Proper Transformation Research Articles

Statistical analysis of bioconvective EMHD tangent hyperbolic nanofluid with thermal radiation and heat source/sink

AbstractThis study examines the influence of thermal radiation and heat source/sink of the tangent hyperbolic fluid on EMHD boundary layer flow through stretching sheets. Motile gyrotactic microorganism is considered in the fluid flow and the flow is analyzed with the impact of thermal radiation, heat source/sink, and electromagnetohydrodynamic. By utilizing the proper similarity transformations, partial differential systems are converted to ordinary differential systems. The Runge–Kutta fifth‐order method with shooting technique is used in the converted systems to solve numerically. Velocity, temperature, concentration, and microorganism density profile are discussed and represented graphically. The numerical values of drag force rate, heat transfer rate, mass transfer rate, and density of motile microorganisms are specified, compared, and results enhancement in heat transfer rate as 64.31% by radiation parameter, mass transfer rate as 97.28% by heat source/sink parameter and microorganism density rate as 28.33% by Peclet number, respectively. The buoyancy parameter diminishes the drag force by 30.39%. The multiple and quadratic regression coefficient for adjusted , multiple , residual standard error, F‐statistic, and p‐value is estimated for skin friction, Nusselt number, Sherwood number, and density of microorganism. It has significant applications which are widely used to transport biological material in bio‐microfluidics, enhance heat dissipation in high‐performance electronics, thermal management systems on spacecraft and satellites, and solar energy systems.

A 5 mW 28 nm CMOS Low-Noise Amplifier with Transformer-Based Electrostatic Discharge Protection for 60 GHz Applications

This paper presents a low-power 60 GHz low-noise amplifier (LNA) designed for Gbit/s applications using 28 nm CMOS technology. The LNA exploits a single-stage pseudo-differential architecture with integrated input transformer for both electrostatic discharge (ESD) protection and simultaneous noise/impedance matching. An effective power-constrained design strategy is adopted to pursue the lowest current consumption at the minimum noise figure (NF), with the best tradeoff between gain and frequency bandwidth. The LNA, which has been designed to drive an on–off keying (OOK) demodulator, is operated at a supply voltage as low as 0.9 V and achieves a voltage gain of about 21 dB with a 3 dB bandwidth of 2 GHz around 60 GHz. Thanks to the proper impedance transformation at the 60 GHz input, the amplifier exhibits an NF of 6.3 dB, also including the input transformer loss with a very low power consumption of about 5 mW. The adoption of a single-stage topology also allows an excellent input 1 dB compression point (IP1dB) of −4.7 dBm. The input transformer guarantees up to 2 kV human body model (HBM) ESD protection.

Electroosmotic peristaltic transport of magnetohydrodynamic Casson nanofluid in a non-uniform wavy porous asymmetric micro-channel

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

Quaternion and Biquaternion Representations of Proper and Improper Transformations in Non-Cartesian Reference Systems

Quaternion and biquaternion symmetry transformations have been applied to non-Cartesian reference systems of direct and reciprocal crystal lattices. The transformations performed directly in the sets of crystal reference axes simplify the calculations, eliminate the need for orthogonalization, permit the use of crystallographic vectors for defining the directions of rotations and perform the computations directly in the crystal coordinates. The applications of the general quaternion transformations are envisioned for physical, chemical, crystallographic and engineering applications. The general quaternion multiplication rules for any symmetry-unrestricted lattices have been derived for the triclinic crystallographic system and have been applied to the biquaternion representations of all point-group symmetry elements, including the crystallographic hexagonal system. Cayley multiplication matrices for point-groups, based on the biquaternion symbols of proper and improper symmetry elements, have been exemplified.

Entropy generation of Williamson hydromagnetic non-linear radiative nanofluid flow near a stagnation point over a porous stretching sheet

Purpose This study aims to analyze the multi-slip effects of entropy generation in steady non-linear magnetohydrodynamics thermal radiation with Williamson nanofluid flow across a porous stretched sheet near a stagnation point. Also, the qualities of viscous dissipation, Cattaneo–Christove heat flux and Arrhenius activation energy are taken into account. Thermophoresis, Brownian motion and Joule heating are also considered. Design/methodology/approach The Navier–Stokes equation, the thermal energy equation and the Solutal concentration equations are the governing mathematical equations that describe the flow and heat and mass transfer phenomena for fluid domains. By using the proper similarity transformations, a set of ordinary differential equationss are retrieved from boundary flow equations. The classical Runge–Kutta fifth-order algorithm along with the shooting technique is implemented to solve the obtained first order differential equations. Findings The study concludes that the temperature distribution boosting for thermal radiation, magnetic field and Eckert number where as the velocity and entropy generation escalate for the Williamson parameter, diffusion parameter and Brinkman number. The skin-friction and heat and mass transfer rate increases with the fluid injection. In addition, tabulated values of friction drag and rate of heat and mass transfer for various values of constraints are provided. Originality/value The comparison of the present results is carried out with the published results and noted a good agreement.

Heat Transfer Flow of Ternary Hybrid Nanofluid (Al2o3-Zro2-Mgo) Over A Sinusoidal Wavy Surface

This study examines how the hybrid nanofluid over a vertically wavy surface enhances heat transmission. The flow through a porous media is investigated using Darcy law. The sine wave characterizes the non-uniform behaviour of the vertical wall. The governing equations1 for the conservation of mass, momentum in the x and y directions, and energy are obtained. With the help of the proper transformations, they are non-dimensionalized. The PDE is converted to an ODE using the Similarity transformation. The resulting ODEs are solved using the spectral collocation method, and the results are shown together with several nanoparticle thermos-physical parameters.

Study of hybrid nanofluid flow in a porous medium over an exponentially stretching sheet under Joule heating and thermal radiation: Finite difference

The significant purpose of present investigation of the behavior of a nanofluid's in magneto-hydrodynamics (MHD), mass transfer, Joule heating, and boundary layer transfer characteristics over an exponentially stretching sheet in a porous medium and thermal radiation effects. The article's goal is to look at the fluid flow and heat transmission characteristics from a sheet of hybrid nanoparticles. The partial differential equations (PDEs) that were derived for the mathematical model were converted using the proper similarity transformation into ordinary differential equations (ODEs). The hybrid nanofluid composed of 97 % of ethyl glycol (EG) and the volume concentration of Magnetite (Fe3O4) and Copper(Cu) are ranging from 0.5 % to 2.5 % both respectively. The effects of thermal radiation, stretching rate, Joule heating, porous medium permeability, and nanoparticle volume fraction on the flow and heat transmission properties are investigated by numerical simulations using the finite difference method (FDM). The analysis reveals that the inclusion of nanofluids enhance the thermal conductivity and enhance the heat transfer rate. Additionally, the influence of variable viscosity on the flow behavior and thermal characteristics are examined graphically. The effects of variable viscosity and thermal conductivity are examined, as it has significance in optimizing system under various thermal and magnetic effects. This study offers a pathway to develop more efficient thermal management solutions, by contributing to technological advancement and energy saving. The key findings of present study reveal that the temperature profile rises significantly due to Joule heating effects. The Nusselt number reveal an improvement of about 12 % when the volume fraction of nano particles is increased by 1–4 % indicating the enhancement in heat transfer efficiency. Similarly, the velocity profile was influenced by porous medium permeability as 11 % increase in porosity result a 18 % decrease in velocity profile.By using parametric research, the role of physical parameters in determining the local skin-friction coefficient, temperature, nanoparticle volume percentage, and longitudinal velocity profiles, local Nusselt number, and local Sherwood number are thoroughly examined. A graphic representation of the velocity, temperature, and concentration distribution findings is presented.

Entropy optimization on Casson nanofluid flow with radiation and Arrhenius activation energy over different geometries: A numerical and statistical approach

This study employs numerical and statistical approaches to investigate the entropy optimization of steady Casson nanofluid flow over three different geometries subject to boundary conditions induced by convective flow. Multiple linear regression is employed to statistically examine. The present model incorporates several novel elements, such as Arrhenius activation energy, Brownian motion, the Cattaneo-Christov dual flux, thermophoresis, thermal radiation, and so on. Moreover, a comparison is presented between Newtonian and non-Newtonian fluids. By applying the proper similarity transformations, ordinary differential equations (ODEs) are obtained by converting foundational partial differential equations (PDEs). The Runge-Kutta fourth-order method is utilised to solve the obtained ODEs along with the shooting technique. The outcomes are visually depicted via tables and graphs. The velocity drops with increasing Grashof number, and the magnetic field becomes progressively more forceful as the suction parameter increases. The temperature gets reduced with the increase of the suction parameter, solute Grashof number increases with the magnetic field, thermophoresis, and radiation parameters. The entropy is observed to rise with the increase of the effective parameters (magnetic field, Brinkmann number and radiation). The MAD (mean absolute deviation), MSE (mean squared error), and RMSE (root mean square error) values are approaching zero, indicating that the derived outcomes are highly accurate. A lower MAPE (mean absolute percentage error) suggests that the model has a higher level of precision. Therefore, the outcomes of the present model are more precise and reliable. This study has various potential applications such as power plant heat exchangers, material processing industries, and solar thermal energy systems.

Analysis of Entropy Generation via Non-Similar Numerical Approach for Magnetohydrodynamics Casson Fluid Flow with Joule Heating.

This analysis emphasizes the significance of radiation and chemical reaction effects on the boundary layer flow (BLF) of Casson liquid over a linearly elongating surface, as well as the properties of momentum, entropy production, species, and thermal dispersion. The mass diffusion coefficient and temperature-dependent models of thermal conductivity and species are used to provide thermal transportation. Nonlinear partial differential equations (NPDEs) that go against the conservation laws of mass, momentum, heat, and species transportation are the form arising problems take on. A set of coupled dimensionless partial differential equations (PDEs) are obtained from a set of convective differential equations by applying the proper non-similar transformations. Local non-similarity approaches provide an analytical approximation of the dimensionless non-similar system up to two degrees of truncations. The built-in Matlab (Version: 7.10.0.499 (R2010a)) solver bvp4c is used to perform numerical simulations of the local non-similar (LNS) truncations.

Three-Dimensional Radiative Rotating MHD Nanofluid Flow of Over a Stretched Sheet with Homogeneous-Heterogeneous Chemical Reactions

CNTs are employed in energy storage, device modelling, automobile parts, water filters, thin-film electronics, coating, and more. The continuous three-dimensional (3D) magnetohydrodynamics (MHD) rotational flow of water-based nanofluid comprising SWCNT and MWCNT past a stretching/shrinking sheet under magnetic field and homogeneous-heterogeneous chemical processes is examined in this study. Heat transport is also examined with thermal radiation and heat source/sink. The governing partial differential equations (PDEs) are transformed to non-linear ODEs using proper similarity transformations and solved numerically using MATLAB's bvp4c package. Graphs and tables show how magnetic field, rotational, suction/injection, thermal radiation, heat source/sink parameters, nanoparticle (NP) volume fraction, and homogeneous and heterogeneous reactions affect velocity, temperature, concentration, skin friction coefficient, and Nusselt number. For larger rotational parameters, the main velocity declines and the second velocity increases, and MWCNTs flow more than SWCNTs.

Thermo diffusion and diffusion thermo effects on unsteady flow over a curved surface

Application, Purpose, and Methodology: The Soret and Dufour effects, which are also referred to as cross-diffusion gradients, are advantageous to the manufacturing of binary alloys, the transmission of groundwater contamination, the extraction of oil, and the separation of gas. These are an example of a gradient, which occurs when substances diffuse over one another. The Dufour effect is responsible for the transfer of heat, whereas the Soret effect is concerned with the movement of materials. Both effects are caused by differences in concentration. Temperature differences are the link between the two effects. The Soret and Dufour statistics, in conjunction with the joule heating process, are utilized by us. Through the use of the convergent series, solutions for temperature, speed, and concentration are ultimately found. Core Findings: The findings of these investigations may give researchers engineering and industrial solutions that are unique and advantageous. The computation that is being done right now demonstrates that the sense of radial velocity diminishes as the Hartman number increases. In addition, the temperature of the fluid drops when there is a greater quantity of Prandtl and Soret than before. Methodology: Using the proper transformations, the numerical solution to the micropolar fluid flow problem over a curved stretched disk entails simplifying the partial differential equation system into an ordinary differential equation. This is done to solve the problem. In the process of converting partial differential equations into ordinary differential equations, similarity transformations are utilized. During the shooting process, we use the Runge-Kutta method to solve coupled equations and obtain numerical solutions. By utilizing the nondimensional radius of curvature, we can determine the nondimensional radius of curvature and report the fluid. Future Work: When compared to flat sheets, curved stretched sheets exhibit differences that result in significant boundary layer strain. This is something that will be worked on in the future. Research in the future might concentrate on further investigating these distinctions and the practical ramifications they have, with the possibility of expanding the scope of the investigation to include a variety of engineering and industrial applications in which these effects play an important role.

Mathematical analysis of heat and mass transfer efficiency of bioconvective Casson nanofluid flow through conical gap among the rotating surfaces under the influences of thermal radiation and activation energy

In the current proceeding, the flow of incompressible non-Newtonian nanofluid called Casson nanofluid is considered. A conical gap occurred among the rotating disc and the cone filled with the fluid flow. Heat and mass transport through this nanofluid is done by the convection mode of heat transfer. The impacts of microorganisms, chemical processes, thermal radiation, minimal amount of energy, and magnetic field are also considered in the mathematical model of flow problem. The Casson nano-fluid governing equations are interpreted in cylindrical coordinates. By implementing proper similarity transformations, the modeling PDEs of energy, momentum, concentration, and microorganism density are transformed into non-linear ODEs. A set of non-linear ODEs that deals with the distributions of temperature, velocity, concentration, and motile microorganisms produced by this technique. MATLAB in-built ‘bvp4c‘ technique is utilized to solve these equations. Findings are displayed graphically and elaborated theoretically. The primary goal of this work is to examine the effects during the rotation of the disc and cone as well as the impacts of other variables on the rotation. The nano-fluid temperature and radial velocity are found to be negatively impacted by the rotation parameter whereas azimuthal velocity is positively impacted. The parametric values are taken as 0.1<Nb<0.7, 0.1<λ<0.4, 1.0<Pr<2.50.1<M<0.4, 1.0<Rb<4.0, 0.1<Nr<0.4, 0.1<Sc<3.0, 0.1<Nt<0.4 for the purpose of generating modified results. From published and current results noted that rotation parameter effects impacted the transfer rate of the nanofluid.

Numerical simulation of Darcy–Forchheimer flow of Casson ternary hybrid nanofluid with melting phenomena and local thermal non-equilibrium effects

The Casson fluid flow over a stretching sheet is studied in this work in the presence of porous media with melting heat transfer and chemical reaction, combining nanoparticles of Ti4Al6V,AA7072 and AA7075 with a base fluid of sodium alginate (NaAlg). The porous medium Darcy Forchheimer effect is included in the momentum equation. Through the effects of melting, the process of heat transfer is described. In order to explore the features of heat transmission in the absenteeism of LTECs (local thermal equilibrium conditions), the current study employs a mathematical model that has been simplified. For both the solid and liquid phases, the LTNE model yields two different fundamental thermal gradients. This proposed model compares the YOM (Yamada-Ota model) and XM (Xue model), two well-known trihybrid nanofluid models, in terms of performance. After applying the proper transformations, modulated non-linear PDEs (partial differential equations) are simplified in ODEs (ordinary differential equations) and the bvp4c method is used to solve them numerically. A graphic discussion of the relevant factors' significance on the pertinent fields has been presented. It is observed that the Casson ternary hybrid nanofluid temperature and velocity distributions predominate at higher melting parameter. The solid phase's heat transport rate rises with an upsurge in the interphase heat transfer parameter.

Designing machine learning based intelligent network for assessment of heat transfer performance of ternary hybrid nanofluid flow between a cone and a disk: Case of MLP feed forward neural network

In the current study, authors have studied the heat transfer through ternary hybrid nanofluid (THNF) between the gap of a disk and cone, where both are co-rotating with regard to the other. The authors have developed a mathematical model of THNF flow inside a gap between a cone and a disk with the effects of magnetic field, Hall effects, and radiation parameters. The unique aspect of this study is the implementation of a powerful artificial neural network (ANN) that exhibits improved robustness and accurate predictive performance for the Nusselt number at the surface of both the cone and disk. Through the use of proper similarity transformations, the model equations are transformed into a collection of nonlinear ODEs. Using MATLAB and an inbuilt bvp4c function, these equations are numerically solved. The main objective of this research is to examine the impacts of cone and disk rotation within the co-rotation system. The heat transfer rate is seen to be higher at the surface of the disk. It is followed from the analysis of the ANN model that the regression value for each case varies between 0.99574 and 1, and in many cases, it is exactly equal to 1. In addition, the mean square error (MSE) for every dataset is notably very close to zero. The effect of the angle of the conical gap is also one of the noteworthy subjects due to the significance of its effects in several engineering sector applications.

Neural network-based adaptive optimal tracking control for hypersonic morphing aircraft with appointed-time prescribed performance

In this paper, an adaptive optimal attitude tracking controller for hypersonic morphing aircraft with appointed-time prescribed performance is presented. A proper error transformation methodology is developed to ensure the performance constraints are met without knowing initial tracking conditions. Subsequently, an adaptive composite control scheme is devised for the transformed system, comprising a feedforward neuro-backstepping controller and a feedback optimal controller. The former is employed to convert the optimal tracking problem into an equivalent optimal regulation problem, while the latter is constructed using adaptive dynamic programming (ADP) with a single critic network to achieve optimality. A novel weight-tuning law for the critic network is introduced, incorporating a stability indicator and the concurrent learning technique. This approach relaxes the underlying restrictive conditions in ADP, improving the robustness and availability of the system. The stability of the closed-loop system is analyzed using the Lyapunov direct method. Finally, the effectiveness and improved performance of the proposed control scheme are validated through numerical simulations.

Melting heat transfer of a quadratic stratified Jeffrey nanofluid flow with inclined magnetic field and thermophoresis

Recently, researchers are facing great challenges to form the homogeneous solutions of various liquids at biomedical and industrial levels. Such homogeneous solutions can be controlled through stratification phenomenon directly which is ignored by the researchers in the existing literature specifically quadratic stratification and melting heat mechanism which is valid only for higher temperature processes. Thus, to form the homogeneous and stable liquid solutions for various industrial processes, we investigate the melting heat phenomenon in quadratic stratified Jeffery Nano fluid flow deformed due to linearly stretching sheet along with stagnation point. Inclined constant magnetic field is implemented on the fluid through an arbitrary angel. Characteristics of heat and transportations are disclosed through viscous dissipation, Brownian motion and thermphoresis. Temperature and concentration of the surrounding fluids are assumed higher than the stretching surface. The resultant governing equations are reduced to ordinary differential equations through proper transformations. Convergent analytical series solutions are computed via homotopic approach. Impact of various emerging parameters on temperature, velocity and concentration fields are illustrated and discussed comprehensively. Sherwood and Nusselt numbers and drag force are scrutinized mathematically, physically and graphically. It is analyzed from the study that (i) dominant melting reduces the temperature field (ii) higher thermal and solutal stratification decay the temperature and concentration fields respectively (iii) higher thermophoresis enhances the temperature field. Further, it is concluded that stable and homogeneous solutions may be made by increasing melting and reducing stratification phenomena. This study will help us to provide actual amount of heat for heating processes in industries and biomedicine which is the basic requirement for excellent quality of products.

Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Abstract Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation. The nonlinear steepest decent method is extended to study the 4 × 4 matrix Riemann–Hilbert problem, from which the various Deift–Zhou contour deformations and the motivation behind them are given. Through some proper transformations between the corresponding Riemann–Hilbert problems, the basic Riemann–Hilbert problem is reduced to a model Riemann–Hilbert problem, by which the long-time asymptotic behavior to the solution of the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation is obtained with the help of the asymptotic expansion of the parabolic cylinder function and strict error estimates.

Comparative Analysis with Data Prediction of Non-linear Radiative Nano Second-Grade and Newtonian Fluid in Presence of Sinusoidal Magnetic Force

This study aims to enhance the comprehension of the fundamental fluid behavior by comparing Newtonian fluid with second-grade fluid under the influence of periodic magnetic fields, nonlinear radiative nanomaterial, and a porous stretched surface featuring a heat source. The governing equations' dimensionless forms are generated by applying the proper transformations, and the explicit finite difference (EFD) method is used to solve the numerically-derived solution while carefully maintaining stability and convergence standards. The results include velocity, heat, and mass transfer oscillation profiles; streamlines, and isothermal lines. Nusselt and Sherwood numbers are correlated with different factors according to tabular studies, and data prediction and regression are done using graphical representations. This study revealed that, in contrast to Newtonian fluid, second-grade fluid flow elevates velocity profiles with variations in chemical reaction parameters and mass Grashof numbers. Conversely, the thermal non-linear radiation and heat source in second-grade fluid particles effectively enhance the temperature field, although the temperature increase is more pronounced in Newtonian fluid compared to second-grade fluid. Also, second-grade fluid flow exhibits a lower mass transmission rate but higher stress sharing and heat transmission rates compared to Newtonian fluid flow. The implications of this research may impact prostate cancer treatment, as cancer patients have already benefited from the use of magnetic fields to regulate drug release from nanoparticles. Although the greater stress sharing and heat transmission rates may be used for targeted therapy, the lower mass transmission rate raises the possibility of benefits in controlled release scenarios.

Computational workflow to monitor the electroosmosis of nanofluidic flow in the vicinity of a bounding surface

This investigation studies the flow of a boundary layer with electroosmotic forces on a nanofluid with gyrotactic microorganisms along the vertical Riga plate. This sort of fluid movement necessitates specific mathematical techniques and numerical simulations. In addition, the boundary-layer flow is induced by the mass and heat transfer, Joule heating, and viscous dissipation. A mathematical model is simulated by non-linear partial differential equations (PDEs). The combination of PDEs is turned into a set of non-linear ordinary differential equations using proper transformations. Some analysis tools are used to investigate the morphological characteristics of the problem while applying suitable boundary conditions. The influence of parameters on the derived solutions is numerically and visually explained through sets of figures. It is elucidated that the concentration of the microorganisms reduces due to an increase in Lewis number which leads to a decrease in the motile microorganism’s density profile. It is seen that the temperature distribution is improved when the chemical reaction and Casson parameter increase. In addition, we find that the application of electro-osmotic forces applied to the surfaces helps to dewater and separate microorganisms from incompressible solid and liquid mixtures.

Analytical Investigation of Magnetohydrodynamic Hybrid Nanofluid Flow Over a Permeable Shrinking Sheet

The flow and heat transfer of Cu-Al2O3/water hybrid nanofluid over a shrinking sheet were investigated taking account of the magnetic field, suction, variable heat sink, and thermal radiation. At first, the governing equations were completely changed into ordinary differential equations (ODEs) with proper transformations. The novelty of this investigation is that the ODEs were analytically solved and the dual characteristics of flow properties and heat transfer were graphically presented. Results revealed that an increase in the volume fraction of Cu nanoparticles (φ2), magnetic parameter (M), and suction parameter (S) caused an increase in the local skin friction coefficient (Rex1/2Cf), local Nusselt number (Rex-1/2Nux) and region of the existence of dual solutions. With the increase of φ2, M, and S, fluid velocity increased and temperature decreased. Contrary to this, the converse was observed for increasing the volume fraction of Al2O3 nanoparticles (φ1). These findings indicated that with proper tuning of these parameters, the cooling rate of a shrinking sheet could be controlled and the possible working conditions of a system might be increased.