageous as far as the heat transfer enhancement is concerned. Although the physical features highly rely on CNTs and iron oxide nanoparticles, it is concluded that the heat and mass transfer rate is greatly enhanced by the addition of CNTs and Fe3O4 nanofluids. By increasing the velocity of disk rotation, fluid temperature and velocity are significantly increased. The use of CNT + Fe3O4/H2O influences the performance of thermophysical characteristics of carrier fluids more compared to magnetic ferrite nanomaterials.

Modified heat and mass transmission models in the magnetohydrodynamic flow of Sutterby nanofluid in stretching cylinder

Abstract: This exploration addresses the boundary layer flow of Sutterby nanofluid by a stretched cylinder by incorporating the revised models for heat and mass transmissions by engaging Cattaneo–Christov theory. A mathematical model is developed under boundary layer analysis. The physical phenomenon is firstly derived in the form of partial differential equations by engaging the conservation laws. Modified Darcy’s law characterizes the porous medium. The nonlinear equations for the proposed model are analyzed optimally and dynamically. Nonlinear partial differential equations (PDEs) through conservation laws of mass, momentum, energy and concentration are established. Numerical solutions of the nonlinear systems are obtained by Optimal homotopy analysis method (OHAM). Stream plots are given for velocity solution. Graphs of velocity, temperature and concentration profiles are sketched and discussed with physical significances. It is reported that escalating values of the magnetic parameter boost the fluid temperature and concentration whereas the opposite impact on velocity is portrayed. Moreover, temperature and concentration fields decreases by growing the values of thermal and solutal relaxation parameters.

Simulation of Cattaneo–Christov heat flux on the flow of single and multi-walled carbon nanotubes between two stretchable coaxial rotating disks

Abstract: With an objective to unfold the flow and heat transfer characteristics of carbon nanotubes between two stretchable coaxial rotating disks, the present investigation has been carried out. The behavior of single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs) taking water as the base fluid is analyzed. To formulate the energy equation, we have incorporated Cattaneo–Christov heat flux model. Consideration of such kind of model accounts the contribution by thermal relaxation. von Karman transformation has been implemented in order to reconstruct the governing partial differential equations into a system of ordinary differential equations. Employing optimal homotopy analysis method series solutions are obtained. Error analysis has also been performed and presented in tabular form. The physical clarifications for the behavior of fluid velocity, temperature, skin friction coefficient and Nusselt number are well demonstrated with the help of graphs and contour plots. One of the major outcomes of the present study signifies that water-based SWCNTs have a tendency to cause less drag and higher rate of heat transfer as compared to water-based MWCNTs. This investigation finds numerous applications in different mechanisms of thermal conversion for nuclear propulsion and spacecraft.

Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks.

Abstract: Buongiorno’s nanofluid model is followed to study the bioconvection in two stretchable rotating disks with entropy generation. Similarity transformations are used to handle the problem equations for non-dimensionality. For the simulation of the modeled equations, Homotopy Analysis Method is applied. The biothermal system is explored for all the embedded parameters whose effects are shown through different graphs. There exists interesting results due to the effects of different parameters on different profiles. Radial velocity decreases with increasing stretching and magnetic field parameters. Temperature increases with Brownian motion and thermophoresis parameters. Nanoparticles concentration decreases on increasing Lewis number and thermophoresis parameter while motile gyrotactic microorganisms profile increases with increasing Lewis and Peclet numbers. Convergence of the solution is found and good agreement is obtained when the results are compared with published work.

Application of non-Fourier double diffusions theories to the boundary-layer flow of a yield stress exhibiting fluid model

Abstract: This letter highlights the possessions of momentum, heat and mass transmission on mixed convection boundary layer flow of Casson liquid over a linear elongating surface in porous medium. Heat and mass transmission mechanisms are supported out in the form of Cattaneo–Christov heat flux and generalized Fick’s law respectively. Appropriate restorations are smeared to revolutionize nonlinear partial differential equations (PDEs) conforming to momentum, energy and concentration equations into highly nonlinear coupled ordinary differential equations (ODEs) system. Numerical solutions of transformed boundary layer ordinary differential equations (ODEs) are attained by reliable technique namely Optimal homotopy analysis method (OHAM). Graphical interpretation is given for convergence of analytic solutions and flow behavior of convoluted physical parameters on calculated solutions is presented and explicated in this examination. Reliability and efficiency of the proposed algorithm is established by comparing the results of present analysis as a limiting case of available work, and it is found to be in excellent settlement. Moreover, it is reported that augmenting values of magnetic parameter reduces the fluid velocity and upsurges the temperature and concentration profiles.

Numerical analysis of thermal conductive hybrid nanofluid flow over the surface of a wavy spinning disk.

Abstract: A three dimensional (3D) numerical solution of unsteady, Ag-MgO hybrid nanoliquid flow with heat and mass transmission caused by upward/downward moving of wavy spinning disk has been scrutinized. The magnetic field has been also considered. The hybrid nanoliquid has been synthesized in the presence of Ag-MgO nanoparticles. The purpose of the study is to improve the rate of thermal energy transmission for several industrial purposes. The wavy rotating surface increases the heat transmission rate up to 15%, comparatively to the flat surface. The subsequent arrangement of modeled equations is diminished into dimensionless differential equation. The obtained system of equations is further analytically expounded via Homotopy analysis method HAM and the numerical Parametric continuation method (PCM) method has been used for the comparison of the outcomes. The results are graphically presented and discussed. It has been presumed that the geometry of spinning disk positively affects the velocity and thermal energy transmission. The addition of hybrid nanoparticles (silver and magnesium-oxide) significantly improved thermal property of carrier fluid. It uses is more efficacious to overcome low energy transmission. Such as, it provides improvement in thermal performance of carrier fluid, which play important role in power generation, hyperthermia, micro fabrication, air conditioning and metallurgical field.

Entropy generation in MHD Casson fluid flow with variable heat conductance and thermal conductivity over non-linear bi-directional stretching surface.

Abstract: This consideration highlights the belongings of momentum, entropy generation, species and thermal dissemination on boundary layer flow (BLF) of Casson liquid over a linearly elongating surface considering radiation and Joule heating effects significant. Transportation of thermal and species are offered by using the temperature-dependent models of thermal conductivity and mass diffusion coefficient. Arising problem appear in the form of nonlinear partial differential equations (NPDEs) against the conservation laws of mass, momentum, thermal and species transportation. Appropriate renovation transfigures the demonstrated problem into ordinary differential equations. Numerical solutions of renovated boundary layer ordinary differential equations (ODEs) are attained by a proficient and reliable technique namely optimal homotopy analysis method (OHAM). A graphical and tabular interpretation is given for convergence of analytic solutions through error table and flow behavior of convoluted physical parameters on calculated solutions are presented and explicated in this examination. Reliability and effectiveness of the anticipated algorithm is established by comparing the results of present contemplation as a limiting case of available work, and it is found to be in excellent settlement. Decline in fluid velocity and enhancement in thermal and species transportation is recorded against the fluctuating values of Hartman number. Also reverse comportment of Prandtl number and radiation parameter is portrayed. Moreover, it is conveyed that supplementing values of the magnetic parameter condenses the fluid velocity and upsurges the thermal and concentration distributions. Negative impact of elevating Joule heating phenomenon is noted on the molecular stability of the system via Brinkman number [Formula: see text] Furthermore, the system's stability at a molecular level is controlled by diminishing values of radiation [Formula: see text] temperature difference [Formula: see text] concentration difference [Formula: see text] diffusion parameters [Formula: see text] and Brinkman number [Formula: see text].

A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects

Abstract: The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropolar fluid in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov (C-C) heat and mass flux expressions. Besides, the thermal radiation effects are contributed in the energy equation and aspect of the radiation parameter, and the Prandtl number is specified by the one-parameter approach. The formulated expressions are converted to the dimensionless forms by relevant similarity functions. The analytical solutions to these expressions have been erected by the homotopy analysis method. The variations in physical quantities, including the velocity, the temperature, the effective local Nusselt number, the concentration of nanoparticles, and the local Sherwood number, have been observed under the influence of emerging parameters. The results have shown good accuracy compared with those of the existing literature.

Impact of induced magnetic field on second-grade nanofluid flow past a convectively heated stretching sheet

Abstract: Here, the main purpose of our current research work is to analyze the aspects of buoyancy force on viscoelastic (second grade fluid) magnetized nanofluid. Features of Brownian moment, viscous dissipation and thermophoretic aspects are introduced in the formulation of the problem. More specifically, the non-dimensionalization process is adopted to reduce governing system of equation (PDE) into self-similar form (ODE). Optimal homotopy analysis method (OHAM) is employed on ODE to analyze the behavior of the viscoelastic magnetized nanofluid. Moreover, comprehensive discussion related to arising physical parameters of viscoelastic liquids vs significant profiles is presented in this work. Quantities of physical interest such as Sherwood and Nusselt numbers are presented in tabular form. It has been observed that larger values of rise in the values of viscoelastic parameter (second grade fluid) results in an increment in temperature distribution.

Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

Abstract: In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method

Abstract: Viruses have different mechanisms in causing a disease in an organism, which largely depend on the viral species. The recent advancement, through coupling data analysis and mathematical modeling, has allowed the identification and characterization of the nature of the virus. In the present paper, the homotopy analysis method is applied to provide an approximate solution of the basic HIV viral dynamic model describing the viral dynamics in a susceptible population. The proposed method allows for the solution of the governing system of differential equations to be calculated in the form of an infinite series with components which can be easily calculated. The homotopy analysis method utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. By using the homotopy series solutions, firstly, several β − curves using an appropriate ratio are plotted to demonstrate the regions of convergence and the optimum value of ℏ, then the residual and absolute errors are obtained for different values of these regions. Secondly, the residual error functions are applied to show the accuracy of the applied homotopy analysis method. Also, the convergence theorem of homotopy analysis method for the HIV viral dynamic model is proved. Mathematica software is used for the calculations and numerical results. The results obtained show the effectiveness and strength of the homotopy analysis method.

On the Cattaneo–Christov Heat Flux Model and OHAM Analysis for Three Different Types of Nanofluids

Abstract: In this article, the boundary layer flow of a viscous nanofluid induced by an exponentially stretching surface embedded in a permeable medium with the Cattaneo–Christov heat flux model (CCHFM) is scrutinized. We took three distinct kinds of nanoparticles, such as alumina (Al2O3), titania (TiO2) and copper (Cu) with pure water as the base fluid. The features of the heat transfer mechanism, as well as the influence of the relaxation parameter on the present viscous nanofluid flow are discussed here thoroughly. The thermal stratification is taken in this phenomenon. First of all, the problem is simplified mathematically by utilizing feasible similarity transformations and then solved analytically through the OHAM (optimal homotopy analysis method) to get accurate analytical solutions. The change in temperature distribution and axial velocity for the selected values of the specific parameters has been graphically portrayed in figures. An important fact is observed when the thermal relaxation parameter (TRP) is increased progressively. Graphically, it is found that an intensification in this parameter results in the exhaustion of the fluid temperature together with an enhancement in the heat transfer rate. A comparative discussion is also done over the Fourier’s law and Cattaneo–Christov model of heat.

Thermal Characteristics of 3D Nanofluid Flow over a Convectively Heated Riga Surface in a Darcy–Forchheimer Porous Material with Linear Thermal Radiation: An Optimal Analysis

Abstract: This paper focuses primarily on the thermal analysis of the steady, three-dimensional flow of CMC (sodium carboxymethyl cellulose) base fluid with Cu nanoparticles through the implantation plate of Riga in a porous Darcy–Forchheimer material with internal heat generation (absorption) effects. Thermophysical feature of CMC is taken into account with Al2O3 nanoparticle in it. Also, thermal radiation and convective boundary constraint are considered into account. Adequate transformations of the issue controlling formulas produce a system of nonlinear ordinary differential equations. The optimal homotopy analysis method is used for calculating the parameters values impacts. The expressions of local Nusselt number and skin friction coefficient are studied and debated. The physical influences of all emerging parameters are debated on graphically forms. The findings suggest that with higher values of Hartmann number, the skin friction in y-direction decreases on the contrary in the case of x-direction, while the Hartmann number increases the rate of heat transportation. Besides, the addition values of thermal radiation and Biot number enhance the rate of heat transport. Comparisons have been made with published literature, and an excellent agreement is clear. This underlines the importance of the study in potential medical and industrial cooling applications.

Mathematical modeling and numerical simulation of HIV infection model

Abstract: In this work we implement two numerical schemes namely continuous Galerkin–Petrov (cGP(2)) and Legendre Wavelet Collocation Method (LWCM) for the approximate solution of the mathematical model which describes the behavior of CD4 + T-cells, infected CD4 + T-cells and free HIV virus particles after HIV infection. The present study discuss and analyze the effect of constant and different variable source terms (depending on the viral load) used for the supply of new CD4 + T-cells from thymus on the dynamics of CD4 + T-cells, infected CD4 + T-cells and free HIV virus. Furthermore, the model is also solve using fourth order Runge Kutta (RK4) method. Finally, the validity and reliability of the proposed schemes are verified by comparing the numerical and graphical results with the results of RK4-method. Comparison of the numerical and graphical results of cGP(2) and LWCM with RK4-method confirmed that cGP(2) and LWCM performs excellent accuracy. The present study highlights the accuracy and efficiency of the proposed schemes with the other traditional schemes such as the Laplace Adomian Decomposition Method (LADM), Variational Iteration Method (VIM), Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM), Genetic Algorithm (GA), Interior Point Algorithm (IPA), Active Set Algorithm (ASA), Multistep Laplace Adomian Decomposition Method (MSLADM) etc.

The Shape Effect of Gold Nanoparticles on Squeezing Nanofluid Flow and Heat Transfer between Parallel Plates

Abstract: The focus of the present paper is to analyze the shape effect of gold (Au) nanoparticles on squeezing nanofluid flow and heat transfer between parallel plates. The different shapes of nanoparticles, namely, column, sphere, hexahedron, tetrahedron, and lamina, have been examined using water as base fluid. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by suitable transformations. As a result, nonlinear boundary value ordinary differential equations are tackled analytically using the homotopy analysis method (HAM) and convergence of the series solution is ensured. The effects of various parameters such as solid volume fraction, thermal radiation, Reynolds number, magnetic field, Eckert number, suction parameter, and shape factor on velocity and temperature profiles are plotted in graphical form. For various values of involved parameters, Nusselt number is analyzed in graphical form. The obtained results demonstrate that the rate of heat transfer is maximum for lamina shape nanoparticles and the sphere shape of nanoparticles has performed a considerable role in temperature distribution as compared to other shapes of nanoparticles.

Interaction of heat generation in nonlinear mixed/forced convective flow of Williamson fluid flow subject to generalized Fourier's and Fick's concept

Abstract: This research communication deals with the steady, incompressible two-dimensional (2D) nonlinear mixed/forced convective flow of Williamson fluid towards a flat and stretchable surface of sheet. The flow is discussed in semi-infinite domain and generated via linear stretching phenomenon. Nonlinear mixed convection is considered. The most prominent feature of mixed convection is buoyancy force caused by fluctuating temperature and density. The energy and concentration equations are modeled in the presence of generalized Fourier's and Fick's laws. Furthermore, variable thermal conductivity and mass diffusivity are accounted. The governing equations are first altered into ordinary differential equations through implementation of appropriate similarity variables and then series solutions are calculated for the flow field, temperature and concentration via homotopy analysis method. Novel characteristics of non-dimensional variables are discussed subject to graphical representation. It is noticed that the thermal field is more in the presence of Generalized Fourier Law (GFL) as compared to Fourier Law (FL).

Inquiry of entropy generation in stratified Walters’ B nanofluid with swimming gyrotactic microorganisms

Abstract: This article focuses on the study of Walters B nanofluid, under the impact of Joule heating, inclined magnetic field, viscous dissipation, swimming microorganisms, and stratification flowing past a horizontal cylindrical surface. The mathematical model is reduced to higher-order ordinary differential equations using Von Neumann similarity transformations. To obtain analytical solutions, the Optimal homotopy analysis method (OHAM) has been applied to the mathematical form. The analysis of skin friction, heat transfer rates and mass transfer rates of nanoparticles as well as swimming microorganisms is done using variation in different parameters and these results are portrayed using contour plots. Entropy is studied through dimensionless entropy generation parameter N G and Bejan number B e . The internal molecular stability is seen to reduce for temperature difference parameter Ω ‾ .

Three-dimensional magnetohydrodynamic flow of micropolar CNT-based nanofluid through a horizontal rotating channel: OHAM analysis

Abstract: An examination of simultaneous effects of Hall current and heat radiation on three-dimensional micropolar CNT-based nanofluid flow between two rotating sheets is carried out. The upper sheet is considered to be porous, and the fluid flow is induced due to stretching of the lower sheet. The flow model is presented by a system of nonlinear partial differential equations (PDEs). The leading PDEs are transformed into dimensionless coupled ordinary differential equations by the usual procedure of transformation. The transformed differential equations are solved by the optimal homotopy analysis method in order to analyze the velocity as well as temperature of nanofluid and microrotation of nanotubes. Analysis for physical quantities of interest, viz. skin friction coefficient and Nusselt number, are also carried out for the two kinds of nanotubes, single-wall carbon nanotubes and multiwall carbon nanotubes. It is observed that microrotation of nanotubes increased with the increase in coupling parameter, whereas it slows down with an increase in spin gradient viscosity parameter. An intense magnetic field results in a reduction of skin friction coefficient, whereas an increase in the suction of fluid through upper plate forces a surge in the value of skin friction coefficient.

Stability analysis for multiple solutions of boundary layer flow towards a shrinking sheet: Analytical solution by using least square method

Abstract: The Purpose: 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 λ and 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.

Viscous dissipated hybrid nanoliquid flow with Darcy–Forchheimer and forced convection over a moving thin needle

Abstract: The study of hybrid nanoliquid can help achieve innumerable advanced features that make heat and mass transmission more convenient, such as in hybrid-powered engines, pharmaceutical processes, microelectronics, domestic refrigerators, engine cooling, and so on. The intention behind this work is to escalate the performance of water based hybrid nanoliquid containing magnetic ferrite and CNTs. The viscous dissipated convective flow of hybrid nanoliquid passing over a horizontal moving thin needle is scrutinized. The nonlinear structure of the differential equations is transfigured into dimensionless ordinary differential equations, making use of Karman’s scaling. The results are deciphered via manipulating the homotopy analysis method. The physical entities out-turn on velocity, concentration, and the temperature profile are sketched and discussed in brief. The numerical outcomes are the skin friction, Nusselt number, and Sherwood number. It is perceived that the design of the needle including its size and shape strongly affects the thermal characteristics and fluid velocity. The energy and flow boundary layers of both CNTs and Fe3O4 are significantly diminished with the increase in the needle size. The uses of CNT + Fe3O4/H2O are more dominant for the enactment of thermo physical characteristics of carrier fluids associated with iron oxide nanomaterials.