Non-dimensional Equations Research Articles

Artificial neural network analysis of Jeffrey hybrid nanofluid with gyrotactic microorganisms for optimizing solar thermal collector efficiency

This article investigates solar energy storage due to the Jeffrey hybrid nanofluid flow containing gyrotactic microorganisms through a porous medium for parabolic trough solar collectors. The mechanism of thermophoresis and Brownian motion for the graphene and silver nanoparticles are also encountered in the suspension of water-based heat transfer fluid. The gyrotactic microorganisms have the ability to move in an upward direction in the nanofluid mixture, which enhances the nanoparticle stability and fluid mixing in the suspension. Mathematical modeling of the governing equations uses the conservation principles of mass, momentum, energy, concentration, and microorganism concentration. The non-similar variables are introduced to the dimensional governing equations to get the non-dimensional ordinary differential equations. The Cash and Carp method is implemented to solve the non-dimensional equations. The artificial neural network is also developed for the non-dimensional governing equations using the Levenberg Marquardt algorithm. Numerical findings corresponding to the diverse parameters influencing the nanofluid flow and heat transfer are presented in the graphs. The thermal profiles are observed to be enhanced with the escalation in the Darcy and Forchheimer parameters. And the Nusselt number enhances with the escalation in the Deborah number and retardation time parameter. Entropy generation reduces with an enhancement in Deborah number and retardation time parameter. Solar energy is the best renewable energy source. It can fulfill the energy requirements for the growth of industries and engineering applications.

Comparative study for heat transfer characteristics of magnetohydrodynamic viscous fluid in a multilayer flow flanked between nanofluids

This article examines the mixed convection heat transfer analysis of magnetohydrodynamic (MHD) viscous fluid flow over a multilayer channel flanked between nanofluids comprising a porous medium. The research highlights the significance of multilayer nanofluid flow in practical applications such as petroleum filtration process, cooling of electronic systems, nuclear reactors, and solar thermal systems. Ethylene glycol (EG) serves as a coolant due to its excellent miscibility with copper (Cu), enhancing its corrosion resistance properties in the fluid flow system. The purpose of this study is to analyze the impact of magnetic fields on heat transfer in a multilayer flow of Cu-EG-based nanofluids with different nanoparticles. The comparative performance of copper, copper oxide, and silver nanoparticles in enhancing the heat transfer rate is investigated. The non-dimensional equations are highly coupled, and non-linear differential equations are resolved analytically by utilizing regular perturbation approaches to get a closed-form solution. A comparative analysis between analytical results and numerical methods was done, demonstrating excellent agreement for the fluid flow momentum profile. This study reveals the magnetic field reduces heat transfer in the fluid flow system EG as a base fluid, and silver nanoparticles outperform copper, and copper oxide nanoparticles in thermal conductivity. These findings give rise to optimizing nanofluid-based systems in engineering and industrial applications.

Artificial neural networks computing system for Ree-Eyring hybrid nanofluid flow over a solar panel sheet: Hamilton–Crosser model

Background: The utilisation of solar radiation for generating thermal energy has garnered a significant amount of attention, especially with the rising demand for sustainable power and heating sources. Nanofluids appeared as promising options for enhancing the efficiency of solar-thermal systems owing to their superior heat transmission properties. In this aspect, the present research deals with Ree-Eyring hybrid nanofluid ( SWCNT − MWCNT / H 2 O ) flow in the presence of thermal radiation effect and shape factor to examine the thermal behaviour in solar panels. Additionally, the innovation lies in the field of artificial neural networks and fluid flow analysis as an integrated approach. Methodology: The considered physical interpretation is stated in the form of nonlinear partial differential equations. To facilitate the computation process, the governing equations turned into nondimensional ordinary differential equations with the help of invariant transformations. The converted equations are treated scientifically using the NDSolve methodology, which automatically adjusts the step size. In further, an artificial neural network-based multi-layer perceptron deploying the Levenberg–Marquardt model is employed to forecast the measurements of physical quantities. Core Findings: The markable outcomes from this advanced work imply that the stretching surface has an important role in analysing the thickness of the boundary layer. The improving Weissenberg number enhances the boundary layer thickness, leading to a magnification in the momentum field of the non-Newtonian fluid. In addition, thermal radiation is captured as a second significant influence on temperature distribution. It follows that enhancing the Radiation parameter upsurges the thermal layer. The variation of the volume fraction of nanoparticles resulted in higher temperatures due to the Hamilton–Crosser model, which involves the cylindrical shape of the nanoparticles. Validation: The validation of the current work is explored by comparing it with the existing literature in certain instances. The incorporation of multi-layer perceptron for hybrid nanofluid delivers the performance capacity of high prediction with the error 4.83E−06, 1.11E−10 and 2.4E−08. Applications: The existing optimisation approach provides a new perspective on solar-powered offshore, solar vehicles, solar-powered charging stations, solar power greenhouse and solar water pump implementation.

Numerical investigation of unsteady magnetohydrodynamic flow of a Newtonian fluid with variable viscosity in an inclined channel

This research investigates the unsteady flow dynamics of an electrically conducting Newtonian fluid with variable viscosity in an inclined channel under the influence of a uniform magnetic field. The flow is driven by a constant pressure gradient applied at the entrance of the channel, and the governing equations are derived from the Navier–Stokes equation, incorporating the impact of magnetic fields, gravitational force, and viscosity variations. The no-slip boundary condition at the channel walls and appropriate initial conditions are applied. A numerical solution to the non-dimensionalized flow equations is obtained to analyze key flow characteristics, such as velocity profiles, flow rate, and wall stresses. The impact of various dimensionless parameters, including viscosity variation, magnetic field strength, Froude number, and channel inclination angle, on the flow behavior is explored through graphical and tabular presentations. The results provide insights into how these parameters influence the velocity distribution, volumetric flow rate, and wall stresses in the inclined channel, contributing to a deeper understanding of magnetohydrodynamic flows in practical applications.

THE EFFECT OF MAGNETIC PARAMETER OVER A VERTICAL WAVY SURFACED RIGHT CIRCULAR CONE IN PRESENCE OF NATURAL CONVECTION

The novelty of this study lies in the combination of wavy cone and magnetic field. The interaction between the velocity decrease and the temperature increase has a various applications. This phenomenon has potential applications in fields such as heat transfer, where there is ability to control temperature profiles. Employing magnetic field can be useful in heat exchangers, cooling systems and other thermal processes. The effects of magnetic fields on fluid flow and heat transfer can be relevant in material processing and manufacturing. This work presents the influence of magnetic field on a vertical wavy cone immersed in viscous fluid, in the presence of natural convection flow with viscosity inversely proportional to linear temperature function. The dominating problem is nonlinear partial differential equations, which is transformed into non-dimensional partial differential equations by using the dimensionless variables, and the wavy surface effect is eliminated from the boundary conditions applying these dimensionless variables. The transformed equations are solved numerically by finite difference (fully implicit method). The numerical results are obtained for magnetic parameter, Prandtl number, surface amplitude, cone half-angle and viscosity variation parameter and their effect on velocity, temperature and Nusselt number. The effect of increasing the magnetic parameter reduces the velocity and increases the temperature. Redundancy of Prandtl number increases the temperature, while the increase of Cone half-angle (CHA) increases the velocity profile. The influence of increasing the viscosity parameter tends to increase the Nusselt number.

Exploring bioconvective heat transfer dynamics on curved surfaces: Insights into non‐Newtonian behavior and multifaceted influencing factors

AbstractThis research article investigates the bioconvective flow of a second‐grade fluid along a curved surface, considering non‐Newtonian behavior and diverse influencing factors such as heat generation, chemical reactions, slip, Lorentz force, and viscous dissipation. By employing MATLAB's bvp4c tool and the similarity transformations, the nondimensional partial differential equations are solved. We discover that the stable and unstable solutions differ significantly from one another, which has significant consequences for industries including microfluidic devices and curved surface manufacturing. The study also examines the effects of homogenous and heterogenous reaction parameters on reactant concentrations, revealing that higher values reduce concentration, particularly for the second solution. Designing effective heat exchangers and chemical reactors requires consideration of the sensitivity of skin friction coefficient and Nusselt number to curvature, slip, and heat generation, as demonstrated by this work. The findings may guide future experimental study and yield important insights for optimization of bioconvective systems.

Wavy mathematical modeling of dynamically reactive shear thinning materials under the influence of gravity and wavy structures amplitude

PurposeResultant leading equations are formed with non-linear partial differential equations by adopting a low Reynolds theory approximation. For a better and easier understanding of the role of physical features of the main problem, the equations are reduced to non-dimensional ordinary differential equations by incorporating the locally similar and non-similar dimensionless variables. In light of practical importance, all the significant findings are approximated by solving the equations with the assistance of a modified bvp4c built-in package. The effective speed, temperature and volume fraction of the same materials are displayed to address the behaviors of different controlling influences.Design/methodology/approachThis work is inaugurated to investigate thermal cycling, thermal striping and thermal stratification, which cause thermally induced damage during the wavy confined flow domains. Such physical constraints are imposed on the wavy surface while considering the wavy dynamics of shear thinning materials. The impact of gravity is assumed on the vertical wavy surface, which is observed as the main source for the wavy flow occurrence. The surface’s amplitude plays a critical role in generating a high temperature difference. The same phenomenon is further extended with the applications of thermal radiation, mixed convection and dynamical homogeneous/heterogeneous reactions.FindingsFor instance, the higher stratification factor causes a reduction in the liquid wavy speed and temperature, and the rising chemically reactive rate factor declines the volume fraction during the typical wavy motion of the materials. Moreover, the larger amplitude and mixed convective factor reduced and uplifted the speed of the materials, respectively. The surface resistive forces are monitored with the graphical visualization of local similar skin friction and are determined larger by varying the Weissenberg and mixed convective factors. The affective liquid speed, temperature and volume fraction are plotted to address the behaviors of different controlling factors. These impacts are listed, i.e. with higher stratification factors, a reduction is noticed in the liquid velocity and temperature. On the other hand, an opposite depict is noticed for higher heat generation factors. The reduction in volume fraction is reported with variation in the reaction factor and Schmidt number.Originality/valueAfter carefully assessing the previously referenced work, it is evident that the literature has yet to incorporate thermally stratified Williamson fluid. Meanwhile, the motion of the materials is noticed due to the gravitationally affected wavy surface. Such physical phenomenon is further approximated by testing a dynamical reaction during its motion. An effective presentation of all the outcomes is portrayed via graphs and approximated numerical results.

Influence of Thermal Wall and Velocity Slips on Non-Darcy MHD Boundary Layer Flow of a Nanofluid over a Non-linear Stretching Sheet

Abstract This study investigates the characteristics of magnetohydrodynamic nanofluid flowing via a non-linearly stretched surface within a porous media along with thermal and velocity slips. The similarity transformation is implemented to derive non-dimensional ordinary differential equations from partial differential equations. The finite difference Keller box implicit method yields the numerical solutions. Notably, our findings reveal the intricate influence of several factors, such as velocity slip factor, permeability parameter, thermophoresis parameter, thermal slip factor, Brownian parameter, magnetic parameter and stretching factor on temperature, concentration and velocity, also unveiling nuanced insights into the enhancement of mass and heat transfer attributes. The finding shows that the concentration and temperature of the nanofluid are enhanced and reduced respectively on increasing the thermal slip factor. Further, both mass and heat transfer rates decrease with increasing thermal slip, while the influence of skin friction coefficient is negligible. Further, Both concentration as well as temperature increase on enhancing velocity slip parameter, but opposite behaviour has been observed for the velocity profile. Further, for the higher value of velocity slip, the skin friction coefficient and the rate of heat transfer are increased. While, the mass transfer rate decreases. Furthermore, As the permeability increases, temperature and velocity profiles both indicate an upward trend, which is an acceptable result because more permeability propels more flow and low permeability induces weak flow in the system. The achieved results are depicted graphically.

A generalized coarse-graining discrete-element method with variable scaling ratios based on non-dimensional contact equation

A generalized coarse-graining discrete-element method with variable scaling ratios based on non-dimensional contact equation

Numerical analysis of bioconvective heat transport through Casson nanofluid over a thin needle.

Bioconvective flows over a thin needle hold significant importance in various fields, particularly in biomedical engineering, microfluidics, and environmental science. This paper examines the bioconvective flow properties of a copper and blood-based Casson nanofluid over a thin needle, accounting for gyrotactic microorganisms in the presence of a magnetic field. The two-phase nanofluid model is applied to formulate the flow problem. The system of non-dimensional ordinary differential equations is obtained by reducing the governing partial differential equations with the help of similarity variables. Further, the ODEs are numerically solved using the 4th-order Runge-Kutta method based Shooting technique. The similar solutions of the non-dimensional ODEs are represented graphically and the blood-based nanofluid's velocity, temperature, concentration, and presence of microorganisms are examined with reference to the accompanying diagrams. A detailed analysis is provided for skin friction, Nusselt number, and microorganism density number. The primary outcomes reveal that the augmentation of the mixed convection parameter and buoyancy ratio parameter enhance the rate of heat transfer.

Case study of radiation absorptive and chemical reactive impacts on unsteady MHD natural convection flowing of Cu-Al2O3/H2O hybridized nanofluid

Magnetohydrodynamic hybrid nanofluid (Cu-Al2O3/H2O) flow along an infinitely long plate accelerated exponentially with constant species diffusion, varying heat source and under the chemical reactive, radiation absorptive influences are analysed. Non-dimensional partial differential equation system is derived from the governing nonlinear boundary layer equations. Both analytical and numerical solutions to these equations are obtained using Laplace transform approach and finite difference method. The investigation has been conducted across a broad spectrum of magnetic parameters, thermal Grashof numbers, mass Grashof numbers, radiation absorption parameters, and chemical reaction parameters. Graphical representations are used to show the implications of factors like Schmidt number, mass Grashof number, chemical reactive variable, thermal Grashof number, absorption of radiation on flow, heat, mass transfer and on their gradients as well. Velocity enhances with rising amounts of thermal and solutal buoyancy forces. Reversal tendency is noticed in situation of chemical reaction parameter and magnetic field parameter. Temperature transmission rate of hybrid nanofluids is higher than conventional nanofluids and pure fluids.

Optimization of Thermal Performance by Enhancing Natural Convection of Diverse Configurations of Fin Heat Sink Filled With Nano‐Enhanced Phase Change Materials: A Numerical Study

ABSTRACTElectronic components require faster propagation of heat to prevent overheating as well as to maintain a stable operating condition. Incorporating phase change materials (PCMs) in fin heat sinks (FHSs) can be a viable solution to enhance natural convection. In the present work, an extensive investigation has been carried out on three types (square, circular, and triangular) of FHSs filled with PCMs to find the best combinations for the thermal cooling of a heat sink. To increase the thermal conductivity of the PCMs, Cu–water nanofluid is added. The effects of three types (paraffin wax, stearic acid, and polyethylene glycol) of PCMs have been studied. Nondimensional equations have been solved numerically by using Galerkin's finite element method. A parametric investigation has been conducted by varying the Rayleigh number within the range of 103–106 to calculate the Nusselt number. Results reveal that a heat sink with PCMs can reduce the temperature rise by 6.41% and increase the Nusselt number by 4.6% compared to a heat sink without PCMs. As the height of the fins increases from 10 to 16 mm, thermal efficiency increases. Moreover, square FHSs show the best thermal performance by reducing the temperature rise by as much as 13.41% compared to circular and triangular FHSs. Therefore, this comparative study shows that the dimensional configurations of FHSs with varying PCMs have a great impact on thermal performance and thus provide one the opportunity to obtain an effective arrangement of heat sinks.

Soret and radiation influence on Magneto Casson fluid flow over a non-linear inclined sheet in a Forchheimer porous medium with viscous dissipation

This article emphasis on the impacts of Soret and viscous dissipation on Magneto Casson fluid flow past a non-linear inclined sheet in a porous Forchheimer medium with thermal radiation. In this mathematical model, the impacts of chemical reaction, heat source/sink, velocity and thermal slips are also examined. The velocity, temperature, and concentration of the inclined surface are presumed to exhibit nonlinear fluctuations with respect to distance. The partial differential equations controlling the investigation are transformed into non-dimensional ordinary differential equations that include a set of physical factors. By implementing the Keller Box approach, the resultant equations are numerically solved. As the Soret parameter rises, the concentration profile increases the coefficient of skin friction values falls and Nusselt number values rise with the Soret parameter. The temperature rises for the increasing values of Ec. Numerical data is also used to analyze the outlines in the changing rates of thermal and mass transport as well as the drag force factor. The results of the current investigation indicate that the rising magnetic and suction components have reduced fluid motion while enhancing thermal profiles. Furthermore, the suction component adversely affects both temperature and concentration gradients. In this perspective, these factors have a substantial influence on numerous engineering applications, including the nuclei of nuclear reactors, the production of polymers, metal layers, paper sheets, and the biochemistry industry. To advance and enhance the computational analysisfor this work, the computational findings are corroborated by comparing specific instances of the current research with those from previous studies, yielding strong concordance.

Submesoscales are a significant turbulence source in global ocean surface boundary layer

The turbulent ocean surface boundary layer is a key part of the climate system affecting both the energy and carbon cycles. Accurately simulating the boundary layer is critical in improving climate model performance, which deeply relies on our understanding of the turbulence in the boundary layer. Turbulent energy sources in the boundary layer are traditionally believed to be dominated by waves, winds and convection. Recently, submesoscale phenomena with spatial scales of 0.1~10 km at ocean fronts have been shown to also make a contribution. Here, by applying a non-dimensional turbulent kinetic energy budget equation, we show that the submesoscale geostrophic shear production at fronts is a significant turbulent energy source within the ocean boundary layer away from the sea surface. The contribution reaches 34% of the total dissipation in winter and 17% in summer at the mid-depth of the boundary layer, despite its intermittency in space and time. This work indicates fundamental deficiencies in previous conceptions of ocean boundary layer turbulence, and invites a reappraisal of the sampling scale in observations, model resolution and parameterizations, and other consequences of the global energy budget.

Rate dependency and fragmentation response of phase field models with micro inertia and micro viscosity terms

We present elliptic, parabolic, and hyperbolic phase field (PF) equations, referred to as EPF, PPF, and HPF, for cohesive zone model (CZM) and Linear Elastic Fracture Mechanics (LEFM) PF models. The micro viscosity and micro inertia terms result in PPF and HPF, that can be solved explicitly in time. The additional advantage of the HPF is implying a finite damage propagation speed and a more favorable time advance limit. The desired micro-viscosity for the HPF is shown to correspond to a damping factor of one. The appropriate length and time scales, nondimensional equations, and (asymptotic) strain-stress solutions are provided for each differential equation. Two sources of rate sensitivity are discussed. First, when the fields are spatially uniform (0D solution) the rate effect arises from the form of differential equation. Asymptotic solutions show that at high loading rates, the energy dissipation has the rates of 2/3 and 1 for the PPF and HPF, respectively, with the former matching the Grady’s rate-sensitivity. The dynamic strength and failure strain show half of this rate. The analysis is extended to damage models with stress-based and bounded driving forces. Second, the rate effect arises from the deviation of 1D from 0D solutions as the damage exceeds a critical value and fragments form. Since this critical value tends to zero for quasi-static loading, this rate-effect is mainly present for low loading rates. This results in lower- and upper-shelf energy limits for the EPF at low and high loading rates, resembling some experimentally observed sigmoidal rate models for energy dissipation.

Vieta–Lucas polynomials-based collocation simulation to analyze the solvent fraction factor in active and passive control flow induced by torsional motion

The present research explores the Boger fluid flow past a stretching cylinder with torsional motion in the presence of the magnetic field. It is assumed that the cylinder rotates continuously around its axis and that the starting point's position along the axis correlates with the cylinder wall's expansion rate. Additionally, the consequence of active and passive control of nanoparticles, activation energy, thermophoresis, and Brownian motion effects are considered. Similarity variables transform the governing partial differential equations into non-dimensional ordinary differential equations (ODEs). Furthermore, the Vieta–Lucas polynomials-based collocation method (V-LPBCM) is employed to solve the resulting ODEs. The V-LPBCM outcomes of Nusselt and Sherwood numbers are compared with Runge–Kutta Fehlberg's fourth-fifth-order scheme for validation purposes. The impact of various dimensionless parameters on the different profiles is depicted in the graphical representation. The increase in values of the magnetic parameter, the ratio of relaxation time, and the Reynolds number decline the velocity profile. The velocity profile increases as the values of the solvent fraction parameter rise. The thermal profile increases as the heat source/sink, and thermophoretic parameters rise. The increase in values of activation energy parameter increases the thermal profile.

Physics-informed neural networks approach for pollutant dispersion flow caused by magnetic dipole

Abstract Research on the liquid flow and distribution of waste discharge concentration over cylindrical surfaces might lead to the growth of efficient waste management and pollution controlling strategies. In view of this, the pollutant concentration and magnetic dipole impact on the liquid flow through the cylinder with a porous medium are explored in the present analysis. Moreover, Fourier’s and Fick’s laws are considered to explore heat transport features. The governing partial differential equations (PDEs) of the present study are converted into non-dimensional ordinary differential equations (ODEs) utilizing similarity variables. Also, the current study proposes a novel implementation of neural networks based on physics knowledge for the liquid flow past a cylinder. The self-updating weights and bias facilitate the network to satisfy the minimization objective function and provide accurate results. Additionally, the solution obtained by Runge Kutta Fehlberg's fourth-fifth order (RKF-45) method is utilized to validate the physics-informed neural network (PINN) results, presenting mean squared errors from 10-9 to 10-11. Furthermore, it is found that the increase in temperature relaxation time parameter decreases the Nusselt number gradually at the rate of 1 to 5%. An upsurge in the values of the pollutant external source parameter and the pollutant external source variation parameter decreases the concentration profile.

Analysis of multi-phase lag gradients for a spherical cavity due to prescribed internal pressure

A refined multi-phase lag model is proposed here for a homogeneous unbounded thermoelastic spherical cavity in a curvilinear coordinate system. The associated solutions are obtained by forming non-dimensional vector matrix equations and applying Eigen value approach in the transform domain. The results have been verified using the valid boundary conditions associated with physical and field variables. Mathematica and MATLAB platforms are used for numerical analysis and graphical representation.

Nonorthogonal stagnation‐point flow of micropolar fluid past a stretching sheet in the presence of thermal radiation and chemical reaction

AbstractThis work has broad applications in areas such as materials engineering, particularly in the manufacturing of polymers, textile fibers, and nanocomposites, thus, inspired the study to examine a continuous two‐dimensional flow of micropolar fluid steadily fluctuated in an oblique impinging on a stretched surface theoretically and computationally. In addition, heat radiation and chemical reactions are taken into account in this work. The flow is composed of a uniform shear flow parallel to the sheet surface and a stagnation‐point flow. Assuming a linear variation in surface temperature, the sheet is extending at a velocity proportionate to the distance from the stagnation point. In terms of partial differential equations, the boundary‐layer regime under discussion is modeled. The nondimensional ordinary differential equations were developed using appropriate similarity variables via a similarity transformation approach. The most effective and powerful too of the numerical approach, known as the pseudospectral collocation technique, is used to solve the micropolar flow model problem. The velocity, angular velocity, temperature, and concentration profiles are portrayed through graphs. Moreover, the impression of the input values on the wall drag coefficient, thermal, and solutal transfer rate are computed in a table. A table is used to compare the numerical findings with the results found in the literature to verify the correctness of the results. It is noted that there is great agreement between the found answer and the earlier investigations. Graphs are used to show the impacts of the relevant factors in the problem, which include the magnetic parameter, the impinging angle heat transfer characteristics, the Prandtl number, the Lewis number, Brownian motion, and the thermophoresis parameter.

Combined fluid and ferrofluid buoyancy force, heat absorption and non linear ferro-viscosity effects on ferro- hydrodynamics fluid flow in orthogonal porous surface

Mixed convection incompressible ferro-hydrodynamic (FHD) boundary layer fluid flow on vertical porous curvilinear orthogonal surfaces is examined in our present study in presence of combined fluid and ferro-fluid buoyancy force, nonlinear ferro-viscosity parameter, and heat absorption/generation effects. Design/Methodology/Approach: Types of Prandtl momentum and thermal boundary layer partial differential equations in a curvilinear system are converted into non-dimensional ordinary nonlinear differential equations (ODE) by introducing dimensionless velocities, temperature functions and similarity variable. Missing initial conditions are found by shooting method and solving the system of nonlinear ODEs by Runge-Kutta integration scheme of order six. With the help of MATLAB, the numerical solutions are graphically displayed in the forms of primary velocity profile, secondary velocity profile, and temperature profile. Three types of magnetic nano-ferrofluid are considered such as water-based ferrofluid (Taiho W-40), Hydrocarbon based ferrofluid (EMG-901) and kerosene-based ferrofluid (C1-20B) whose Prandtl numbers are 44.3, 79.3 and 128 respectively shown in Table 1. For kerosene based ferro-fluid, Table 3 presents the coefficient of skin friction and heat flux. Finding: The effects of combined fluid and ferrofluid buoyancy forces, nonlinear ferro-viscosity parameter, suction/injection, and heat absorption/generation parameters on the velocity and temperature profiles are investigated. Our physical interest is to calculate the local shearing stresses and the local heat flux at the surface. Finally, we have made comparisons of the results which are highlighted the validity of our numerical calculations adopted for the presence study.