Matlab Bvp4c Solver Research Articles

Carbon Nanotubes (CNTs) Nanofluids Flow and Heat Transfer under MHD Effect over a Moving Surface

The 2D steady flow of CNTs nanofluids and heat transfer over the moving plate through a uniform free stream under the effect of magnetohydrodynamics (MHD) is studied. The movement of plate is presumed in the opposite or same direction. A mathematical modelling that is governed by a system of partial differential equations (PDEs) subjected to boundary conditions is transformed into a system of nonlinear ordinary equations (ODEs). An attempt at finding the expected outcomes is successfully executed by solving ODEs system using MATLAB bvp4c solver. The effect of various parameters such as magnetic field, CNTs volume friction and moving parameter on velocity and temperature profile, skin friction, Nusselt number and heat transfer rate are investigated numerically. The results are presented using tabular and graphical illustration. From the results, the increment of magnetic field into the flow will increase in both the skin friction and the heat transfer coefficient. Besides that, non-unique solutions are obtained when the plate moves in the range of and . For comparing the performance of base fluid, kerosene works better than water as a base liquid. We are also showing that SWCNTs is more effective both in the skin friction and the heat transfer coefficient compare to MWCNTs.

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

AbstractMagnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self‐similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth‐order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.

Radiative transport of MHD stagnation point flow of chemically reacting Carreau nanofluid due to radially stretched sheet

The flow of Carreau nanofluid with generation/absorption and magnetic field can be valuable for modifying solar energy production. In this work, we extended the study of the MHD boundary layer flow of Carreau nanofluid with heat generation/absorption close to a stagnation point over the radially extending plate. Likewise, the features of radiation and magnetic field with convective boundary conditions are considered. Further, keeping in view the importance of chemical reactions, their effect is also incorporated during the modelling process. For motivation, the impact of thermophoresis and Brownian motion has been taken into account. Using appropriate similarity transformation, we converted nonlinear governing partial differential equations of Carreau nanofluid into a couple of nonlinear ODEs. Using a recognized shooting technique and the MATLAB bvp4c solver and Mathematica ND-solve built-in command, we were able to get numerical results for these modeled ODEs. Through graphs and tables, the effects of different physical parameters like magnetic, Weissenberg number, Brownian motion, thermal radiation, thermophoresis, Prandtl number, chemical reaction, and rate of heat generation/absorption on non-dimensional velocity, temperature, and concentration profile are discussed.

Impact of Thermal Radiation on MHD GO-Fe2O4/EG Flow and Heat Transfer over a Moving Surface

The heat transmission in a non-Newtonian hybrid nanofluid that combines particles of graphene oxide (GO) and iron dioxide (Fe2O4) with the base fluid chosen as ethylene glycol (EG) is analyzed, including the effects of radiation and magnetic influence. The hybrid nanofluid flow is assumed to be asymmetric because it flows along a horizontal shrinking surface in response to external inducements. The mathematically modelled partial differential equations (PDEs) form is then derived into ordinary differential equations (ODEs) by implementing a proper similarity transformation to the PDEs. The mathematical formulation is then algorithmically estimated employing the bvp4c solver in MATLAB. The parameters’ effects on the skin friction measurement, local Nusselt number, entropy generation, velocity profile, and temperature profile are investigated and explained. This finding illustrated that the skin friction is augmented between 13.7% and 66.5% with the magnetic field, velocity slips, and the concentration of GO particles. As for the heat transmission ratio, only thermal radiation and velocity slip effects will affect the heat upsurge with the range of 99.8–147% for taken parameter values. The entropy for the shrinking case is found to increase between 16.6% and 43.9% with the magnetic field, velocity slip, and Eckert number.

Darcy-Forchheimer flow of maxwell nanofluid flow over a porous stretching sheet with Arrhenius activation energy and nield boundary conditions

This work investigates the effect of heat transfer and mass transfer on the convective Darcy-Forchheimer flow of a Maxwell nanofluid through a linear porous stretched sheet. In addition, the impacts of chemical reaction, thermal conductivity, and thermophoresis are investigated. The analysis of heat and mass transfer in the presence of nanoparticles in a Maxwell fluid under convective and nield conditions is examined. To convert the governing PDEs of velocity, temperature and nano concentration with activation energy into a couple of nonlinear ODEs we apply the appropriate similarity variables. Shooting method is applied to solve the set of highly nonlinear ordinarily differential equations numerically and obtained numerical results are associated with those gained by the help of MATLAB bvp4c solver and Mathematica ND-solve built in command. The influence of prominent parameters of interest like chemical effusion, Prandtl number, Biot number, radiative heat flux Brownian motion, Lewis number, thermophoresis parameter, magnetic parameter, Reynolds number, thermophoresis parameter, on, non-dimension velocity, heat and nano concentration distribution has been deliberated and heat transfer features is also encompassed. The numerical values obtained for defined profiles are presented through graphs and tables.

Magnetized mixed convection hybrid nanofluid with effect of heat generation/absorption and velocity slip condition

Through a vertically shrinking sheet, a two-dimensional magnetic nanofluid is numerically analyzed for convection, heat generation and absorption, and the slip velocity effect. In this research, Al2O3–Cu/water composite nanofluid is studied, where water is deemed the base liquid and copper (Cu) and alumina (Al2O3) are the solid nanoparticles. Modern composite nanofluids improve heat transfer efficiency. Using the Tiwari-Das model, the current study examines the effects of the solid volume fraction of copper, heat generation/absorption, MHD, mixed convection, and velocity slip parameters on velocity and temperature distributions. Introducing exponential similarity variables converts nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). MATLAB bvp4c solver is used to solve ODEs. Results showed dual solutions for suction with 0%–10% copper nanoparticles and 1%–500% heat generation/absorption. As copper (Cu) solid volume percentage increases from 0% to 10%, reduced skin friction f″(0) boosts in the first solution but falls in the second. When Cu is added to both solutions, heat transport −θ′(0) decreases. As heat generation/absorption increases 1%–500%, −θ′(0) decreases in both solutions. In conclusion, solution dichotomy exists when suction parameter S≥Sci in assisting flow case, while no fluid flow is possible when S<Sci.

Computation of Stagnation Point Convection Flow of Carbon Nanotube Nanofluids From a Stretching Sheet With Melting: Dual Solutions

Abstract A theoretical study in stagnation point flow is presented where melting heat transfer effects of carbon nanotube (CNT) from a stretching surface is appeared. Both carbon nanotubes like single-wall CNT (SWCNT) and multiwall CNT (MWCNT) are homogeneously dispersed in the base fluid. As the ordinary (or base) fluids, water and kerosene oil are employed. A set of nonlinear ordinary differential equations with appropriate boundary conditions is formed by transforming the governing equations via similarity transformations. The transformed nonlinear ordinary differential equations are then solved numerically using the bvp4c solver in matlab, an efficient numerical finite difference method. The impact of nanoparticle volume fraction, velocity, melting, stretching parameter, and CNT type on transport characteristics are explored and visualized graphically and in tabular forms. Verification of the matlab computations with available data in certain limiting cases is included showing excellent agreement. Existence of dual (upper and lower branch) solution is shown for a certain range of stretching sheet parameter. The obtained dual solutions are examined for velocity and temperature in detail. A stability analysis demonstrates that the first solution is a stable solution, and the second solution is an unstable solution. Local skin friction and local Nusselt number are also computed in order to determine critical values that can permit dual solutions. It is observed that when a dimensionless melting parameter is greater than 1, SWCNT nanofluids attain greater velocities than MWCNT nanofluids for water as well as kerosene oil base fluids. Moreover, the flow is accelerated for SWCNT compared with MWCNT for both water and kerosene oil. With increasing stretching parameter, the heat transfer rate (Nusselt number) increases, whereas skin friction coefficients decrease. Higher skin friction and Nusselt number are obtained for SWCNTs compared to MWCNTs due to their greater density and thermal conductivity. The study is relevant to phase change manufacturing fluid dynamics of nanomaterials.

Stability analysis for heat transfer flow in micropolar hybrid nanofluids.

Objective: hybrid nanofluids have superior thermal efficiency and physical durability in contrast to regular nanofluids. The stagnation point flow of MHD micropolar hybrid nanofluids over a deformable sheet with viscous dissipation is investigated. Methodology: the controlling partial differential equations are converted to nonlinear ordinary differential equations using the transmuted similarity, and are subsequently solved using the bvp4c solver in MATLAB. The hybrid nanofluids consist of aluminum and copper nanoparticles, dispersed in a base fluid of water. Results: multiple solutions are obtained in the given problem for the case of shrinking as well as for the stretching sheet due to the variation in several influential parameters. Non-unique solutions, generally, exist for the case of shrinking sheets. In addition, the first branch solution is physically stable and acceptable according to the stability analysis. The friction factor is higher for the branch of the first solution and lower in the second branch due to the higher magnetic parameters, while the opposite behavior is seen in the case of the local heat transfer rate. Originality: the novelty of this model is that it finds multiple solutions in the presence of Cu and Al2O3 nanoparticles and also performs the stability analysis. In general, non-unique solutions exist for the phenomenon of shrinking sheets.

A numerical scheme for Darcy-Forchheimer flow of non-Newtonian nanofluid under the effects of convective and zero mass flux boundary conditions

This research aims to propose a numerical scheme for solving boundary value problems. It is a two-stage, third-order accurate scheme known as a predictorcorrector scheme. The two main results are finding the region of the scheme where it is stable and determining the stability criterion for a set of linearized first-order differential equations. In addition, a mathematical model for heat and mass transfer of Darcy-Forchheimer flow of non-Newtonian nanofluid over the sheet is presented. The similarity transformations reduce PDE into a system of ODE for easier manipulation. The results are compared with the past research and those obtained by MATLAB SOLVER BVP4C. The results show that the velocity profile slightly decays by enhancing the Weisenberg number.

Nanoparticle Shapes Effects on MHD Flow of Hybrid Nanofluid over a Stretching/Shrinking Sheet with Slip and Chemical Reaction

The impact of nanoparticle shapes (i.e., blade, brick, cylindrical, platelet, and spherical) on the MHD flow of Ag-MgO/water hybrid nanofluid over a stretching/shrinking sheet is scrutinized in this study. Chemical reaction and activation energy are included in the governing partial differential equations of the flow problem. On the boundary, velocity slip and zero mass flux conditions are considered. The simplification of the governing equations and boundary conditions into non-linear ordinary differential equations is done through similarity transformation. Then, the bvp4c solver in Matlab is deployed for computation, with the results generated in the form of numerical solutions and graphs. It is found that the usage of spherical-shaped nanoparticles produces the lowest magnitude of skin friction coefficient, and the implementation of blade-shaped nanoparticles in the hybrid nanofluid provides the highest enhancement of heat transfer rate. The increment in activation energy slows down the chemical reaction that raises the concentration profile of the hybrid nanofluid. However, the concentration profile decreases as the reaction rate increases.

The modified finite element method for heat and mass transfer of unsteady reacting flow with mixed convection

This study reveals the extension of a mathematical model of heat and mass transfer of fluid flow over a sheet by incorporating the effect of non-linear mixed convection. The governing equations of flow phenomena are expressed as partial differential equations (PDEs). Similarity transformations are employed to get a dimensionless set of boundary value problems. Most of the existing relevant literature employed some solver to solve a set of differential equations, but this study implements the finite element method to tackle the boundary value problems. The employed finite element method is based on the Galerkin approach. For verifications of the obtained results, a set of linear and non-linear boundary value problems is also solved with Matlab solverbvp4c. The results are displayed in graphs by varying Grashof number, modified (solutal) Grashof number, non-linear convection parameters in heat and mass transfer, radiation parameter, Prandtl number, Schmidt number, and reaction rate parameter. Also, numerical values for the friction at the wall and local Nusselt and Sherwood numbers are given in tables. The problem in PDEs form is also solved with software that implements the finite element method to solve problems. The simulations are also provided, which is the outcome of the software. It is shown that the velocity profile escalates by growing values of thermal and solutal Grashof numbers. Problem-solving techniques from this study may be used in future research to address other unsolved heat transfer fluid physics issues.

Dynamics of magneto-electric hybrid nanoparticles with chemically reacting and radiated moving plate: Entropy analysis

In this new era of fluid field, researchers are interested in hybrid nanofluid because of its thermal properties and potential, which are better than those of nanofluid when it comes to increasing the rate at which heat is transferred. In comparison to the dynamics of chemically reactive Ethylene Glycol - Zinc Oxide (nanofluid) and Ethylene Glycol - Zinc Oxide - Titanium dioxide (hybrid nanofluid) over a moving surface, nothing is known in terms of thermal radiation, entropy formation, viscous dissipation, and the Lorentz force. The thermo-physical characteristics of Ethylene Glycol, Zinc Oxide nanoparticles, and Titanium dioxide nanoparticles are used in this study to derive the governing equations for the transport of both dynamics. Flow-driven equations are transformed into nonlinear ODEs and solved using MATLAB bvp4c solver. It is noticed that, when magnetic field parameter (M) takes input in the range 0 ≤ M ≤ 3, skin friction coefficient decreases at a rate of 0.22052 (in case of hybrid nanofluid) and 0.19203 (in case of nanofluid) per unit value of magnetic field parameter. It is detected that the rise in Brinkmann number causes a rise in entropy generation and Bejan number decreases as Brinkmann number increases. Furthermore, when Eckert number rises, the heat transmission rate decreases. The heat transmission rate drops at a rate of 0.0869 (in case of hybrid Nanofluid) and 0.07429 (in case of nanofluid) when Eckert number (Eck) takes input in the range 0 ≤ Eck ≤ 0.7. The mass transmission rate increases at a rate of 1.013383 (in case of hybrid nanofluid) and 1.013125 (in case of nanofluid) when Schmidt number (Sc) takes input in the range 0 ≤ Sc ≤ 1. A comparison of the current results to previous results indicated a satisfactory agreement under certain conditions.

Irreversibility Analysis in the Ethylene Glycol Based Hybrid Nanofluid Flow amongst Expanding/Contracting Walls When Quadratic Thermal Radiation and Arrhenius Activation Energy Are Significant

In this new era of the fluid field, researchers are interested in hybrid nanofluids because of their thermal properties and potential, which are better than those of nanofluids when it comes to increasing the rate at which heat is transferred. Compared to the dynamics of radiative Ethylene Glycol-Zinc Oxide (nanofluid) and Ethylene Glycol-Zinc Oxide-Titanium Dioxide (hybrid nanofluid) flows between two permeable expanding/contracting walls, nothing is known in terms of Lorentz force, heat source, and the activation energy. The thermo-physical characteristics of Ethylene Glycol, Zinc Oxide nanoparticles, and Titanium Dioxide nanoparticles are used in this study to derive the governing equations for the transport of both dynamics. Governing equations are converted as a set of nonlinear ordinary differential equations (with the aid of suitable similarity mutations), and then the MATLAB bvp4c solver is used to solve the equations. This study’s significant findings are that rise in the reaction rate constant increases mass transfer rate, whereas an increase in the activation energy parameter decreases it. The mass transfer rate decreases at a rate of 0.04669 (in the case of hybrid nanofluid) and 0.04721 (in the case of nanofluid) when activation energy (E) takes input in the range 0≤E≤5. It has been noticed that the velocity profiles are greater when the walls are expanding as opposed to when they are contracting. It is detected that the heat transfer rate reduces as the heat source parameter increases. The heat transfer rate drops at a rate of 0.9734 (in the case of hybrid Nanofluid) and 0.97925 (in the case of nanofluid) when the heat source parameter (Q) takes input in the range 0≤Q≤0.3. In addition, it has been observed that the entropy generation increases as the Brinkmann number rises.

Numerical modeling of MHD micropolar fluid flow and melting heat transfer under thermal radiation and Joule heating

The purpose of this paper is to discuss the melting heat transfer and flow of a micropolar fluid due to an exponentially stretching sheet, analogous to ordinary fluid. The impacts of slip parameter, viscous dissipation, Joule heating, heat source, and thermal radiation are anticipated. The transport of heat, momentum, and angular momentum is expressed mathematically using a set of partial differential equations (PDEs). The PDEs are turned into a set of dimensionless ordinary differential equations by employing similarity variables adequately and interpreted numerically utilizing a well-known computer language in-built software bvp4c solver in MATLAB. It is noticed that the impacts of several parameters (Prandtl number, Eckert number, magnetic, heat generation parameters, etc.) on physical quantities and flow fields (velocity, temperature, and microrotation profiles) are remarkable and which are exhibited graphically and discussed in details. It is detected that, by enhancing the melting parameter, the microrotation profile appears to be dwindling near the wall; however, it is eventually lifted. Increasing the slip parameter depletes the velocity and microrotation fields, whereas it has reverse effect on the thermal field. Moreover, the thermal field is positively affected by viscous dissipation and heat generation, but slightly more enhancement has been seen for ordinary fluid compared to micropolar fluid.

Influence of Activation Energy on the Hybrid Nanofluid Flow over a Flat Plate with Quadratic Thermal Radiation: An Irreversibility Analysis

Dissipative (Water – Iron (II, III) Oxide – MWCNT) hybrid nanofluid dynamics over a flat plate at varied Lorentz forces, volume fraction, and activation energy are unknown when quadratic thermal radiation is taken into account. Paper's novelty is addressing this gap, which is to examine the impact of activation energy on the hybrid nanofluid flow by a flat plate with viscous dissipation and magnetic field. Nonlinear ordinary differential equations are constructed from flow-driven equations, and the MATLAB bvp4c solver is used to solve them. Entropy generation increases as the volume fraction of nanoparticles increases, and the rate of mass transfer decreases as the activation energy parameter increases are the major findings of this study. As thermal radiation and Eckert number increase, observed an increase in the fluid temperature. Increasing the volume fraction of nanoparticles causes a rise in shear stress, while increasing the magnetic field parameter decreases it. It is noticed that, when magnetic field parameter () takes input in the range , skin friction coefficient decreases at a rate of 1.10078 per unit value of magnetic field parameter. It is detected that, when Eckert number increases, Nusselt number decreases. The decrement rates are observed as 0.02457 when Eckert number takes input in the range . It is discovered that the mass transfer rate decreases at a rate of 0.08123 when activation energy parameter takes input in the range .

Dual solutions for MHD hybrid nanofluid stagnation point flow due to a radially shrinking disk with convective boundary condition

PurposeThis paper aims to study the stagnation point flow of Al2O3–Cu/H2O hybrid nanofluid over a radially shrinking disk with the imposition of the magnetic field, viscous-Ohmic dissipation and convective boundary condition.Design/methodology/approachSimilarity variables are introduced and used in reducing the governing partial differential equations into a system of ordinary differential equations. A built-in bvp4c solver in MATLAB is then used in the computation of the numerical solutions for equations (7) and (8) subject to the boundary conditions (9). Then, the behavior of the flow and thermal fields of the hybrid nanofluid, with various values of controlling parameters, are analyzed.FindingsThe steady flow problem resulted in multiple (dual) solutions. A stability analysis performed to identify the stable solution applicable in practice revealed that the first solution is stable while the second solution is unstable. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than the Al2O3–H2O nanofluid. Thus, the hybrid nanofluid has a better heat transfer performance than the nanofluid. Besides that, the presence of the magnetic field, suction, convective boundary condition and the enhancement of nanoparticle volume fraction of Cu augments the skin friction coefficient and Nusselt number of the hybrid nanofluid. Meanwhile, the presence of viscous-Ohmic dissipation reduces the heat transfer performance of the fluid.Originality/valueTo the best of the authors’ knowledge, the present results are original and new for the study of the flow and heat transfer of Al2O3–Cu/H2O hybrid nanofluid past a permeable radially shrinking disk. Considerable efforts have been directed toward the study of the boundary layer flow and heat transfer over stretching/shrinking surfaces and disks because of its numerous industrial applications, such as electronic, power, manufacturing, aerospace and transportation industries. Common heat transfer fluids such as water, alumina, cuprum and engine oil have limited heat transfer capabilities due to their low heat transfer properties. In contrast, metals have higher thermal conductivities than these fluids. Therefore, it is desirable to combine the two substances to produce a heat transfer medium that behaves like a fluid but has higher heat transfer properties.

The Novelty of Thermo-Diffusion and Diffusion-Thermo, Slip, Temperature and Concentration Boundary Conditions on Magneto–Chemically Reactive Fluid Flow Past a Vertical Plate with Radiation

The significance of radiation, Soret and Dufour’s effects on MHD flow in a porous media near a stagnation point past a vertical plate with slip, temperature, and concentration boundary conditions were investigated. Local similarity variables are used in the solution, which reduces the PDEs into analogous boundary value problem for ODEs. Symmetry analysis can be used to detect these variations in local similarity. To numerically explain the problem, a shooting approach and the MATLAB bvp4c solver are utilized. As the magnetic field and porous medium parameters are raised, the skin friction increases, and the temperature increases as the radiation pointer is increased. As the Soret number grows, the concentration profile rises.

Performance analysis of variable thickness longitudinal fin with functionally graded material in dry and fully wet conditions

PurposeWhen the temperature of an air conditioning unit’s fin surface goes below its dew point temperature, condensation forms on the unit’s surface. As a result, the cooling coil’s performance is compromised. By altering the cross-section and heat conductivity of the fins, the performance of such systems can be improved. This study aims to analyze the thermal performance of longitudinal fins made up of a variable thickness (assuming constant weight) and functionally graded material.Design/methodology/approachDifferent grading parameters are considered for an exponential variation of thermal conductivity. The humidity ratio and the corresponding fin temperatures are assumed to follow a cubic relationship. The Bvp4c solver in MATLAB® is used to solve the differential heat transfer equation resulting from balancing heat transfer in a small segment.FindingsValidation of the methodology is provided by previous research presented in this area. For different combinations of grading parameters, geometry parameters and relative humidity, the normalized temperature distribution along the fin length and fin efficiency contours are plotted, and the results are very promising.Originality/valueWhen compared to the efficiency of an isotropic homogenous rectangular longitudinal fin with optimal geometry and grading parameters, a 17% increase in efficiency under fully wet conditions is measured. When it comes to fin design, these efficiency contour plots are extremely useful.

Wall jet flow and heat transfer of a hybrid nanofluid subject to suction/injection with thermal radiation

The current work describes the 2 dimensional hybrid nanofluid (HNF) flow of incompressible wall jet with mass transpiration, heat transfer and radiation effect, where the jet streamwise velocity varies in a power-law. On applying the appropriate similarity transformations to these equations, a system of nonlinear ordinary differential equation (ODEs) was obtained. Then, this resulted system was numerically solved using MATLAB bvp4c solver and the results of velocity profiles and temperature distributions were demonstrated in the graphical form. Further, analytical investigating for the flow equation was introduced with distinguishing of three cases for suction, impermeable and injection as relation of the power-law. It was found that increase in the volume fraction of nanoparticles inclines the velocity profile in suction. Further, the temperature distribution shrinks with the increase in suction and injection parameter.

Dual solution of MHD mixed convection flow and heat transfer over a shrinking sheet subject to thermal radiation

In this paper, the steady-state two-dimensional incompressible, magnetohydrodynamics, stagnation point flow and heat transfer of viscous fluid having mixed convection over the linearly shrinking porous sheet is studied. The governing non-linear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by exercising the pertinent similarity variables. Numerical results are obtained by using the bvp4c solver in MATLAB to solve the resulting ODEs. The dual solution is obtained for a certain range of shrinking and mass suction parameters. The resulting dual solution projects that local skin friction coefficient and Nusselt number escalates in the upper branch solution and decelerates in the lower branch solution with the increase in the mass suction and magnetic parameter. However, the heat transfer rate is diminishing in both the upper and lower branch solutions due to an escalation of the radiation parameter. In addition, temporal stability analysis has been performed by which the upper branch solution is physically trustworthy and stable while the lower branch solution is not physically stable (unstable).