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This study examines the effects of viscous dissipation, thermal radiation, nanofluid over a stretched surface, and viscous dissipation on a two-dimensional couple stress blood base for the enhancement of heat transfer rate. Gold and multiwall carbon nanotubes are two forms of nanoparticles that are taken into consideration, with blood serving as the base fluid. The NLPDE controls the considering problem. The NLPDE was converted to NODEs using the mentioned similarity transformation. The analytical method known as HAM was used to analyze the transform NODE analytically. Graphs are used to illustrate the effects of many parameters, such as magnetic factors, nanoparticle volume friction, velocity power index, PN, thermal radiation factors, and EN, which are derived from TE and VE. The current research work highlights how important it is to include viscous dissipation in nanofluid dynamics. The results show complex interactions among stretching, thermal properties, and micro-scale effects. The results may have an impact on the development and enhancement of biomedical devices and treatments that use nanofluidic systems, especially those that deal with blood.

This theoretical study examines the effects of thermal radiation, viscous dissipation, and a magnetic field effect on a nanofluid that contains carbon nanotubes in blood and moves over a two-way expanding surface. We consider both the stretching and contracting directions when examining the bidirectional nature of the expanding surface. We define the problem’s governing equations, which include energy and momentum, and transform them into a set of ordinary differential equations using suitable similarity transformations. We semi-numerically solve the resulting equations using HAM methods and the BVPh. 2.0 program. We also discuss the consequences of heat radiation and viscosity dissipation in the nanofluid. The Rosseland approximation models the effect of thermal radiation, while the incorporation of fluid’s internal friction represents viscous dissipation. This research aims to investigate the combined effects of various parameters, such as thermal radiation, Eckert number, nanoparticle volume fraction, couple stress parameter, power law index, magnetic field, and Prandtl number, on the heat, flow, and transfer properties of single-walled carbon nanotube (SWCNT), multi-walled carbon nanotube (MWCNT), and blood-based nanofluids. A fascinating field of study, this study will reveal useful details about the possible uses of carbon nanotube blood-based nanofluids across bidirectional expanding surfaces in drug delivery systems, heat transfer processes, and biomedical engineering. Blood-based nanofluids can benefit from the inclusion of carbon nanotubes to improve fluid behavior and thermal conductivity, which is crucial for a number of industrial and medicinal applications.

The problem of a steady boundary layer MHD slip flow over a stretching sheet in a water-based nanofluid containing different type of nanoparticles: Cu, Al₂O₃ and Ag has been investigated. An external strong magnetic field is applied perpendicular to the plate and the Hall effect is taken into consideration. The surface of the stretching sheet is assumed to move with a linear velocity and subject to power-law variation of the surface temperature. The governing partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by a Runge–Kutta–Fehlberg method with shooting technique. Effects of the physical parameters on the primary velocity, the secondary velocity and the temperature as well as on the wall shear stress and the rate of heat transfer have been presented graphically and discussed in detail. Investigated results indicate that the nanoparticle volume fraction and the slip parameter produce opposite effects on the skin friction coefficients of the primary and secondary flow. Also, the nanoparticle volume fraction and the types of nanoparticles demonstrate a more pronounced influence on the secondary flow than that on the primary flow and temperature distribution.

This study describes a novel application of artificial intelligent-based computing paradigm via knacks of neural networks backpropagated through Levenberg–Marquardt scheme (NNs-BLMS) to investigate the mathematical model of Carreau nanofluid thin film flow over a stretching sheet under the magnetic field effect (CNTFFSSM). The system of PDEs of the designed model is transformed by using suitable transformations to the system of ODEs. The Adams deterministic numerical technique is utilized for generation of a dataset for the proposed technique for six varients to produce corresponding six scenarios of the designed model by varying magnetic parameter, Brownian motion parameter, unsteadiness parameter, Weissenberg number, thermophoresis number and Lewis number. The computational intelligent solver NNs-BLMS is applied to the CNTFFSSM model by performing processes on training, testing and validation samples. The efficiency of the proposed technique is validated by comparison of the standard solution and outcomes of the proposed solver for designed model through histograms, error analysis and regression analysis. The outcomes disclosed that velocity field is a decreasing function of magnetic parameter, while an increasing function of the Weissenberg number. The temperature and concentration profiles enhance with higher thermophoresis parameter, while diminish with higher Weissenberg number. Moreover, higher Lewis number causes lower concentration profile.

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values’ accuracy is upto ${10}^{-10}$ which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms.

The current communication has as its goal the investigation of the flow properties of carbon nanotubes (CNTs) across a stretching surface, which has been accomplished. Furthermore, the effects of radiation, chemical reactions and activation energy are considered. With the use of boundary layer approximations, we can obtain flow expressions. The nondimensional form of flow equations is achieved by applying appropriate transformations. The bvp4c code from MATLAB is used to solve the model that has been obtained. The graphic representation of the relationship between pertinent variables and momentum, temperature field and concentration is used. It is observed that, for larger values of $\varphi$ booms, the micro-rotation distribution. Furthermore, the solutal boundary layer thickness if thinner for thicker values of $\sigma$.

As a means of influencing technological advancements in engineering applications and various fluid products, the generalized Fourier’s and Fick’s models have proven to be of great importance. Industries such as power station engineering, high thermal material processing, and bio-heat elements apply the concept of anomalous heat and mass transfer mechanism. The objective of this study is to stimulate the flow of a radiative magnetohydrodynamics Jeffery fluid over an expanding surface with anomalous heat and mass transfer dynamics subjected to nth order reaction and variable thermophysical properties. A set of similarity transformations is used to neutralize the governing equations into a nondimensionless form. To obtain the model parametric analysis, a numerical tool via the spectral local linearization method (SLLM) is deployed after transformation of the governing flow equation from a two-unknown partial differential equations to a one-variable ordinary differential equation. It is observed that the thermal boundary layer thickness is found to be enhanced with increasing parametric values of magnetic, Eckert and radiation parameters. For the radiation parameter $R\in [0.50,2.50]$, the skin drag force, Nusselt and Sherwood number increase by $0.61\%$, $48.00\%$ and $0.91\%$, respectively. Additionally, a $200\%$ increment in the nth order parameter boosts the rate of heat transfer by $0.78\%.$ while it downsizes the Sherwood number by $14.32\%$.

This paper reports the flow and heat transfer augmentation on Reiner–Philippoff nanofluid over stretching sheet. The effect of transverse magnetic field and thermal radiation are explored for temperature distributions. Transformations are used to reduce system of partial differential equations into ordinary ones and are solved numerically by using RKF-45 Method. Expressions for velocity and temperature profile are derived and plotted under the assumption of flow parameter. Influence of various parameters on surface drag force and heat transfer rates have been discussed with the help of tables and plots. It is noticed that the impact of pseudo plastic fluid, Newtonian fluid and dilatant fluid are highly contrasted in higher Ha. Furthermore, production of heat transfer is more in nonlinear radiation when compared to linear radiation.

The aim of this research paper is to analytically investigate graphene oxide blood base nanofluid with the impact of dynamic viscosity and viscous dissipation. The increased thermal conductivity of nanofluids over regular fluids motivates this research. The basic flow equations are used to model the flow problem in nonlinear partial differential equations (NLPDEs). The dimensionless parameters, classical lie group, and thermo-physical properties are applied to transform the developed NLPDEs into dimensionless ordinary differential equations (ODEs). The resultant ODEs are resolved using the homotopy analysis method (HAM), and graphical and tabular interpretations are used to note the effects of contributing parameters including magnetic parameter, dynamic viscosity, nanoparticle volume friction, Eckert number, and Prandtl number on the velocity profile and temperature distribution. From the obtained results, we see that the velocity profile is decreasing by increasing magnetic parameter, dynamic viscosity, nanoparticle volume friction, and the temperature profile is increasing by increasing dynamic viscosity and Eckert number. The tabular descriptions of convergence of the presented fluid flow are also provided.

In this research work, we will carry out analytical investigation of MgO–CuO∖H₂O, hybrid nanofluid magnetohydrodynamics (MHD) stagnation point flow with the influence of viscous dissipation for enhancement of heat transfer ratio. The flow system takes into account the impact viscous dissipation and transport dependence on the shape factor. Furthermore, velocity and temperature at the stretching surface are also considered in this study. To convert a collection of PDEs to nonlinear ODEs, we applied appropriate transformations. We utilize the Homotopy analysis method (HAM) to solve this set of equations. A physical description is used to simulate and evaluate the structures of flow features such as velocity, skin friction, Nusselt number and temperature profiles in response to changes in developing factors, the effects of different factors on temperature and velocities are shown in the form of graphs. It is hoped that this theoretical approach would contribute positively to improve the heat transformation ratio to satisfy the demands of the manufacturing and engineering sectors.

Cross-diffusion effects are essential in industry because they can improve process efficiency, optimize product development, improve environmental sustainability, and drive technological advancements. The effects of cross-diffusion, aligned magnetization, and radiation are considered and adequately reported on the micropolar fluid boundary layer. The momentum, energy, and species reaction models are utilized to quantitatively represent the flow equations containing the thermophysical parameters at an aligned angle. The described fluid models are transformed into ordinary systems of derivatives. The solution to the resulting equations is determined via Fehlberg Runge–Kutta. The impacts of related terms are presented on various plots. The investigation revealed that the aligned angle strengthens magnetic field parameters, which can also lower the flow. For injection cases, microrotation has a parabolic distribution. An inclined value of radiation term contributed to improving the temperature profile. Temperature and concentration profiles rise and decrease with the Soret number, affecting heat, and species transport rates. The porosity and the thermal buoyancy parameter exhibit conflicting behaviors for both the coefficient of plate drag and the couple stress.

This study examines the analytical study of magnetic hydrodynamic stagnation point flow with the impact variable viscosity on a movable surface along with the impact of thermal radiation. The problem is modeled with the help of momentum and energy conservation laws in the form of NLPDEs. The novelty of this study is the combined impact of variable viscosity and thermal radiation with the analytical method. Aluminum oxide nanoparticles and water are used as base fluids in this research work. The authors applied appropriate transformations to convert a collection of dimension forms of NLPDEs to dimensionless forms of NODEs. The transformed NODEs are solved with the help of an approximate analytical method known as the HAM. The effects of different parameters, including electric field, magnetic field, stagnation point flow, thermal radiation PN, and EN on energy and momentum profiles intended, and the results are planned with the help of graphs.

The present paper deals with the study of three-dimensional boundary layer flow of biomagnetic Maxwell fluid over a plane horizontal surface stretched linearly along two mutually perpendicular directions. Basic principles of magnetohydrodynamics (MHD) and ferro-hydrodynamics (FHD) have been employed. The effect of heat generation/absorption has been taken into consideration. The study is theoretical and is conducted by using a combination of approximate and numerical techniques. By using the method of similarity transformation, the governing nonlinear partial differential equations are converted into a set of coupled ordinary differential equations. In the sequel, a suitable numerical method has been developed to solve the coupled differential equations. The accuracy of the numerical method has been checked by comparing the numerical results with those of an earlier study reported in available literatures. Effects of various parameters involved in the study, viz. the magnetohydrodynamic and ferromagnetic parameters, Deborah number, stretching ratio and heat generation on the fluid flow profiles are investigated and the results have been presented graphically. Variations of the skin friction, heat transfer rate and relative wall pressure with change in hydrodynamic and ferromagnetic parameters have also been illustrated. It is found that due to the influence of the Kelvin force, the velocity component in $x$-direction is greater than the corresponding one in the hydrodynamic case, but the opposite is true for the velocity component in the $y$-direction. We also found that the temperature of the fluid for hydrodynamic flow is greater than that for MHD or FHD flow. It is even greater for BFD flows. The numerical results of the study reveal that the characteristics of blood flow are significantly affected by the presence of a magnetic field.