This paper investigates how ester-based nanofluids flow between two parallel disks when subjected to micropolar effects. Compared to traditional Newtonian fluids, micropolar fluids which exhibit spin inertia and micro-rotation provide a more thorough knowledge of the behaviour of complicated fluids. The ester-based nanofluid, selected due to its exceptional thermal characteristics and favourable environmental effects, is examined with different micropolar parameters to evaluate their impact on heat transfer rates and flow dynamics. Initially, we created a mathematical model to explain the fluid dynamics of ester-based micropolar nanofluids between two parallel disks using the Navier-Stokes equations. The suggested mathematical problem is converted into a non-linear ordinary differential equation (ODE) using the similarity transformation technique. We then solved the governing equations numerically using MATLAB's built-in BVP4c method. Through numerical simulations, we explored the velocity distribution, micro-rotation profiles and temperature profiles within the disk system. The results reveal that micropolar effects significantly enhance the thermal conductivity and viscosity of the nanofluid, leading to improved heat transfer efficiency and altered flow patterns. Nanoparticles in porous disk flow increase velocity and micro-rotation profiles, resulting in a more streamlined flow. Nanoparticle volume fraction also increases temperature, reducing thermal boundary layer thickness and enhancing convective heat transfer.

The study presents a mathematical model to predict the impact of interfacial nanolayers on mass and heat transfer phenomena in ternary hybrid nanofluid (THNF) flow. It also investigates the effect of TiO2, SiO2 and Al2O3 in non-Newtonian biological fluids (i.e. blood) using porous surfaces. The study includes uniform transverse magnetic flux (MF) and reduces the nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs) using similarity transformations then solved analytically and numerically, the analytical method has been established using the Adomian Decomposition Method (ADM) and by the numerical procedure (Explicit Runge Kutta Method), the present findings in specified cases are compared to findings obtained by the Homotopy Analysis Method (HAM)-based Mathematica package and by the previous literature for validation. The research focused on the influence of active parameters on various parameters, numerically and graphically examining their impact. Results show that the velocity profile experienced a 20% enhancement in the channel centerline region when using a 0.5 unsteadiness parameter (alpha) together with M = 1 as the magnetic parameter value. This enhancement was possible through the 15% reduction in momentum boundary layer thickness. The heat transfer capabilities of ternary hybrid nanofluids containing 2% nanoparticle volume fractions boost the performance by 25% better than pure base fluids.

This research examines the radiative components in heat and mass transfer phenomena in an unsteady MHD flow of Casson fluid past a vertical plate, set in a rotating porous medium. The fluid on the surface of the plate is maintained at a constant temperature while the mass transfer is set to vary. To examine the impact of heat generation, radiation, and variable mass diffusion on the velocity, temperature, and concentration profiles, the appropriate models are devised. The governing nonlinear partial differential equations are addressed through the use of Laplace transformations. The findings indicate that buoyancy forces imparted by the Grashof numbers considerably increase the velocity due to convection currents. However, the magnetic parameter counteracts velocity due to the Lorentz force while larger porosity increases fluid flow. Furthermore, radiation was demonstrated to decrease velocity and temperature from loss of heating while heat transfer increased temperature and velocity by injecting energy into the system. From the above results it can be seen that there are applications of these findings in the industrial and environmental context for example during MHD flow and filtration processes.

This article presents a method for numerically modeling how nonlinear velocity affects the flow of Newtonian and non-Newtonian fluids with magnetic or non-magnetic nanoparticles. The flow is generated by a stretchable sheet in a porous medium. We focus on examining the behavior of magnetite and aluminium oxide nanoparticles suspended in water and Sodium Alginate base fluids, respectively. To maintain physical accuracy, we analyze non-Newtonian flow using the Casson model. The model is first converted into a dimensionless form through similarity transformation and then solved using the fourth-order Runge-Kutta method along with a shooting iteration approach. Graphical representations are used to show the impact of different parameters on velocity and temperature distributions. The findings reveal that the velocity profile rises with the shape parameter, and the porosity parameter boosts the temperature profile. Additionally, skin friction is higher when using aluminium oxide nanoparticles in water based fluid, whereas heat transfer rates are higher when using aluminium oxide nanoparticles in a sodium alginate based fluid.

This study investigates the dynamic behavior of natural ester-based ferrous oxide (Fe3O4) nanofluid flow around an unsteady contracting cylinder under the influence of a magnetic field, heat generation, and homogeneous-heterogeneous reactions. The governing equations for the flow, heat transfer, and chemical reactions are solved numerically using appropriate mathematical models. The bvp4c built-in MATLAB package is applied to address the complexity of the problem. The effects of magnetic field, heat generation, and reactive chemistry on the flow field, temperature distribution, and species concentration profiles are analysed comprehensively. As part of the validation process, we validate the reliability of our findings by comparing them to established benchmarks. Motivated by the increasing interest in environmentally friendly and sustainable fluid mediums, natural esters are chosen as the base fluid due to their biodegradability, low toxicity, and excellent insulating properties. This research aims to provide valuable insights into optimizing processes involving nanofluid flow in magnetohydrodynamic systems with reactive heat generation, utilizing natural esters as a promising alternative to conventional fluids. Insights gained from this study offer potential applications in various engineering and industrial contexts, contributing to the advancement of eco-friendly technologies.

This study delves into the intricate interplay of magnetic and electric fields (EMHD) on the flow characteristics of a non-Newtonian bio-hybrid nanofluid, consisting of Ag+Graphene/blood, within converging and diverging geometries. The investigation takes into account the effects of velocity slip at the walls, offering a comprehensive examination of this complex fluid system. A novel bio-hybrid nanofluid model was introduced, featuring a unique combination of Ag+Graphene/blood nanoparticles. To address this multifaceted problem, the research employed mathematical modeling based on nonlinear partial differential equations (PDEs), encompassing continuity and momentum equations. These PDEs were then transformed into a system of nonlinear ordinary differential equations (ODEs) through similarity transformations. The study explored both numerical and analytical solutions, with a particular focus on the application of the Adomian decomposition method (ADM). To validate the findings, the study compared the analytical results with those obtained using the HAM-based Mathematica package and the Runge-Kutta Fehlberg 4th-5th order (RKF-45) method in specific scenarios. Active parameters, including nanofluid volume fraction, slip factors, and the influence of magnetic and electric fields, were systematically examined to unveil their impacts on velocity and skin friction within this multifaceted nanofluid system. It is found that the skin friction coefficient decreases with the Increasing both the nanoparticle volume fraction, Hartmann number and the angle in both channels. Results obtained also reveal an in the converging section, higher Casson parameters lead to increased yield stress but are offset by the higher shear rates, resulting in a higher velocity profile. In the diverging section, the fluid resists flow due to the reduced shear stress, leading to a decreased velocity profile.

In this study, we investigate the influence of quartic auto catalysis with equal diffusivity in the flow past a rotating cylinder. The flow-thermal fields are modeled using partial differential equations (PDEs), assuming a homogeneous–heterogeneous reaction. The resulting flow-thermal equations are appropriately ordered and solved using the BVP4c function in MATLAB. Our analysis focuses on examining the effects of varying the Reynolds number, magnetic field, radiation, and homogeneous–heterogeneous reaction parameters on the velocity, temperature, and concentration of the bulk fluid. Through extensive simulations, we find that the concentration, temperature, and velocity of the homogeneous bulk fluid are predominantly determined by the Reynolds number. We observe that higher Reynolds numbers lead to increased mixing and enhanced fluid motion, resulting in higher concentrations and temperatures. Moreover, the strength parameters associated with the homogeneous–heterogeneous reaction significantly favor the auto catalysis reaction at the surface of the rotating cylinder, indicating a self-catalytic process. To validate our findings, we compare our results with earlier studies that investigated reduced cases. Remarkably, our obtained results exhibit excellent agreement with these prior studies, further bolstering the reliability and accuracy of our research.

The primary objective of this study is to quantify the rate of entropy generation within the magnetohydrodynamic (MHD) slip flow system over the inclined needle. Entropy generation is a measure of the irreversibility and inefficiency in the flow process. The slip flow condition at the fluid interface can significantly impact the flow characteristics and heat transfer rates. In the hybrid nanofluid flow, which consists of non-magnetic and magnetic (Al2O3 and Fe3O4) nanoparticles, H2O+C2H6O2 (50:50) are considered as the base fluid. Furthermore, the effects of inclined magnetic fields are taken into interpretation. The PDE’s governing equations are converted into ODE’s using similarity transformations and solved by a numerical technique based on BVP4C. The results illustrate that crucial parameters such as the magnetic parameter, mixed convection parameter, nanoparticles of solid volume fractions, and Prandtl numbers are pointedly impacted by momentum and thermal profiles. The entropy and Bejan number also consider being various relationship-combined parameters. These analyses protest that raising the magnetic parameter estates an increase in the hybrid nanofluid thermal profile under slip circumstances. Examined magnetic field impact on flow and entropy generation in MHD flows, revealing significant changes in entropy generation due to interaction between magnetic field and nanoparticles. This analysis understands the impact of MHD and slip effects on entropy generation, particularly in the context of the newly emerging 50:50 fluid mixture. Hybrid nanofluids have been shown to have improved thermal conductivity compared to traditional fluids, which can enhance the cooling or heating capabilities of the inclined needle.

Hybrid nanofluids have several potential applications in various industries, including electronics cooling, automotive cooling systems, aerospace engineering, and biomedical applications. The primary goal of the study is to provide more information about the characteristics of a steady and incompressible stream of a hybrid nanofluid flowing over a thin inclined needle. This fluid consists of two types of nanoparticles: non-magnetic nanoparticles (Aluminium oxide) and magnetic nanoparticles (Ferrous oxide). The base fluid for this nanofluid is a mixture of water and ethylene glycol in a 50:50 ratio. The effects of inclined magnetic fields and Joule heating on the hybrid nanofluid flow are considered. The Runge-Kutta fourth-order method is used to numerically solve the partial differential equations, governing equations, which are then converted into ordinary differential equations using similarity transformations. Natural convection refers to the fluid flow that arises due to buoyancy forces caused by temperature differences in a fluid. In the context of an inclined needle, the shape and orientation of the needle have significantly affected the flow patterns and heat transfer characteristics of the nanofluid. These analyses protest that raising the magnetic parameter estates an increase in the hybrid nanofluid thermal profile under slip circumstances. Utilizing the potential of hybrid nanofluids in a variety of technical applications, such as energy systems, biomedicine, and thermal management, requires an understanding of and ability to manipulate these effects.

Bio-convection is used in many ecologically beneficial applications, including pharmaceuticals, biological polymer production, and other eco-friendly uses. Several of these applications, such as the production of plastic films and polymer sheets, rely on stretching surface technology because the heat transfer rate determines the ultimate product quality at the stretching surface. Therefore, this study examines the bio-convective heat transfer caused by the swimming of gyrotactic micro-organisms in a nanofluid flowing over an unsteady curved stretched sheet. Local similarity transformations are utilized to alter the nonlinear partial differential equations. The resulting nonlinear system of ordinary differential equations is solved using the shifted Legendre collocation method. The effects of many influential parameters on motile micro-organism concentration and temperature, velocity, and nanoparticle concentration profiles are plotted and discussed. The velocity field is reduced when the slip parameter increases. According to this focused study's results, the concentration of motile bacteria drops dramatically when the curvature parameter increases. The Brownian motion parameter, thermophoresis parameter, and Peclet number reduce the motile micro-organism number. Motile micro-organism dispersal improves with an increase in bio-convective Schmidt number.

In the present study, the magnetohydrodynamics (MHD) bio-convective flow and heat transfer of nanofluid, due to the swimming of the gyrotactic micro-organisms over a curved stretched sheet, is examined. In addition, thermophoresis and Brownian motion behaviors are also investigated by assuming slip conditions at the boundary. A non-linear system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs). For convergent solutions, the obtained ODE system is solved by the use of the BVP4C routine integrated MATLAB package. In addition, the impacts of different influential parameters on motile micro-organisms, temperature, velocity, and concentration profiles are deliberated. The velocity field is observed to be reduced when the slip parameter increases. As the main results, it is demonstrated that the distribution of motile microorganisms against the curvature parameter decreases significantly. Similarly, it is found that the nanofluid parameters (i.e., Brownian motion and thermophoresis parameters) and the Peclet number reduce the motile micro-organisms’ number. On the other hand, it is evidenced that the motile micro-organisms’ distribution can be improved with an increase in bio-convective Schmidt number.

This research paper explores the implications of nonlinear Rosseland thermal radiation and temperature-dependent heat generation on non-Darcian steady MHD convective Casson nanofluid flows over a radially extended rotating disk. Besides, the significance of the activation energy is also taken into account in the present modeling during the chemical reaction process. Based on the boundary layer theory, the associated dimensionless boundary layer equations are derived mathematically in the context of Von Kármán’s proposition. By invoking a trustworthy BVP4C numerical algorithm, the nonlinear differential system defining the resulting boundary value problem is handled successfully with the help of an iterative shooting procedure, whose results are profiled graphically and tabularly versus the varying values of the pertinent flow parameters. Furthermore, the displayed findings show that the radial and azimuthal nanofluid motion slows down significantly with the strengthening in the Casson nanofluid parameter, the Forchheimer number, the porosity parameter, and the magnetic parameter. However, the stretching parameter exhibits a dual dynamical tendency. A thermal enrichment can be provided by intensifying the heat generation parameter, the temperature difference parameter, the thermal radiation parameter, the thermophoresis process, and the Brownian motion of nanoparticles. On the other hand, it is perceived a remarkable boosting up in the concentration profile with the higher estimation in the thermophoresis and activation energy parameters.

This examination is passed on to decide the properties of three-dimensional flow of H 2 O/NaC 6 H 9 O 7 base liquid with F e 3 O 4 /Al 2 O 3 nanoparticles confined by a Riga plate. Mathematical model is detailed as PDEs and afterward transmuted into ODEs with the assistance of similarity transformations. The subsequent system is numerically dealt with the aid of the Runge-Kutta procedure bolstered by shooting technique. Highlights of the flow field and thermal field are exemplified quantitatively through plots. Results for the local skin friction coefficient and local Nusselt number are registered and examined tabularly. It is induced that the modified Hartmann number and stretching ratio parameter ameliorate the velocity profile. Additionally, it is likewise explained that H 2 O − Al 2 O 3 nanofluid has high skin friction values and the rate of heat transfer of NaC 6 H 9 O 7 − Al 2 O 3 nanofluid is more desirable.

The effective applications of Casson fluid in drilling processes, biological treatments, food processing, and bio-engineering activities have caught the interest of a wide range of researchers. The suitable knowledge of heat transfer via non-Newtonian fluid is essential for the achievement of best quality products in industry. Thus, the three-dimensional Casson nanofluid flow over a stretching sheet with Arrhenius activation energy and exponential heat source effects is investigated in this paper using a computational process based on iterative power series (IPS) method. To provide useful insights into the physical and dynamic examinations of this topic, convective heat and convective mass boundary conditions are used. The developed model of nonlinear partial differential equations (PDEs) has been transformed into ordinary differential equations (ODEs) using similarity transformations. The numerical solution of the transformed ODEs is obtained by employing the IPS technique combined with shooting iteration approach. The results of this study are validated with the previous studies, and excellent agreements have been obtained. The behavior of various capable physical parameters is analyzed. It is observed that the thermal and concentration fields show an enhancement with respect to the exponential heat source parameter and thermal and concentration Biot numbers. Further, the Arrhenius activation energy parameter has shown a significant effect on the concentration field.

The present examination is for the most part centered on the flow of a magnetohydrodynamic nano-second grade fluid over a stretching sheet implementing the second-order slip and thermal jump model. To analyze the problem elaborately, numerical simulations are carried out. For that, the partial differential equations that were employed to characterize the flow were transformed to ordinary differential equations with the aid of similarity transformations. Solving them with the much known Runge–Kutta strategy in association with shooting iteration technique, the outcomes for the nano-second grade fluid velocity, temperature, concentration, the local skin friction coefficient, the local Nusselt number and the local Sherwood number are discussed. Some of the notable results of second grade, thermophoresis and Brownian motion parameters along with Lewis number are brought out, which might be relevant for future research work.

Numerous techniques in designing zones happen at high temperature and functions under high temperature are in a way that involves non-linear radiation. In weakly conducting fluids, however, the currents induced by an external magnetic field alone are too small, and an external electric field must be applied to achieve an efficient flow control. Gailitis and Lielausis, devised Riga plate to generate a crossed electric and magnetic fields which can produce a wall parallel Lorentz force in order to control the fluid flow. It acts as an efficient agent to reduce the skin friction. So, in this paper, we start the numerical investigation on the three-dimensional flow of nanofluids with the inclusion of non-linear radiation past a Riga plate. To this end, the numerical investigation is conducted on the three-dimensional flow of nanofluids with the inclusion of non-linear radiation past a Riga plate. Water (H2O) and Sodium Alginate (NaC6H9O7) are the base fluids, whereas Magnetite (Fe3O4) and Aluminium oxide (Al2O3) are the nanoparticles. The mathematical formulation for Sodium Alginate base fluid is separated through the Casson model. Suitable transformations on governing partial differential equations yield strong non-linear ordinary differential equations. Numerical solutions for the renewed system are constructed by fourth-order Runge-Kutta method with shooting technique. Various deductions for flow and heat transfer attributes are sketched and discussed for various physical parameters. Furthermore, the similarities with existing results were found for the physical quantities of interest. It was discovered, that the temperature ratio parameter and the radiation parameter enhance the rate of heat transport. Moreover, the NaC6H9O7 - Al2O3 nanofluid improves the heat transfer rate. Likewise, H2O-Fe3O4 nanofluid stimulates the local skin friction coefficients.

In this study we showed the numerical analysis on the steady, three dimensional flow of different nanofluids past a Riga plate with non-uniform heat source/sink effects. Similarity transformations were used for the conversion of the partial differential equations that govern the flow to the ordinary differential equations. Owing to the complexity in solving these non-linear ordinary differential equations, we employ Runge-Kutta method of fourth order in association with shooting iteration procedure. The three-dimensional flow fields influenced by the parameters pertaining to this problem is discussed with the graphs and tables. The computations on the physical quantities of interest were also performed. The results end up to signify that the local skin friction coefficient enhances for modified Hartmann number and the local Nusselt number is diminished for larger values of heat source/sink parameter. A comparison between the numerical results and already existing data has been done and was found to be in good quantitative agreement.

This paper is mainly concerned with the investigation of steady, three-dimensional flow of H 2 O/NaC 6 H 9 O 7 base fluids with Fe 3 O 4 /Al 2 O 3 nanoparticles past a Riga plate implanted in a non-Darcian porous medium with internal heat generation/absorption effects. Water (H 2 O) and Sodium Alginate (NaC 6 H 9 O 7 ) are the base fluids, whereas Magnetite (Fe 3 O 4 ) and Aluminium oxide (Al 2 O 3 ) happens to be the nanoparticles. The numerical plan for non-Newtonian fluid Sodium Alginate is isolated through the Casson model. Suitable transformations on governing equations yield strong non-linear differential equations. The non-linearity of the basic equations and additional mathematical difficulties led to use numerical method. Plots for the outcomes of various related variables are furnished. The local skin friction coefficient and the local Nusselt number have been expounded. The results end up to signify that the local skin friction coefficient and the local Nusselt number are diminished for larger values of porosity parameter and the local inertia coefficient.

This work investigates the two-dimensional steady convective boundary layer flow and heat transfer of Newtonian/non-Newtonian base fluids with magnetic/non-magnetic nanoparticles over a flat plate which incorporates non-linear thermal radiation and slip effects. We considered magnetite and aluminium oxide as magnetic and non-magnetic nanoparticles suspending inside the two sorts of base fluids specifically Water and Sodium Alginate. For physical significance we analyzed the behavior on non-Newtonian profiles by employing Casson model individually. The particular intrigue lies in looking the impacts of non-linear thermal radiation on the behavior of the flow. The solution of wide class of boundary value problems are facilitated by the change of the partial differential equations administering the flow utilizing similarity transformations into ordinary differential equations. The ODE's are numerically handled by applying fourth order Runge-Kutta integration scheme in association with shooting procedure. The novel results for the dimensionless velocity and temperature inside the boundary layer are exhibited graphically for various parameters that describe the flow. A graphical demonstration is given for the skin friction coefficient and the local Nusselt number. (C) 2018 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.