Nonlinear Radiative Heat Flux Research Articles

3D-MHD mixed convection in a darcy-forchheimer maxwell fluid: Thermo diffusion, diffusion-thermo effects, and activation energy influence

In this article, the three-dimensional upper-convected Darcy-Forchheimer Maxwell (UCM) nanofluid flow over a stretching surface is analyzed to investigate the effects of activation energy, thermodiffusion, diffusion thermo, and magnetohydrodynamics (MHD) on heat and mass transfer. The energy equation incorporates a nonlinear radiative heat flux. Using similarity transformation, the nonlinear partial differential equations are reduced to ordinary differential equations, which are then solved using the well-known shooting technique via the fourth-order Runge-Kutta integration method. To validate our results, we also employ MATLAB's built-in function bvp4c. The impact of various parameters, such as activation energy, diffusion thermo, thermodiffusion, Brownian motion parameter, Prandtl number, thermophoresis parameter, and magnetic parameter, on velocity, temperature, and concentration is discussed both graphically and numerically. It is observed that the flow velocity decreases with an increasing magnetic field parameter. Additionally, higher values of the activation energy parameter reduce the nanoparticle concentration profile. The temperature and concentration exhibit opposite behaviors when thermodiffusion and diffusion thermo effects are enhanced.

Non-linear radiative second-grade nano fluid with sinusoidal magnetic force and arrhenius activation energy: A computational exploration

The goal of this work is to further improve our knowledge of the nonlinear radiative second-grade nano fluid flow boundary layer phenomena which is associated with an Arrhenius activation energy, a sinusoidal magnetic field, and a stretched peripheral with a heat source. The unsteady governing equations are transformed into a proper dimensionless arrangement, and then the explicit finite difference (EFD) method is applied to numerically calculate the equations. However, precise stability and convergence criteria have been developed to make the solution convergent. Along with the typical profile of other flow fields, the oscillatory forms of the velocity are shown. Tabular research has even demonstrated a relationship between the Nusselt number and other parameters, and graphical depiction has been used for regression and data prediction. The novel conclusions drawn from this research indicate that, in comparison to linear patterns, nonlinear radiative heat flux significantly raises (30.35 %) flow profiles with second-grade characteristics. Moreover, the heat transfer rates of second-grade Nano fluids are seen to be significantly influenced (35.14 %) by the sinusoidal magnetic component. When considering nonlinear thermal radiation, activation energy principles cause a major change (34.19 % more) in mass transmission, as high-temperature processes become an essential part of chemical reactions.

Flow of nanofluid past a radially stretching disk in an absorbent medium in company of multiple slips, nonlinear radiative heat flux and Arrhenius activation energy

AbstractAn investigation is carried out to analyze the flow, heat and mass transport phenomena of nanofluids over a disk stretched radially in a porous medium. Besides nonlinear radiative heat flux and Arrhenius activation energy, multiple slips are considered in this model. This ensures the novelty of the present research. The main goal of the current investigation is to explore the mutual impacts of nonlinear radiative heat flux, various slip factors and Arrhenius activation energy on flow, heat and mass transfers. The highly nonlinear central equations which are partial differential equations (PDEs) are transformed into nonlinear ordinary ones (ODEs) by employing suitable similarity alterations and then for finding the approximate numerical solutions, shooting technique with 4th order “Runge–Kutta method” are applied. The impact of a variety of parameters on “skin friction coefficient,” “Nusselt number,” “Sherwood number,” velocity of the fluid, heat and mass transfers are computed and presented graphically. It is interesting to observe that fluid velocity diminishes with the growing porosity, suction and velocity slip parameters. Nanofluid's temperature reduces for enhanced values of thermal slip parameter but for rising thermal radiation parameter, temperature is boosted up. Also, nanoparticle concentration diminishes for increasing values of mass slip parameter.

Entropy optimization on magnetized radiative bioconvective flow of Carreau-Yasuda hybrid CNTs through a spherical surface in a non-Darcian porous medium with activation energy

This work inspects entropy generation and heat transfer induced by a bioconvection slip flow of nonlinear radiative Carreau-Yasuda hybrid nanofluid (NF) over a convectively heated sphere. Activation energy for microbes is contemplated in order to comprehend its contribution toward flow features. The original partial differential equations (PDEs) are rendered non-dimensional through appropriate conversions, and the resulting PDEs are solved using the overlapping grid spectral collocation algorithm. The impact of diverse flow factors on flow profiles, entropy generation, skin friction, heat, mass, and motile microbes transport rates is analyzed. Key outcomes reveal that hybrid NF flow demonstrates a supplementary indispensable feature in the operation of heat transport compared to mono NF flow. More entropy is generated in the system by using the hybrid NF model along with magnetic field, heat source, convective heating, nonlinear radiation, and viscous dissipation. Thermal fields and rate of heat transport are improved by including nonlinear radiative heat flux in the system. Mass and motile microbes transport rates are respectively enhanced by chemical and microbial reactions, but both quantities are reduced by activation energy. The effects of microbial reactions on flow quantities substantiate the significance of these features for the dynamics of microorganisms. The findings of this study can be useful in the upsurge of thermal performance of the working fluid and contribute toward the improvement of microbial fuel cell performance.

Three-dimensional MHD Mixed Convention Upper Convective Flow of Maxwell Fluid Throughout the Past in Thermophoresis and Brownian Motion with the Effects of Diffusion Thermo and Thermal Diffusion Utilizing Nonlinear Radiative Heat Flux

This article aims to investigate the impact of nanoparticles and magnetohydrodynamics (MHD) on the transfer of heat and mass using a three-dimensional upper-convected Maxwell (UCM) nanofluid flow across a stretched surface. A nonlinear radiative heat flow was included in formulating the equation that describes energy. The nonlinear partial differential equations of the issue are transformed into ordinary differential equations utilizing the similarity transformation. These equations are then solved using the well-known shooting approach in conjunction with the Runge-Kutta integration process of order four. To increase the dependability of our findings make use of the MATLAB. On the velocities, temperatures, and concentrations of the particles, the graphical and numerical representations of the effects of the main parameters, such as the Dufour parameter, the Brownian motion parameter, the Prandtl number, the thermophoresis parameter, and the magnetic parameter, are presented. It has been shown that the flow velocity decreases as a function of both the linear and nonlinear thermal radiation parameters. In addition, increasing values of the Brownian motion parameter have the effect of reducing the nanoparticle concentration profile, the same behavior has observed in the case of thermal diffusion and Diffusion thermo parameters.

Numerical Investigation of Diffusion Thermo, Hall Current, Activation Energy and Soret of MHD Darcy-Forchheimer Casson Fluid Flow with Inclined Plates

The present article is about the study of Darcy-Forchheimer flow of Casson fluid over a linear stretching surface. Effects like variable Hall current, Diffusion thermo, activation energy and Soret, is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs) with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs) with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method. The impact of different physical parameters like Activation energy, Diffusion thermo, Brownian motion, thermophoresis parameter, hall current, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that the fluid velocity and concentration profile enhance with increasing hall parameter and Activation energy respectively.

Effects of nonlinear thermal radiation on magnetized - nanofluid flow through an inclined microporous channel: An investigation of second law analysis.

This study aimed at studying the variational effect of nonlinear thermal radiation on the flow of Casson nanofluid ( ) through a porous microchannel with entropy generation. The novelty of this investigation includes the incorporation of porous media, nonlinear radiative heat flux, and convective heat transfer at the channel interface into the energy equation, which results in an enhanced analysis for the cooling design and heat transfer of microdevices that utilize nanofluid flow. Particularly, alumina ( ) is considered as the nanoparticles in this blood base fluid due to associated advanced pharmaceutical applications. With dimensionless variables being utilized, the governing equationsare minimized to their simplest form. The Chebysev-based collocation technique was employed to numerically solve the resultant ordinary differential equations with the associated boundary conditions and the impact of flow, thermal, and irreversibility distribution fields are determined through graphs. The findings identified that higher levels of Hartmann number produce the Lorentz force, which limits fluid flow and lowers velocity, the response of nonlinear thermal radiation diminishes the heat transfer rate, and a rise in the Casson parameter also reduces the Bejan number. The results of this research can be used to improve heat transfer performance in biomedical devices, design-efficient energy conversion cycles, optimize cooling systems, and cover a wide range of energy technologies from renewable energy to aerospacepropulsion.

Falkner-Skan aspects of a radiating (50% ethylene glycol + 50% water)-based hybrid nanofluid when Joule heating as well as Darcy-Forchheimer and Lorentz forces affect significantly

Falkner-Skan aspects are revealed numerically for a non-homogeneous hybrid mixture of 50% ethylene glycol-50% water, silver nanomaterials Ag, and molybdenum disulfide nanoparticles MoS2 during its motion over a static wedge surface in a Darcy-Forchheimer porous medium by employing the modified Buongiorno model. The Brownian and thermophoresis mechanisms are included implicitly along with the thermophysical properties of each phase via the mixture theory and some efficient phenomenological laws. The present simulation also accounts for the impacts of nonlinear radiative heat flux, magnetic forces, and Joule heating. Technically, the generalized differential quadrature method and Newton-Raphson technique are applied successfully for solving the resulting nonlinear boundary layer equations. In a limiting case, the obtained findings are validated accurately with the existing literature outcomes. The behaviors of velocity, temperature, and nanoparticles volume fraction are discussed comprehensively against various governing parameters. As crucial results, it is revealed that the temperature is enhanced due to magnetic field, linear porosity, radiative heat flux, Brownian motion, thermophoresis, and Joule heating effects. Also, it is depicted that the hybrid nanoliquids present a higher heat flux rate than the monotype nanoliquids and liquids cases. Moreover, the surface frictional impact is minimized via the linear porosity factor. Furthermore, the surface heat transfer rate receives a prominent improvement due to the radiative heat flux inclusion.

MHD 3D Mixed Upper Convective Flow of Maxwell Nanofluid Flow Past in the Presence of Diffusion Thermo and Thermophoresis Effect using Nonlinear Radiative Heat Flux

This article aims to investigate the impact of nanoparticles and magnetohydrodynamics (MHD) on the transfer of heat and mass using a three-dimensional upper-convected Maxwell (UCM) nanofluid flow across a stretched surface. A nonlinear radiative heat flow was included in formulating the equation that describes energy. The nonlinear partial differential equations of the issue are transformed into ordinary differential equations utilizing the similarity transformation. These equations are then solved using the well-known shooting approach in conjunction with the Runge-Kutta integration process of order four. To increase the dependability of our findings, make use of the MATLAB. On the velocities, temperatures, and concentrations of the particles, the graphical and numerical representations of the effects of the main parameters, such as the Dufour parameter, the Brownian motion parameter, the Prandtl number, the thermophoresis parameter, and the magnetic parameter, are presented. It has been shown that the flow velocity decreases as a function of both the linear and nonlinear thermal radiation parameters. In addition, increasing values of the Brownian motion parameter have the effect of reducing the nanoparticle concentration profile

Model-based comparison of hybrid nanofluid Darcy-Forchheimer flow subject to quadratic convection and frictional heating with multiple slip conditions

Hybrid nanofluids provide several advantages over conventional fluids, including improved thermal characteristics, increased stability, customizable features, multifunctionality, and environmental advantages. Hybrid nanofluids are an appealing alternative for a variety of applications due to these benefits. This study aims to compute the non-similar solution of single-multi wall carbon nanotubes (SWCNTs-MWCNTs)-based hybrid nanofluid flow over an inclined extending surface. Heat transmission and flow are observed under the effects of quadratic convection, Darcy-Forchheimer quadratic drag forces, viscous dissipation, and non-linear thermal radiative heat flux. The velocity and thermal slip constraints are imposed at the inclined surface. For the model-based comparison, Xue, and Modified Hamilton Crosser thermal conductivity models for carbon nanotubes (CNTs) are adopted. The irreversibility of the system is also investigated using the second law of thermodynamics for the distinct CNTs-based thermal conductivity models. Non-similarity variables are adopted to convert nonlinear partial differential equations into dimensionless PDEs. Analytical modeling of non-similar systems is done by adopting non-similarity transformations up to second-level truncation, and the bvp4c technique is then used to compute the results numerically. The research found that at 75° of plate inclination, the Modified Hamilton Crosser model for CNTs outperforms the Xue model in terms of heat transfer rate. Further, entropy generation is significantly larger for the Xue model than for the Modified Hamilton Crosser model for CNTs against higher values of viscous dissipation and porosity parameters. It is also revealed that for opposing buoyancy force G R < 0, the temperature of the fluid escalates. This study possesses multiple applications including petroleum engineering, heat exchangers, environmental remediation, and biomedical applications.

Biomedical and engineering aspects of nonlinear radiative peristaltic transport in chemically reactive blood flow of Ellis nanofluid in an asymmetric channel with activation energy

• Here peristaltic transport phenomenon is examined via asymmetric channel. • Ellis fluid model is utilized for the flow behavior. • Streamlines is presented. • Nonlinear radiative heat flux is used in energy expression. In the recent couple of decades, a momentous curiosity has been established in reviewing a peristaltic transport due to its noteworthy utilizations in biomathematics, biomedical engineering and biosciences. Peristaltic phenomenon is a significant mechanism of peristaltic pumps and physiological phenomenon. With the development of clinical and medical sciences, it has been demonstrated that the physiological materials don't act like Newtonian materials. Thus, in order to comprehend the salient characteristics of physiological materials (fluids) during peristalsis, the choice of suitable fluid model is important. In the present research letter, effects of heat and mass transport is addressed in flow of Ellis fluid nanofluid via asymmetric channel. The nonlinear radiative effects are imposed to studying the heat transfer transport. Features of activation energy is considered in the modeling of concentration equation. The governing expressions of proposed model is followed under the assumptions of small Reynolds number hypothesis and long wavelength. To investigate the salient characteristics of flow features and heat and mass transport, analytical solutions have been obtained for the velocity, temperature, pressure gradient and concentration. The obtained outcomes is presented through graphically and discussed in details physically. Furthermore, streamlines is sketched for different parameters. The current theoretical attempt discloses various motivating performance that warrant further investigation on different Newtonian as well as non-Newtonian materials. It is observed from the current flow analysis that the impact of slip factor highlights reverse behavior on the channel wall whereas the impact of Prandtl and Schmidt number respectively on the temperature and concentration equations have a decreasing and increasing trend.

Effects of Hall Current, Activation Energy and Diffusion Thermo of MHD Darcy-Forchheimer Casson Nanofluid Flow in the Presence of Brownian Motion and Thermophoresis

The present article is about the study of Darcy-Forchheimer flow of Casson nanofluid over a linear stretching surface. Effects like variable Hall current, activation energy, Diffusion thermo is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs) with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs) with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method. The impact of different physical parameters like Activation energy, Diffusion thermo, Brownian motion, thermophoresis parameter, hall current, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that the fluid velocity and concentration profile enhance with increasing hall parameter and Activation energy respectively.

Combined impacts of low oscillating magnetic field and Shliomis theory on mono and hybrid nanofluid flows with nonlinear thermal radiation

Hybrid nanofluids have become a popular choice for various engineering and industrial applications due to their advanced properties. This study focuses on investigating the consequences of a low oscillating magnetic field on the flow of unsteady mono and hybrid nanofluids over a vertically moving permeable disk. Initially, iron oxide nanoparticles are mixed with water to create a mono nanofluid, which is later transformed into a hybrid nanofluid by adding cobalt nanoparticles. The shape of nanoparticles used is brick-shaped, and an external magnetic field is applied to regulate the flow and heat transfer mechanism using ferromagnetic nanoparticles. Additionally, the nonlinear thermal radiative heat flux is considered for the heat transfer phenomenon. The momentum and rotational motion of the magnetic fluid caused by the rotating disk are formulated using the Shliomis fundamental concept. The numerical analysis of the ordinary differential equations (ODEs) is carried out using the bvp4c technique, and the results are presented in tabular form for the surface drag coefficient and heat transmission at the walls. Moreover, the temperature and velocity distributions are illustrated using graphical representations against relevant parameters. The findings highlight that for a constant negative value for the magnetization parameter the heat transfer rate for hybrid nanofluid is witnessed stronger at a volume fraction whereas a minimal heat transfer rate is observed for positive values of magnetization parameter at the same value of volume fraction.

Bioconvective radiative unsteady Casson nanofluid flow across two concentric stretching cylinders with variable viscosity and variable thermal conductivity

The role of variable viscosity and variable thermal conductivity in nanofluid flows is significant, as they can strongly influence the flow behavior and heat transfer performance of nanofluids. Keeping in mind the importance of these effects of variable characteristics, our motivation in this study is to investigate the role of nonlinear radiative heat flux on unsteady Casson nanofluid flow across two concentric stretched cylinders in the presence of temperature-dependent viscosity and thermal conductivity. A convective condition on the inner cylinder wall is also considered. In addition, the nanofluid is immersed with microorganisms that can swim and move independently. The addition of microorganisms has a significant role in the stability of the nanofluid flow. The influence of thermophoresis and Brownian motion on the flow, heat, mass, and microorganisms are scrutinized by employing the Buongiorno model. The governing flow equations are converted into a system of differential equations engaging similarity transformations, and the bvp4c method is employed to solve it numerically. Engineering parameters are computed and tabulated numerically. The findings demonstrate that as the unsteadiness parameter upsurges, the radial profile intensifies while the axial profile diminishes near the outer cylinder surface. It is also comprehended that both Lewis and bioconvective Lewis numbers reduce the motile density profiles. The accuracy of the presented model is also given in a graphical illustration by comparing it with a published result in a limiting case.

Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability

This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. The Brinkman-Forch-heimer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant injection, heat sources and nonlinear radiative heat flux of the Rossland approximation are accounted for. The nonlinear system of partial differential equations governing the velocity, temperature and pollutant concentration is presented in non-dimensional form. A convergent numerical algorithm is formulated using an upwind scheme for the convective part and a conservative-type central scheme for the diffusion parts. The convergence of the scheme is discussed and verified by numerical experiments both in the presence and absence of suction. The scheme is then used to investigate the flow and transport in the channel. The results show that the velocity decreases with increasing suction and Forchheimer parameters, but it increases with increasing porosity.

Non-linear radiative heat flux of Williamson nanofluid with gyrotactic microorganisms, activation energy and bioconvection

Gyrotactic microorganisms and nanoparticles with bioconvection play an important mantle in heat exchanger, biosensors, cooling devices, biotechnology, heating, pharmaceutical, drying food and many more. The main objective and novelty of this study is to compute the numerical solutions for the transient bioconvection flow of non-Newtonian Williamson nanofluid over a permeable contracting/expanding cylinder under the effects of Arrhenius activation energy and gyrotactic microorganisms. Additionally, binary chemical reactions and nonlinear radiation aspects are considered. Furthermore, Buongiorno nanofluid model and revised nanofluid model are utilized to investigate heat and mass transportation. Numerical solutions of highly nonlinear ordinary differential system are developed through RK45 scheme. It is interesting to investigate that motile number is an enhancing function of bioconvection Lewis number but reverse trend is noticed for higher estimation of Peclet number and microorganisms difference parameter in both cases of stretching and shrinking cylinder.

Numerical heat performance of TiO2/Glycerin under nanoparticles aggregation and nonlinear radiative heat flux in dilating/squeezing channel

ApplicationsNewly developed fluids termed as “Nanofluids” and their study in dilating/squeezing channel cannot be disregarded. Such flows under various physical constraints are important for purification purposes and other industrial applications. Purposeand Methodology: This work comprises the modeling and heat transmission ability of TiO2/G inside a dilating/squeezing channel. The conventional model upgraded including the aggregation effects of nanoparticles and directed nonlinear thermal radiations. The resultant model examined through numerical scheme for actual understanding the heat transport phenomena inside the channel. Major findingsThe results reveal that high viscosity parameter (R1=0.5,1.0,1.5,2.0), porous absorber walls and strong surface-surface interaction due to aggregation of nanoparticles significantly control the fluid movement. The pores at the surface (A1=0.1,0.3,0.5,0.7) attract the fluid particles and strong frictional forces between them resists the motion and is rapid for aggregated nanofluid. Further, thermal radiations (Rd=1.0,1.5,2.0,2.5) produce considerable heat which can be used to breakdown the aggregation between the nanoparticles.

Intelligent computing for entropy generation in Jeffrey nanofluid through radiated flow

This study explores the Entropy generation in the Flow of Jeffery Nanomaterial Model (EFJNM) past a variable thicked surface by considering joule heating effect, convectively heated surface, nonlinear radiative heat flux, and convective boundary conditions via Artificial Back Propagated Levenberg Marquardt Neural Networks (ABP-LMNNs). The ODEs system is obtained by implementing suitable transformation on PDEs for EFJNM. Applying homotopy analysis method (HAM) to create dataset for ABP-LMNNs by the variation of physical parameters of EFJNM. The reference datasets are then segmented in validation/training/testing process to scrutinize the approximated solution for EFJNM and further to compare it with standard solution. The better performance is further investigated by MSE based curves, regression fitting, absolute error, error histogram analysis. Results reveals that performance in form of MSE is in ranges of 10−9, 10−11, 10−9, 10−9, 10−10, 10−9, 10−10, 10−9, and 10−10 with 494, 285, 496, 219, 71, 167, 194, 121, 179, and 738, respectively, for all scenarios. The impact of variants of EFJNM on velocity, entropy production rate, temperature, and concentration are also analyzed. As the entropy generation increase with the increment in Deborah number and Brinkman number. The velocity increases with the escalation in Deborah number and wall thickness variable whereas decreases with the increase in relaxation to retardation ratio. The absolute errors of effective parameters for velocity are 10−7-10−4, 10−7-10−3, 10−7-10−4, and 10−6-10−3, the absolute errors for temperature are 10−7-10−3, 10−7-10−3, and 10−7-10−4 whereas the absolute errors for concentration are 10−8-10−4, 10−8-10−3, and 10−8-10−4, which show the accuracy of proposed ABP-LMNNs. Abbreviations: ABP-LMNNs, Artificial back propagated Levenberg Marquardt Neural Networks; EFJNM, Entropy generation in the Flow of Jeffery Nanomaterial Model; HAM, Homotopy analysis method

Nonsimilar solution of a boundary layer flow of a Reiner–Philippoff fluid with nonlinear thermal convection

AbstractThe thermodynamics modeling of a Reiner–Philippoff‐type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear‐thinning, Newtonian, or shear‐thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature‐ and concentration‐induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral‐based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature‐dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer.

Implications of the third-grade nanomaterials lubrication problem in terms of radiative heat flux: A Keller box analysis

Steady flow of non-Newtonian nanofluid impinging on a vertical lubricated surface is numerically investigated. The rheological behaviour of the base fluid is characterized by the constitutive equation of third-grade fluid and the power-law fluid model is used for lubricant. Higher-order chemical reaction and nonlinear radiative heat flux are also taken into account. The governing nonlinear partial differential equations are simplified using the Prandtl boundary layer theory and similarity transformations. An efficient and accurate implicit finite difference method is applied to approximate the resulting nonlinear coupled differential equations with complicated boundary conditions for several values of parameters of interest. The velocity, temperature, nanoparticles concentration profiles Nusselt number, and streamlines are illustrated through graphs for full slip and no–slip case as well as assisting and opposing flow cases. The temperature and concentration profiles are also described for linear and non-linear thermal radiation and for different order chemical reactions. The numerical results are compared with the existing literature and found good agreement. It is found that heat and mass transfer rates reduces over the lubricated surface compared with the rough surface.