Nonlinear Radiation Parameter Research Articles

Impact of non-linear radiation on magneto - Casson fluid suspended hybrid nanomaterials in sodium alginate: Smarter textiles

BackgroundThe combination of sodium alginate (SA) and nanoparticles in Casson nanofluids can have several advantages in textile applications such as to enhance the dye absorption and finishing properties and uniform and controlled coatings on complex shapes of the fabric and garments with intricate designs or three-dimensional textile structures etc. These fascinating properties attracted us to work on this article, a Casson hybrid nanoflow under the influence of magnetic effects past a curved stretching surface. Key terms & problem definitionThis study examines the heat transfer characteristics of Casson nanofluid flow over a stretching sheet with nonlinear thermal radiation and convective boundary conditions. A Casson fluid is a non-Newtonian fluid that exhibits a yield stress, meaning it behaves like a solid below a certain shear stress. Nonlinear thermal radiation accounts for the effects of temperature-dependent radiative heat transfer. Convective boundary conditions simulate the heat exchange between the fluid and a surrounding environment. The nanoflow has its base fluid as Sodium Alginate (SA) and a mixture of Silver (Ag) and Titanium oxide (TiO2) is suspended in the fluid. MethodologyThe nanoflow model is cracked numerically employing Runge-Kutta Fehlberg technique along with shooting method. Results of flow affecting parameters on the flow characteristic quantities and engineering quantities are portrayed and presented through graphs and tables. Key findingsHybrid Nanoflow momentum decreases with an increase in the Casson parameter due to the yield stress which quite helps in the controlled and complex shape printing on the garments. The temperature of the nanofluid increases with an increase in nonlinear radiation parameter. In the presence of Ag and TiO2 nanoparticles, the non-linear radiation parameter becomes essential for managing their intricate impact on heat transfer within the fabric. Practical relevanceImproved heat transfer can significantly reduce drying times, leading to increased productivity. More efficient heat transfer can reduce energy consumption. Reduced viscosity can allow for better penetration of fluids into fabrics, leading to more uniform dyeing and finishing. Casson hybrid nanofluids can accelerate the dyeing process and improve colour uniformity. Casson hybrid nanofluids can be used in finishing processes to enhance wrinkle resistance and improve fabric appearance.

Non-similar solution of Casson fluid flow over a curved stretching surface with viscous dissipation; Artificial neural network analysis

PurposeThe main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.Design/methodology/approachThe non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.FindingsThe results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.Originality/valueAI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

Simulation of micropolar fluid flow with ternary nanoparticles over a permeable stretching surface involving nonlinear thermal radiation

ABSTRACT The primary goal of this research is to look into the rheological aspects of blood flow that contains ternary nanoparticles ( C u O + T i O 2 + A l 2 O 3 ). For this, the micropolar fluid model is adopted to simulate blood flow transport. Inclined magnetization and porosity characteristics are used to reveal the momentum attributes of flowing fluid, and nonlinearized radiating thermal flux is used to predict the thermal characteristics of the concerned flow. Further, the aspects of suction and injection of fluid over a permeable stretching sheet are also acknowledged. Governing system of partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformation. An effective built-in routine known as bvp4c, which is based on finite differencing, is used to acquire the solution. The results showed that the trihybrid nanofluid significantly boost fluid motion and temperature profiles more in the mass injection effect in comparison to suction phenomena. The increase in heat transfer rate is also noticed for augmented values of non-linear radiation parameter and micropolar parameter. There is a detailed discussion of the effects of the contributing parameters on the resulting dimensionless profiles. This research has significant implications for the delivery of magnetized blood, hyperthermia therapy, understanding of the bloodstream, transfer of complex bio-waste liquids, and capillary heat exchange.

MHD slip effects on (50:50) hybrid nanofluid flow over a moving thin inclined needle with consequences of non-linear thermal radiation, viscous dissipation, and inclined Lorentz force

Due to their enormous implementation in engineering scrupulous, hybrid nanofluids have become a prevailing substance of consideration in mathematical and physical research. The augmentation of thermal conductivity is an exclusive emphasis of hybrid nanofluids. The fluid prototype substance probing in the existing study is the Ethylene Glycol–water (50:50) as base fluid and a mixture of nanoparticles are magnetic (Fe3O4) and non-magnetic (Al2O3) hybrid nanofluid. It is found in heat transfer and cooling in electronic devices, engines, refrigerants, energy storage and the automotive industry. To obtain solutions, the Partial Differential Equations with slip boundary conditions that describe the flow are converted into Ordinary Differential Equations with appropriate transformations using a numerically based technique known as the fourth-order Runge–Kutta method with shooting techniques. The illustration diagram of the gained outcomes accentuates the consequence of numerous physical variables on the flow dynamics in relation to fluid momentum, and thermal silhouette. Also, the consequence of heat transfer rate and surface drag force in multiple variables like Eckert number, magnetic variable, and radiation constant, are tabulated. These studies explain the decline in the thermal outline of hybrid nanofluid under slip situations when upsurges the non-linear radiation parameter. By analyzing these studies of hybrid nanofluids, it is possible to improve heat transfer efficiency and control temperature gradients in systems where nonlinear thermal radiation and viscous dissipation are important factors.

Non-similar solution of mixed convection flow of viscous fluid over curved stretching surface with viscous dissipation and entropy generation

The non-similar solution of a viscous fluid caused by a curved stretching surface with a convective boundary condition is considered in this article. The momentum equation is modified by considering the effects of MHD and mixed convection. The energy equation is modeled as subjected to joule heating and thermal radiation effects. The independent variable "s" is present in the Eckert and Grashof numbers, which is incompatible with dimensionless parameters. In this regard, a non-similar technique is used to tackle the problem. The non-similar approach has not been tried on a curved stretching surface. Moreover, the entropy rate is discussed under these observations. The non-similarity transformation is used to convert the modeled governing equations into dimensionless PDEs. A local non-similarity method is employed for the conversion of PDE’s into ODE’s, and the numerical solution of the resulting equations is obtained via bvp4c. The novelty of the problem is that when the thermal radiation, Hartman number, and Brinkman number increase, the entropy generation increases. The Bejan number increases with the Hartman number and thermal radiation, while the Brinkman number shows the opposite behavior in boundary layer. The nonlinear radiation parameter increases the thermal profile while reverse tends noticed for the entropy generation and Bejan number. The behaviors of velocity and temperature profiles are discussed graphically for the different parameters. Physical quantities like heat transfer rate and drag force are presented in tabular form.

Analysis of viscously dissipated three-dimensional flow of Williamson fluid with nonlinear radiation and activation energy

The main purpose current exploration is to examine the influence of viscous dissipation and nonlinear radiation in three-dimensional (3D) Williamson fluid flow on an exponentially stretching through porous medium with the effect of activation energy along with chemical reaction. By employing suitable transformation, the nonlinear partial equations (PDEs) are transmuted to nonlinear ordinary differential equations (ODEs) which are subsequently solved numerically by using Range-Kutta method with shooting technique by utilization Matlab script. Characteristics of resulting physical parameters appearing in modeling like the Weissenberg number, Prandtl number, nonlinear radiation parameter, porosity parameter, Eckert number and chemical reaction parameter are comprehensively analyzed in graphical forms with an interest in providing the physical meaning to each parameter. The outcomes anticipate that, the thermal profile is improved by the increase in the values of nonlinear radiation parameter due to inner heat. The thermal profile enhances by strengthening of Eckert number but it has opposite trend through Prandtl number. The impact of obtained parameters on skin friction coefficient, mass and heat transfer rates is illustrated by tables. The validity of the present findings is presented by comparing them with the previous investigations.

A significant study on radioactive cross fluid model with melting boundary near stagnation region

The current research endows the mathematical modeling for the stagnation point flow along with melting nonlinear radiative heat transfer for cross fluid. It has many applications such as synthesis of polymer solutions, plastic manufacturing, food processing, preparation of synthesis, adhesives, etc. A radially stretching sheet has started the flow keeping the assumption of rotational symmetry. Transformation approach is adopted to attain the nonlinear ordinary differential equations based on standard conservation laws of mass, linear momentum and also energy. Numerical solutions of the governing problem are computed via the shooting technique. Characteristics of the parameters appearing in modeling like the melting parameter, power–law index, local Weissenberg number, nonlinear radiation parameter, temperature ratio parameter and Prandtl number are comprehensively analyzed through graphical behavior. In addition, comparative analysis is presented for the cases when the value of free stream velocity overtops the stretching velocity and vice versa. Results are authenticated by taking special cases and excellent compatibility is achieved with the existing literature. The detailed analysis anticipates that the boundary layer structures could be strengthened by growing the melting parameter. Elevation in Weissenberg number caused velocity along with temperature profiles to demonstrate for [Formula: see text]. Further, the temperature behaves oppositely analogous to development in nonlinear radiation parameter besides the temperature ratio parameter.

Non‐Darcy‐Forchheimer flow of Casson‐Williamson nanofluid on melting curved stretching sheet influenced by magnetic dipole

AbstractUsing a non‐Darcy‐Forchheimer model with nonlinear thermal radiation, homo‐heterogenic reactions, Joule heating, exponential heat propagation, suction/injection, and melting heat peripheral conditions, the mathematical possibility of Casson‐Williamson nanofluid flow carried over a magnetic dipole‐enabled curved stretching sheet has been considered. Using similarity catalysts, the complex partial differential equations needed to display the given flow are transformed into more manageable ordinary differential equations. The Runge‐Kutta‐Fehlberg (RKF) 4–5th order tool has been used to draw solution graphs. Each graph has been analyzed in depth and commented on. The research shows that the inverse Darcy parameter and the suction/injection parameter have a detrimental effect on velocity distribution. In addition, the investigation showed that the nonlinear radiation parameter and the melting parameter had contradictory effects on the thermal profile. As a value addition, the flow and temperature distribution have been shown graphically using streamlines and isotherms. Therefore, considered flow over curved geometry is very new with cutting‐edge results which are useful in further research in the field.

Influence of nonlinear radiation on MHD nanofluid flow over a cone with second‐order velocity and thermal slips: A numerical study

AbstractThis computational study discovered the influence of magnetohydrodynamics nanofluid flow over a vertical cone. The nonlinear form of thermal radiation and irregular heat generation/sink takes an active part in this study. The influences of chemical reactions and second‐order slip parameters (velocity and temperature) are taken into account. Copper nanoparticles were mixed with water as base fluid in the present investigation. The leading partial differential equations which model the flow are altered as a set of nonlinear ordinary differential equations by means of self‐similarity alterations and then a numerical solution is cultivated with the support of fourth order Runge–Kutta Fehlberg method with the shooting method. The influence of appropriate parameters such as nonlinear radiation, chemical reaction, and slip parameters (velocity and temperature) on common fields (concentration, temperature, and velocity) are visualized through graphs. Also, we have analyzed the effects of identical parameters on the coefficient of skin friction and rate of transfer (mass and heat) by means of tables. The skin friction coefficient is boosted when the magnetic parameter is incremented. For larger values of nonlinear radiation parameter , the rate of heat transfer was reduced.

Entropy generation analysis for mixed convective flow of Casson fluid in a vertical microchannel with the influence of nonlinear radiation by maintaining inconstant viscosity

AbstractThe study of entropy generation in the fluid flow has great importance in the field of engineering. The present analysis is to investigate the entropy production in Casson fluid flow in a vertically placed porous‐filled microchannel. The flow is influenced by the nonlinear radiation and exponential heat source. Viscosity is kept varying throughout the flow. The equations which govern the considered flow are nonlinear and are nondimensionalized by considering the appropriate nondimensional variables. The flow problem is tackled by converting the ordinary differential equation (ODE) by assigning the new variables. The flow problem is tackled by using the effective mechanism which involves the finite difference technique by converting the equations into a set of first‐order ODE. The results attained are discussed using the graphs. It is noted that by maintaining the lesser values for the Casson parameter and mixed convection parameter, entropy production can be reduced. The Bejan number profile has the highest magnitude for the variation of mixed convection parameter and the same is found to be less for the nonlinear radiation parameter.

MHD CASSON NANOFLUID FLOW OVER A STRETCHING SURFACE EMBEDDED IN A POROUS MEDIUM: EFFECTS OF THERMAL RADIATION AND SLIP CONDITIONS

This article presents a numerical study for a magnetohydrodynamic flow of a non-Newtonian Casson nanofluid over a stretching sheet embedded in a porous medium under the impacts of non-linear thermal radiation, heat generation/absorption, Joule heating and slips boundary conditions. A two-phase nanofluid model is applied to represent the nanofluid mixture. The porous medium is represented via the Darcy model. A similar solution is obtained for the governing equations and a numerical treatment based on the Runge-Kutta method is conducted to the resulting system of equations. In this study, the controlling physical parameters are the Casson fluid parameter , the magnetic field , the radiation parameter , the Brownian motion parameter and the thermophoresis parameter . The obtained results reveal that an increase in the Casson parameter enhances both of the local Nusselt and the Sherwood number while they are reduced as the non-linear radiation parameter increases. In addition, an increase in the magnetic field parameter supports the skin friction coefficient regardless the value of the Casson parameter.

Numerical Investigation of Mixed Convective Williamson Fluid Flow Over an Exponentially Stretching Permeable Curved Surface

The present investigation aims to examine the heat flux mechanism in the hagnetohydrodynamic (MHD) mixed convective flow of Williamson-type fluid across an exponential stretching porous curved surface. The significant role of thermal conductivity (variable), non-linear thermal radiation, unequal source-sink, and Joules heating is considered. The governing problems are obtained using the Navier–Stokes theory, and the appropriate similarity transformation is applied to write the partial differential equations in the form of single-variable differential equations. The solutions are obtained by using a MATLAB-based built-in bvp4c package. The vital aspect of this analysis is to observe the effects of the curvature parameter, magnetic number, suction/injection parameter, permeability parameter, Prandtl factor, Eckert factor, non-linear radiation parameter, buoyancy parameter, temperature ratio parameter, Williamson fluid parameter, and thermal conductivity (variable) parameter on the velocity field, thermal distribution, and pressure profile which are discussed in detail using a graphical approach. The correlation with the literature reveals a satisfactory improvement in the existing results on permeability factors in Williamson fluids.

Transportation of hybrid nanoparticles in forced convective Darcy-Forchheimer flow by a rotating disk

This research article explores the effect of entropy generation through a non-linear radiative flow of viscous fluid of hybrid nanoparticles over a stretchable rotating disk. Mixed convection and slip conditions i-e velocities and thermal are examined. The examination is accomplished in aluminum oxide (Al2O3)-water and copper (Cu)-water nanofluids. Similarity transformations are utilized to reduce the governing problem into the nonlinear ordinary differential equations. Flow in the permeable medium is analyzed by assuming the Darcy-Forchheimer model. The impact of various parameters consisting of mixed convection parameter, porosity parameter, velocities as well as thermal slips parameters, stretching parameter, non-linear radiation parameter, and Reynolds number on radial velocity profile, tangential velocity profile and temperature profile are studied. Also, entropy generation and heat transfer rates have been analyzed in view of different parameters in the current study. The mathematical formulation is numerically solved by the bvp4c techniques

MATHEMATICAL MODELING AND NUMERICAL ANALYSES OF TRANSPORT PHENOMENA WITH VARIABLE CROSS-DIFFUSION AND NONLINEAR RADIATION

This study proposes a mathematical model and the numerical scheme, with rigorous stability and convergence analyses, for a channel flow problem incorporating a nonstandard variable cross-diffusion (Soret-Dufour effects), an unconventional nonlinear radiative heat flux, and time-dependent wall velocity and wall temperature. This led to a system of highly coupled nonlinear partial differential equations. Backward difference scheme is considered for time derivatives, while conservative-type central scheme is adopted for spatial derivatives. The nonlinear terms are discretized by freezing coefficients in discrete time. This resulted in an implicit-explicit algorithm for each nondimensional equation. To investigate the stability, we adopt the discrete maximum principle and derive two-sided estimates for the numerical solution. To establish convergence, we consider a general scheme that encompasses all three schemes, and prove convergence in the grid L2 norm. A problem with nontrivial source terms is used to confirm the theoretical results. Finally, the flow is investigated and the results showed that the nonlinear radiation parameter increased the fluid temperature.

Impact of Hall effect, nonlinear radiation and heat source on MHD Couette–Poiseuille flow of nanoliquid through a rotating channel

PurposeThis report offers the detailed investigation of Couette–Poiseuille flow of nanoliquid with varying viscosity. The analysis is carried out by considering flow between two parallel plates in a rotating permeable channel with the aid of nonlinear thermal radiation and Hall effect. The predominant equations governing the physical phenomenon are demonstrated using the Buongiorno model.Design/methodology/approachNumerical computation for the demonstrated physical problem is achieved through the implementation of the Runge–Kutta–Fehlberg fourth–fifth-order method along with shooting technique.FindingsThe theoretical view of Brownian motion, nonlinear radiation, Hall effect and thermophoresis parameter is presented graphically.Originality/valueIt is revealed that flow velocity increases with the upper wall motion parameter and magnetic field. Also, it is established that an increase in the Nusselt number is achieved for increasing values of nonlinear radiation parameter.

Convective heat transport in a heat generating MHD vertical layer saturated by a non-Newtonian nanofluid: a bidirectional study

PurposeIn this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of nonlinear thermal radiation and convective conditions.Design/methodology/approachInfinite shear rate viscosity impacts are invoiced in the modeling. The heat and mass transport characteristics are explored by employing the effects of a magnetic field, thermal nonlinear radiation and buoyancy effects. Rudimentary governing partial differential equations (PDEs) are represented and are transformed into ordinary differential equations by the use of similarity transformation. The nonlinear ordinary differential equations (ODEs), along with the boundary conditions, are resolved with the aid of a Runge-Kutta-Fehlberg scheme (RKFS) based on the shooting technique.FindingsThe impact of sundry parameters like the viscosity ratio parameter (β*), nonlinear convection parameters due to temperature and concentration (βT, βC), mixed convection parameter (α), Hartmann number (M2), Weissenberg number (We), nonlinear radiation parameter (NR), and the Prandtl number (Pr) on the velocity, temperature and the concentration distributions are examined. Furthermore, the impacts of important variables on the skin friction, Nusselt number and the Sherwood number have been scrutinized through tables and graphical plots.Originality/valueThe velocity distribution is suppressed by greater values of the Hartmann number. The velocity components in the tangential and axial directions of the fluid are raised with the viscosity ratio parameter and the tangential slip parameter, but these components are reduced with concentration to thermal buoyancy forces ratio and stretching sheet ratio.

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

ABSTRACTAn analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.

Non-linear radiative heat transfer analysis during the flow of Carreau nanofluid due to wedge-geometry: A revised model

In this article, an innovative revised Buongiorno's model is employed to investigate the flow of Carreau nanofluids generated by a wedge-shaped geometry. Moreover, heat and mass transfer characteristics are explored under the influence of non-linear thermal radiation. At first, the developed flow equations are made dimensionless via suitable transformations and then resulting set of nonlinear ordinary differential equations are solved numerically using built-in MATLAB solver bvp4c. It is observed that the solution of current flow problem is highly dependent on the contribution of several physical parameters like Weissenberg number, power-law index, wedge angle parameter, velocity ratio parameter, non-linear radiation parameter, suction parameter, Brownian motion and thermophoresis parameters, Lewis and Prandtl numbers. Detailed analysis for the novel results of dimensionless velocity, temperature and nanoparticles concentration with in the boundary layer region is exhibited graphically. The core physical implication of the computed results is that the thermal boundary layer is thinned by higher radiation parameter. This study reveals that an enhancement in the local Nusselt number is noted with higher temperature ratio parameter. On the other hand, an incremental skin friction ate the wall can be achieved by growing values of power-law index. The obtained data is distinguished with earlier studies and admirable agreement has been noted.

Heat generation/absorption and thermal radiation impacts on three-dimensional flow of Carreau fluid with convective heat transfer

The current article numerically investigates the three-dimensional flow and heat transport caused by a bidirectional stretching sheet. One phenomenal aspect of this review is to consider the impacts of infinite shear rate viscosity. For this reason, Carreau rheological model is accounted as a working liquid for the flow mechanism. In addition, heat transport features of the flow fields have been inspected by utilizing the impacts of magnetic field, thermal radiation and heat generation/absorption. We have incorporated the appropriate dimensionless transformations to alter the basic conservation equations into a set of partially couples ODEs. The associated system of reduced ODEs together with physical boundary restrictions are numerically integrated via versatile and extensively validated, Runge-Kutta Fehlberg method. The problem is governed by active physical parameters, such as, viscosity ratio parameter, Hartmann number, Weissenberg number, nonlinear radiation parameter, heat generation/absorption parameter, Biot number, Prandtl number and temperature ratio parameter. We exhibit and explain the impacts of these active parameters on dimensionless fluid velocity, fluid temperature, skin friction and Nusselt number by means of tables and graphs. From this study, it is observed that fluid velocity is depressed by higher Hartmann number, however, a reverse trend is noted for fluid temperature.

A review on slip-flow and heat transfer performance of nanofluids from a permeable shrinking surface with thermal radiation: Dual solutions

A computational study on the stagnation-point flow of an electrically conducting nanofluid over a non-linear stretching/shrinking surface with first-order slip phenomenon is carried out. Because, nanofluids are considered as one of the closest kinds to the practical application of fluid flows owing to its comprehensive properties such as the Brownian motion and thermophoresis. The simulations were performed to understand the heat and mass transfer traits in the presence of non-linear radiation. Moreover, the Rosseland approximation model is incorporated to investigate the mechanisms of radiative heat transfer performance of nanofluids. For all cases, it has been seen that the governing conservation equations of current model possesses a similarity solution. The transformed system of nonlinear ordinary differential equations, is then integrated numerically with a boundary value problem solver, bvp4c in Matlab software. The captured numerical results have been displayed graphically and some interesting features like multiple (upper and lower) solutions are found. The critical values corresponding to the suction parameter fw and the shrinking parameter λ are computed. The rising thermo-physical dimensionless parameters overseeing the flow are power-law parameter, Hartmann number, slip parameter, Eckert number, temperature ratio parameter, radiation parameter, Brownian motion and thermophoresis parameters and Lewis number. It is found that, the slip parameter has a reducing impact on the skin friction coefficient for both upper and lower branch solutions. The major outcome of the present study is that the temperature ratio parameter boosts the temperature profiles for both solutions. While the temperature profiles show a decreasing behavior for higher non-linear radiation parameter. Validation of numerical scheme is accomplished by means of benchmarking with some already reported studies, and a great correlation is illustrated.