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For its application in cancer therapy, targeted drug delivery, radiofrequency ablation, and magnetic resonance imaging, the dynamics of electro-magnetohydrodynamic flow of blood-gold nanomaterial over a nonlinearly stretching surface utilizing the Casson model has been elucidated numerically. The impact of second-order hydrodynamic-slip, nanoparticle radius, first-order thermal-slip, inter-particle spacing and non-uniform heat source are also accounted. The modeled flow equations are transmuted into a nonlinear system of first-order ODEs (with the aid of apposite similarity variables) which are then resolved numerically utilizing the bvp5c scheme. The thermal field augments with an increase and a decrease in the inter-particle spacing and radius of gold-nanoparticles, respectively. However, a reverse trend is noted for the velocity profile when the radius and inter-particle spacing of gold-nanoparticles are altered. The trend and magnitude of the change in the drag rate and heat transfer rate under the influence of effectual parameters have been demonstrated statistically using slope of linear regression. It is noticed that per unit increase in the volume fraction of gold nanoparticles augments the heat transfer rate by 81.71% and reduces the surface drag by 163.51%. Further, per unit increase in the inter-particle spacing of gold nanoparticles augments the drag coefficient by 85.92% whereas per unit increase in the radius of gold nanoparticles reduces the skin friction coefficient by 49.71%. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Significance of nanoparticle radius on EMHD Casson blood-gold nanomaterial flow with non-uniform heat source and Arrhenius kinetics" published in the Journal of Thermal Analysis & Calorimetry. The correction states that figures 1-18 in the original publication were published incorrectly due to a typesetter's mistake, and the corrected figures are provided in this correction article. Additionally, there is a correction to the first sentence in the abstract. The original article has been corrected. The document also includes a note from the publisher stating that Springer Nature remains neutral with regard to jurisdictional claims and institutional affiliations. [Extracted from the article]

For its biomedical applicability, the dynamics electro-magnetohydrodynamic flow of blood-gold nanomaterial over a nonlinearly stretching surface utilizing the Casson model has been numerically elucidated. The impact of second-order hydrodynamic-slip, gold nanoparticles of different inter-particle spacing and radius, and non-uniform heat source are also accounted. The incorporation of nanofluid characteristics in the traditional Casson model improves the applicability, practicality and realistic nature of the modeled flow problem. The present study finds its application in radiofrequency ablation, magnetic resonance imaging, cancer therapy, and targeted drug delivery. Apposite similarity variables are employed to transmute the modeled flow equations into a nonlinear system of first-order ODEs which are then resolved using the bvp5c scheme. It is observed that the intensification in space-dependent heat source, temperature-dependent heat source and heat of reaction ascend the thermal field. It is noted that per unit increase in the inter-particle spacing ascends the drag coefficient by 70.2431176% whereas the nanoparticle radius descends the drag coefficient by 42.2109338%. Further, the impact of heat of reaction 0.1 ≤ α ≤ 0.9 , reaction rate 0.1 ≤ β ≤ 0.9 , nanoparticle radius 0.5 ≤ R np ≤ 2.5 , and inter-particle spacing 0.5 ≤ h ≤ 2.5 on the mass transfer rate Sh x Re x - 1 / 2 has been scrutinized statistically using the five-level four-factor response surface optimized model. The mass transfer rate is maximum for larger values of inter-particle spacing and smaller values of reaction rate, heat of reaction and the radius of gold nanoparticles. [ABSTRACT FROM AUTHOR]

The current work presents the convective Carreau nanoliquid flow along an elongating cylinder in the presence of magnetic field and slip constraints. Thermal radiation, viscous dissipation, and Joule heating effects are also considered. The modeled partial differential equations (PDEs) are solved utilizing BVP5C (MATLAB built‐in function) and appropriate similarity transformations. It is noted that the velocity and temperature are inversely proportional and directly proportional to the Hartmann number, respectively. Consequences of various parameters on Sherwood number, Nusselt number, and drag coefficient are analyzed employing tables and graphs. It is noted that the Eckert number demotes heat transfer rate. Verification of the MATLAB code is guaranteed through a reduced study with previously published papers and a good agreement is observed. The simultaneous impact of parameters on the Sherwood number is analyzed using two‐dimensional plots. The influence of parameters on heat transfer rate and drag coefficient are further scrutinized using statistical techniques like correlation and regression. [ABSTRACT FROM AUTHOR]

Titanium dioxide plays a vital role in cancer therapy methods (including photothermal therapy and photodynamic therapy), skincare products, heat exchangers, and car radiators. Therefore, the dynamics of the TiO2 nanomaterial with H2O as basefluid over a nonlinearly stretched surface is investigated. For realistic nanoliquid modeling, the conventional Buongiorno model has been improvised (called modified Buongiorno model [MBM]) by incorporating the effective thermophysical properties of the nanoliquid. Experimentally derived correlations of the thermal conductivity and dynamic viscosity of the nanofluid are utilized. The significance of passive control of nanoparticles is also studied. The heat transfer analysis includes the mechanism of Rosseland heat flux and exponential heat source. Similarity theory is used to obtain nonlinear ordinary differential equations (ODEs) from the governing partial differential equations which are solved numerically using bvp5c, a finite difference‐based routine in MATLAB. Further, the heat transfer rate is statistically scrutinized for the consequence of magnetic field(0.5≤M≤1.5)$\ ({0.5 \le M \le 1.5})$, thermal radiation (0.5≤Rd≤1.5)$({0.5 \le {R_d} \le 1.5})$ and exponential heat source (0.2≤QE≤0.4)$({0.2 \le {Q_E} \le 0.4})$ by employing Response Surface Methodology (RSM) and sensitivity analysis. The temperature of nanofluid ascends with the exponential heat source, thermal radiation, and thermophoresis aspects. Furthermore, when the MBM is utilised, the thermal field of the nanofluid is greater than when the classic Buongiorno model is used. The rate of heat transfer correlates positively with radiative heat flux. The exponential heat source exhibits a negative sensitivity towards the rate of heat transfer. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) are highly recognized for their diverse biomedical applications. The present study aims to numerically and statistically study the stratification effects of bioconvective electromagnetohydrodynamic flow past a stretching sheet using water-based CNT. The current study, with applications ranging from biomedical imaging, targeted drug delivery, and cancer therapy, provides a theoretical perspective that is beneficial in biomedical engineering. The mathematically modeled system of partial differential equations is then transmuted into a system of ordinary differential equations using apposite transformations, which are then resolved numerically using bvp5c (MATLAB built-in function) algorithm. The impacts of influential parameters on concentration, velocity, microbial concentration, temperature, and physical quantities are illustrated with the aid of graphs and tables. Descending electric field parameter and ascending magnetic field parameter retard the velocity profile, which helps in improving the efficiency of targeted drug delivery and biomedical imaging. Further, statistical techniques, like, correlation, the slope of linear regression, probable error, and multiple linear regression, are employed in scrutinizing the consequence of influential parameters on physical quantities and an excellent agreement is observed between the numerical and statistical results. It is noted that the heat transfer rate is positively correlated with electric and magnetic field parameters. [ABSTRACT FROM AUTHOR]

The bioconvective stagnation point flow involving carbon nanotubes along a lengthening sheet subject to induced magnetic field and multiple stratification effects has been considered for investigation. Relevant similarity formulas are effectuated in converting the modelled equations into a first‐order system of ODEs and are further treated in MATLAB using ODE45 and Newton Raphson method. Illustrations on the consequence of effectual parameters on the physical quantities and the flow profiles are achieved with the aid of graphs. It is observed that the nanofluid temperature profile ascends with augmenting volume fraction and Eckert number. The numerical veracity of the present study is displayed through a restrictive study with prior published works and a commendable agreement is noted. Nusselt number is found to elevate with volume fraction and lower with thermal stratification parameter. Moreover, the findings of the present numerical exploration have applications in biomedical imaging, hyperthermia, targeted drug delivery, and cancer therapy. [ABSTRACT FROM AUTHOR]

The nanofluid flow between two plates is a common topic of research. However, studies dealing with the flow between two vertical plates moving in different directions have not been largely accounted for. The main aim of this study is to analytically and statistically investigate the MHD flow of water‐based nanofluid between two vertical porous plates moving in opposite directions using perturbation technique and multiple linear regression, respectively. The consequence of various parameters on concentration, temperature, and velocity are examined via graphs using MATLAB software. It is observed that the main flow velocity profile is greater when the magnetic field is applied on the upward moving plate as compared to the main flow velocity when the magnetic field is applied on the downward‐moving plate. The physical quantities are scrutinized using statistical tools like probable error and multiple linear regression and an excellent agreement is noted. It is noted that the Nusselt number is highly positively correlated with the injection parameter and highly negatively correlated with nanoparticle volume fraction. Furthermore, the simultaneous effects of parameters on drag coefficients are studied with the aid of three‐ dimensional surface plots. [ABSTRACT FROM AUTHOR]

This study focuses on analyzing the response of a magnetohydrodynamic convective Carreau nanofluid flow over a bilateral nonlinear stretching sheet in the presence of a heat source and zero mass flux condition. The problem has been solved numerically using the MATLAB built‐in function bvp5c. The findings of velocity, temperature, and concentration profiles based on the various parameters are illustrated using graphs. The impact of various parameters on the heat transfer rate is scrutinized using statistical techniques, like, correlation coefficient, probable error, and regression. The effect of various parameters on skin friction coefficients is studied via tables and slope of linear regression. It is observed that the statistical results coincide with the numerical results. It is also noticed that the stretching ratio parameter increases the Y‐directional velocity profile. Accuracy of the numerical procedure has been validated through a restrictive comparison of the present work with previous published results and is found to be in good agreement. [ABSTRACT FROM AUTHOR]

For its applications in nuclear reactors, food processing, chemical engineering, water emulsions and thermal power generating systems, the significance of irregular heat source and Arrhenius energy on electro-magnetohydrodynamic hybrid nanofluid flow over a rotating stretchable disk with nonlinear radiation have been investigated. The flow problem has been modeled utilizing the modified Buongiorno model and the thermophysical characteristics of water-based Cu − F e 3 O 4 hybrid nanoliquid. Effects like passive control of nanoparticles, hydrodynamic slip and convective boundary conditions are also heeded to boost the realistic nature of this work. Further, engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated which boosts the novelty of this research work. The modeled governing equations are transmuted into a system of first-order ODEs, with the help of apposite similarity transformations, which are then numerically resolved using the finite-difference based bvp5c algorithm. It is noticed that per unit increase in the electric parameter decreases the skin friction coefficient by 41.75% and increases the heat transfer rate by 15.31%. It is also observed that the entrainment velocity is directly proportional to the changes in electric field parameter and is inversely proportional to the changes in volume fraction of copper and magnetite nanoparticles. [ABSTRACT FROM AUTHOR]

This study focuses on studying the impact of multiple slip effects on the hydromagnetic Carreau nanofluid flow over an elongating cylinder considering a linear heat source and exponential space‐based heat source. Suitable transformations are used in converting the highly nonlinear system of partial differential equations governing the flow into a system of ordinary differential equations and hence resolved using the Runge–Kutta method of order four coupled with the shooting method. BVP5C and RKF45 are used to compare the numerical accuracy and an excellent agreement is noted. The parallel effect of parameters on Nusselt number is studied using surface plots and the corresponding effects are scrutinized using multiple linear regression. It is observed that the linear heat source parameter, thermal slip parameter and exponential space‐based heat source parameter demote the heat transfer rate. The consequence of different parameters on drag coefficient and mass transfer are quantified using a linear regression slope. [ABSTRACT FROM AUTHOR]

The hydromagnetic convective flow between two parallel plates has been analyzed frequently. However, only a countable number of studies are accounted for the flow between parallel plates moving in opposite directions. The present work aims to analytically explore the three‐dimensional (3D) convective hydromagnetic hybrid nanoliquid (with suspended Al2O3 and Fe3O4 nanoparticles) flow between two oppositely moving vertical porous plates utilizing the perturbation technique. The consequence of effectual parameters on the flow profiles is analyzed with the aid of graphs using MATLAB software. It is perceived that nanoparticle volume fraction ascends drag coefficient and descends temperature and main flow velocity. Furthermore, the rate of heat transfer is statistically scrutinized utilizing response surface methodology and sensitivity analysis. It is noted that the Nusselt number is most sensitive with the injection parameter. 3D surface plots are used to illustrate the parallel effect of pertinent parameters on the drag coefficient. Moreover, the present study finds applications in several engineering, geophysical, and industrial fields, such as in heat exchangers and faulting. [ABSTRACT FROM AUTHOR]

The significance of this investigation is to optimize the heat transfer rate of magnetohydrodynamic bioconvective hybrid nanofluid flow in the presence of heat source and thermal convection. The main focus is to examine the two-dimensional incompressible MHD (Cu-Ag) / H 2 O and ( TiO 2 -Ag) / H 2 O hybrid nanofluid flow across the stretching cylinder with the Cattaneo–Christov heat flux model. The response surface methodological approach and sensitivity analysis have been employed to statistically scrutinize the influences of concentration, bioconvection, and thermo-diffusion on heat transfer rate. By applying suitable similarity vectors in controlling the partial differential equations, a system of equations (ODEs) is formed. A well-known method Runge Kutta with shooting has used for numerical simulations. The role of various involving factors on heat and mass transfer rate and skin friction factor is illustrated using tables, figures, and surface plots. The three-dimensional graphs displayed the synchronized effect of involving factors on physical quantities. The heat transfer rate is least responsive to variations in the magnetic parameter and most sensitive to the fluctuations of the Biot number. It is perceived that the nanoparticle concentration and motile concentration profiles declined with the increasing effect of chemical reaction parameters. The legitimacy of the current conclusions is established by the excellent agreement concerning present and previous consequences. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of steady two-dimensional magnetohydrodynamics (MHD) migration of dusty fluid across a stretching sheet with the inclusion of Darcy–Forchheimer porosity and Brownian dispersion. The most significant aspect of the ongoing problem is elaborating the entire context with dusty and fluid phases. The governing partial differential equations (PDEs) are transmuted into non-dimensional ordinary differential equations (ODEs) by implementing similarity transformations. The MATLAB script has used the bvp4c strategy to accumulate a visualization of the computational observations. Also, this study illustrates an assessment of the effects of significant parameters on non-Newtonian fluids and fluids with a dusty phase. It is observed that the thermal boundary layer is enhanced with the increasing strength of the mass concentration of dusty granules ( Γ ν ) and Eckert number (Ec) for both scenarios, while in the case of fluid interaction temperature parameter ( β t ) the scenario is opposite for dusty and fluid phases. Moreover, the heat transfer rate intensifies with the increasing effect of thermal radiation, and magnetic field. The significant variations in the various physical quantities are represented through tabular and graphs. [ABSTRACT FROM AUTHOR]

The hydromagnetic stagnation‐point flow of magnetite‐water nanofluid due to a rotating stretchable disk has been numerically accessed. The nanofluid flow has been modeled by employing the two‐phase modified Buongiorno model that incorporates the volume fraction dependent effective nanofluid properties, Brownian motion, and thermophoresis effects. Von Kármán's similarity transformations are utilized in transmuting the mathematically modeled equations into a system of first‐order ODEs which are then resolved numerically using the bvp4c numerical scheme. The consequence of influential parameters on the flow profiles and the physical quantities has been presented through graphs and tables. Engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated in this research work. Results show that an augmentation in the Hartmann number descends the velocity profiles and ascends the nanofluid temperature profile. Further, a drop in the drag coefficient and a rise in the heat transfer rate are noted with an increment in the velocity ratio parameter. The tidings of this numerical simulation have applications in spin coating, rotating heat exchangers, and rotating disk reactors. [ABSTRACT FROM AUTHOR]

The proposed study demonstrates the flow phenomenon and thermo-variation of a magnetized stretching sheet induced-radiative nanofluid flow. By incorporating the response surface methodology, the heat transfer rate of the thermally convective flow of nanofluid is optimized. The graphene nanomaterial is used in the water-based nanofluid. A dynamic magnetic field, thermal radiation, and the Cattaneo–Christov heat flux model have used to represent the thermal behavior of the nanofluid. The simulation utilizes experimentally estimated values for the nanomaterial's thermal conductivity and viscosity. To further reveal the thermal enhancement of the flow, the impact of nanoparticle diameter and the solid-liquid interfacial layer is proposed at the molecular level. The response surface methodology and the sensitivity analysis has used to examine the effects of the nanoparticle volume fraction, Biot number, and magnetic parameter on the rate of heat transfer statistically. A set of equations is formed from the governing partial differential equations by implementing suitable similarity transformations. The bvp4c approach is used to solve the problem numerically. The effect of various parameters has displayed through tables, graphs, and surface plots on heat transfer, mass transfer, and the local Nusselt number. It is discovered that as the Biot number increases, so does the concentration and temperature profile. An excellent accord between the present and previously existing solutions is establishing the validity of the achieved results. [ABSTRACT FROM AUTHOR]

This work aims at the numerical exploration of the hydromagnetic alumina –water nanoliquid flow due to a rotating rigid disk. The nanoliquid flow considering different nanoparticle shapes (namely sphere, platelet, cylinder, and brick) and the thermo-hydrodynamic slip constraints have been modeled utilizing the two-phase modified Buongiorno model (MBM). MBM modifies the conventional two-phase Buongiorno model by additionally considering the volume fraction-dependent nanoparticle properties. The present study is relevant in both engineering and industrial fields like aerodynamics, spin coating, extrusion process, etc. Von Kármán's similarity transformations are exercised in the transmutation of the mathematically modeled equations into a system of first-order ODEs and treated numerically using the generalized differential quadrature method. The consequence of pertinent parameters on the physical quantities and the flow profiles are explained with the aid of tables and graphs. It is observed that the nanoliquid temperature increases with the hydrodynamic slip parameter and decreases with the thermal slip parameter. Further, it is noted that the highest drag is exhibited by platelet-shaped alumina nanoparticles. [ABSTRACT FROM AUTHOR]

The flow past a stretching sheet has been explored by many scientists for its application in metal spinning, drawing of plastic films, glass blowing, crystal growing, and cooling of filaments. In addition, the presence of microorganisms enhances the stability of the fluid that plays a significant role in biotechnology, bio-microsystems, and bio-nano coolant systems. Therefore, the dynamics of bioconvective MHD hybrid nanofluid (TiO 2 and Ag in water) flow over an exponentially stretching permeable surface considering thermal radiation, heat generation, chemical reaction, porosity, and dissipative effects has been investigated. Apposite similarity variables are applied in transforming the modeled PDEs into a system of nonlinear ODEs and are then solved utilizing the finite-difference based bvp5c algorithm. It is observed that an increase in the porosity parameter ascends the temperature and descends the velocity. It is also noted that the temperature profile is proportional to augmentations in radiation parameter, magnetic field parameter, Eckert number, and volume fraction of TiO 2 and Ag nanoparticles. The mass transfer rate and the motile density number increase with mounting values of chemical reaction parameter. Further, multiple linear regression has been utilized to statistically scrutinize the effect of pertinent parameters on drag coefficient and heat transfer rate. [ABSTRACT FROM AUTHOR]