Casson Nanofluid Research Articles

Darcy-Forchheimer Flow of Casson Nanofluids Towards a Spinning Disk with Non-Uniform Heat Source

Darcy-Forchheimer Flow of Casson Nanofluids Towards a Spinning Disk with Non-Uniform Heat Source

MHD Stefan Flow of Casson Nanofluid Complete a Porous Medium in The Presence of Chemical Reaction with The Effect of Thompson as Well as Troian Slip Over a Plate in the Company of Radiation

In this work, we report the effects of Thompson, Troian slip, and Stefan blowing on the magnetohydrodynamic (MHD) Cassonnanofluid behavior via a porous media while a chemical reaction is taking place. We also examine the effects of radiation parameters, Joel heat, and velocity distribution using a two-phase model for nanofluids. Similarity transformations may be used to convert the primary Partial Differential Equations (PDEs) into Ordinary Differential Equations (ODEs). MATLAB Shooting and Runge-Kutta algorithms may be used to solve nonlinear equations. The variations in non-dimensional parameters show the effects on mass transfer, heat, and fluid flow properties. It is shown that the skin friction coefficient falls as the Stefan blowing parameter S increases. As the values of the Thompson and Troian slip parameters increase, the fluid concentration decreases. With an increase in Nt, Nb, and k, the fluid's heat rises but its concentration falls. The results of this analysis provide several enticing aspects that are going to give merits for further study of the problems.

A mathematical model of Casson nanofluid flow over a vertically stretched porous surface along with bioconvection, Joule heating and thermal Robin conditions

The current analysis aims is to investigate the steady-state visco-plastic Casson nanofluid flow over an electrically conducting stretching porous surface. Thermophoresis and Brownian motion parameters are utilized for modeling and analysis. Also, Joule heating, thermal radiation, thermal robin condition, thermo-solutal stratifications, and viscous dissipation are considered for energy and nanoparticle concentration. Using appropriate similarity transformation, the partial differential equations (PDEs) system is altered into ordinary differential equatons (ODEs). The Homotopy analysis method (HAM) is used for solving governing equations. The effect of distinct physical parameters on the velocity, concentration, temperature, and microorganism’s density is revealed graphically and discussed tabularly. Additionally, numerical analysis is conducted on designed Nusselt number, Sherwood number, skin friction, and motile microorganism’s density. The major finding of the study is that the fluid velocity decreases as both the magnetic parameter and Casson fluid parameter increases. Instead, increasing the values of the Deborah number and activation energy results in an increase in fluid temperature. The current study is useful for coating deposition of magnetic nanomaterials at comparatively higher temperatures.

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.

Featuring the stagnation point flow of Casson nanofluid with thermal radiation and swimming microorganisms over a stretching sheet: A computational modeling via analytical method

Here, the investigation examines the flow of a nanomaterial toward stagnation point past stretching sheet having microorganism. The thermal radiative and heat generation have been accounted as well as convective boundary conditions. The influence of thermophoretic and Brownian movment has been considered. It has been proposed that the suitable transformation be utilized in order to convert the system of PDEs into ODEs. The analytical solutions are created through the Homotopy Analysis Method (HAM). The physical parameters with modelled equations have been graphically explained with related physical results. The numeric magnitude of drag friction, heat, mass transport and motile microorganism dendity were also computed and described for numerous emerging parameters. The result shows that the flow decreases with the rinsing value of Casson parameter. The impact of enhancing fluid parameters is too depressed the momentum and thermal boundary layer. The augment in the radiation boost the thermal layer whereas an enlargement in the input of the Lb tends to depreciation the motile density. Validation of the work is existed by validating the current outcomes with previous publishing results. The existing and potential applications of bioconvection have generated a new fascination in the theoretical investigation of the synthesis and process control in biofuel cells and bioreactors.

Optimizing heat transfer with electro-osmotic ciliated propulsion in a non-uniform canals with Cu-blood characteristics considering thermal casson nano fluid

Electroosmosis peristaltic flows find promising applications in electro-fluid thrusters in space propulsion, polymer injection systems, ion exchange membrane designs, microbe fuel cells, biochip fabrication and fossil fuel energy process. In light of this, the current work aims to investigate blood based electroosmotic peristaltic flow in a ciliated, non-uniform propagation channel when copper nanoparticles are present. For that purpose, mathematical modeling is done in two dimensional frame and then governing partial differential equations are simplified and converted in ordinary differential equations using dimensionless quantities and long wave length and low Reynolds number approximations. In result we got coupled nonlinear boundary value problem that is solved numerically using three-stage Lobatto IIIa formula known as bvp4c invoking shooting technique. Peristaltic ciliated waves are thought to pass along the channel wall. The properties of both fluid phase and particle phase flow are modeled and investigated. Plotting against various parameters, streamline contours, temperature contours, concentration and temperature profiles, and pressure rise graphs are examined in-depth from a physical perspective. The obtained results revealed that concentration profile α upsurges for rising values of Casson fluid parameter β, nanoparticle volume fraction ϕ and flow rate Q while it drops with an increase in particulate volumetric fraction C, Eckert number Ec, Soret number Sr, Schmidt number Sc and viscosity constant. A decrease in temperature is also caused by an increase in the volumetric percentage of nanoparticles. In the pumping portion, there is a decrease in pressure rise; however, this decrease changes to an increase in the increased pumping zone.

The impact of double‐diffusive convection on electroosmotic peristaltic transport of magnetized Casson nanofluid in a porous asymmetric channel

AbstractThe primary objective of the present article is to investigate the heat and mass transfer in mixed convection peristaltic flow of Casson nanofluid through an asymmetric permeable channel filled with a porous medium in the presence of electroosmosis. Magnetohydrodynamics and radiative heat transfer are also considered. The study is motivated by industrial micro‐pumping systems utilizing multi‐functional nanomaterials. Researchers have investigated the distinct temperature and rheological properties of Casson nanofluids. Solutal molecular diffusion and nanoparticle diffusion are both examined. Mixing nanoparticles with Casson fluid alters its flow characteristics and heat transmission, amalgamating different properties that are useful in a wide range of industrial and scientific applications. Buongiorno's two‐component nanoscale model is deployed for simulating nanofluid transport, and the Rosseland diffusion flux is utilized for optically thick electromagnetic liquids. Heat generation or absorption and cross‐diffusion (Soret and Dufour) effects are also incorporated in the model. An efficient analytical approach known as the long wavelength‐low Reynolds number lubrication approximation (LWL‐LRN) is utilized to solve the non‐dimensional boundary value problem. Validation of the solutions with previous studies is included. Graphs are presented using MATLAB 2022b to visualize the influence of key parameters including permeability, magnetic field, thermal radiation, Grashof number, Brownian motion, thermophoresis, electrical field and Prandtl number on transport characteristics (velocity, temperature, concentration), and trapping phenomena associated with peristaltic propulsion. As thermophoresis and Brownian parameters are intensified, there is a strong response in nanoparticles which induces axial acceleration, as observed at locations y = 0.15, where u = 0.191, and y = 0.33, where u is elevated to 0.14. An increase in radiation parameter () results in a depletion in axial velocity magnitudes along the left half of the wall and also modifies velocity distribution in the right section of the microchannel. An increase in the thermal radiation parameter (Rn) and heat absorption (sink) is found to suppress temperatures. Increasing heat generation, thermal Grashof number (Gr), and solutal Grashof number (Gc) decelerate axial flow in the left half space but accelerate flow in the right half space of the micro‐channel. Increasing radiation parameters and thermal Biot number boost temperatures when heat sink is present but reduce them when heat source (generation) is present. Increasing radiation parameter boosts nanoparticle volume fraction (concentration) whereas an elevation in heat generation and thermal Biot number both induce the opposite effect. Increasing the magnetic field damps the flow and reduces the number of boluses present. However, bolus volume increases with greater thermal Grashof Number , Darcy (permeability) number , and Helmholtz‐Smoluchowski velocity , that is, stronger axial electrical field.

Impact of Autocatalytic Chemical Reactions and Convective Boundary Conditions on NaC6H7O6–SiO2-Based Nanofluid Oblique Stagnation Point Flow Across a Stretching Sheet

The main motivation of this study is to examine the effects and behavior of Casson nanofluid mainly in reference to oblique stagnation points across a stretching surface. Oblique stagnation point (OSP) motions have so many applications, like artificial fibers, sticky materials, drying paper, and freezing electrical equipment, and numerous applications for endothermic and exothermic processes exist, including in heat exchangers, cooking, and drying damp clothes. Because of these applications on various domains, the Casson nanofluid OSP motion via a stretching sheet is studied with endothermic/exothermic chemical processes and convective boundary conditions (CBC). Similarity transformations are employed to convert partial differential equations (PDEs) into a collection of ordinary differential equations (ODEs). Furthermore, some significant engineering coefficients are discussed and also evaluated the behaviors of several nondimensional factors using the Runge–Kutta–Fehlberg-45 numeric method with a shooting scheme and graphical representations. The outcomes signify that temperature and concentration both rise with a rise in the Casson parameter and activation energy (AE) respectively. A higher Biot value leads to a higher temperature profile. A temperature profile increases with an enhance in the Casson parameter. The addition of a solid fraction will enrich the mass transmission rate in combination with AE.

A peristaltic motion for pressure driven flow of Casson nanoliquid along with gyrotactic microorganisms in an entropic porous channel: A numerical study

Pump designs can be optimized for maximum energy efficiency, reduced waste, and enhanced overall performance by taking entropy factors into account. In this regard, the current investigation concentrates on examination of thermodynamic analysis for bio-convection peristaltic phenomenon of a non-Newtonian Casson nanofluid in an asymmetrical elastic channel by considering the generation of entropy. The pressure driven flow is managed by using lubrication approach and converting the system in to laboratory (wave) frame. The resulting findings of physical expressions together with the surface conditions are tackled by shooting numerical algorithm on conventional software Mathematica with the help of built-in tool (NDSolve). Graphical attitude of numerous physical quantities (entropy generation, Bejan number, and velocity profile, density of gyrotactic motile microorganisms and nanoparticles volume fraction) is also added and the results are equated with the existing literature. After detailed discussion on graphical display, it is concluded that with porosity of the medium helps to get the entropy generation reduced while, with the increase in bio-convection Peclet value, the micro-organisms’ density declines. The results of the study can be of great significance in the fields of nanotechnology, bio-microsystems and Bio-nano cooling phenomenon.

Investigation of thermal radiation and joule heating effects on variable viscosity Casson nanofluid flow over a stretching sheet in Darcy–Forchheimer porous medium

Nanofluids possess unique thermal and rheological properties that offer significant advantages in enhancing heat transfer efficiency in various applications, such as heat exchangers, cooling systems, and microdevices. In this study, we investigate the combined effects of thermal radiation, Joule heating, variable viscosity, and a two-phase model on the flow behavior and heat transfer characteristics of a magnetohydrodynamic Casson nanofluid flowing over a stretching sheet in Darcy-Forchheimer porous media. The governing partial differential equations are converted into a system of first-order ordinary differential equations numerically solved using the bvp5c package in MATLAB. Consequently, the result indicates that the velocity profile increases with thermal radiation, variable viscosity, and viscous dissipation, decreasing with the magnetic field, permeability index, and Forchheimer coefficient. Also, the temperature profile shows an increase with the permeability index, viscous dissipation, and thermal radiation, but a decrease with the Forchheimer Coefficient, variable viscosity, and magnetic field. Additionally, the concentration profile exhibits an increase with the Forchheimer coefficient and permeability index, and variable viscosity while it decreases with viscous dissipation, magnetic field, and thermal radiation. Analyzing the skin friction coefficient reveals an increase with magnetic field and thermal radiation and a decrease with permeability index and Forchheimer coefficient as well as variable viscosity. Moreover, the local heat transfer rate demonstrates an increase with the variable viscosity, and magnetic field as well as the Forchheimer coefficient and permeability index. At the same time, it decreases with the viscous dissipation. Furthermore, the local mass transfer rate displays an increase with the magnetic field and thermal radiation and viscous dissipation, while it decreases with the variable viscosity as well as permeability index, viscous dissipation, and Forchheimer coefficient. Finally, the current findings are compared with that of the existing literature and a sound agreement was established.

Exploring heat transfer in magnetized binary nanofluid flows with gyrotactic microorganisms through bioconvection analysis

Many industrial and thermal systems regard continuous thermal propagation as vital because it may improve the efficacy of thermal engineering machinery and engines. Consequently, this is a potential development for bettering power energy through employing magnetized nanomolecules within a heat-carrying non-Newtonian fluid. This study examines nanofluids with Casson and Maxwell nanofluids by considering nonlinear radiation and heat generation because of bioconvection over a stretchable surface with a porous material. Moreover, the interaction between gyrotactic microorganisms and activation energy has been discussed in detail. The flow model under consideration is formulated via Thermophoretic diffusion and Brownian motion. Using similarity conversions, the regulating partial differential equations (PDEs) are made dimensionless, thus reducing them to ordinary differential equations. A shooting technique was employed to solve the problem; MATLAB software used RK methods combined with the shooting method to solve this problem. Many diagrams have been depicted to describe the diverse flow factors; other interesting quantities, such as motile microbes’ density and Sherwood numbers, are computed and plotted. In addition, mixed convection, buoyancy ratio, bioconvection Rayleigh constant, and resistivity due to magnetized significantly affect velocity profile through Casson–Maxwell nanofluid. It is seen that both Casson and Maxwell fluids have nonuniform boundary layers of temperature and concentration fields. Maxwell fluids’ temperature and concentration fields are more sensitive than Casson fluids toward the same parameters.

A novel design of recurrent neural network to investigate the heat transmission of radiative Casson nanofluid flow consisting of carbon nanotubes (CNTs) across a curved stretchable surface

AbstractThis study aims to develop a supervised learning artificial recurrent neural network algorithm supported by Bayesian regularization called (ARNN‐BR) to analyze the impact of physical parameters, including radius of curvature (), Casson parameter (), heat generation parameter () and radiation parameter () on velocity fʹ(η), and temperature profiles θ(η) in Casson nanofluid consisting of carbon nanotubes (CNTs‐CNF) model for single and multiwalled CNTs across a curved stretched surface. The numerical dataset of the proposed model has been constructed by varying various parameters for five scenarios that are used in a Bayesian regularization‐based intelligent computing method to build networks for approximating the numerical solutions of CNTs‐CNF model. It is observed that increment in the dimensionless radius of curvature () causes to rise an increase in the velocity profile fʹ(η) for both SWCNTs and MWCNTs. However, a contrasting trend is observed when the Casson parameter () is increased to higher values. The temperature θ(η) of fluid increases as the heat generation parameter () and radiation parameter () increase. However, an opposite behavior is noticed when the dimensionless radius of curvature () varies. The effectiveness and significance of designed Bayesian regularization based artificial recurrent neural networks (ARNN‐BR) is demonstrated through regression index measurements, error histogram studies, auto‐correlation analysis and convergence curves showing a minimal level of mean square error (E‐11 to E‐04) for the comprehensive simulations of CNTs‐CNF model. The designed ARNN‐BR algorithm is employed in many domains such as voice recognition, machine translation, identification of neurological brain illnesses as well as for automated translation of texts across different languages.

Melting heat transfer and entropy analysis of MHD Casson nanofluid flow through a stretchy surface with Joule heating and complete slip

Purpose The purpose of this study is to examine the melting heat transfer of magnetohydrodynamics Casson nanofluid flow with viscous dissipation, radiation, and complete slip effects on a porous stretching sheet. Since, the study of melting heat transfer has mesmerized the attention of scientists and engineers in the sense of its enormous uses in industrial processes, solidification, casting, and technology. Design/methodology/approach Bejan number and entropy are analyzed. Exploration of irreversibility is modeled using the thermodynamics second law. There is a discussion on thermophoresis and Brownian diffusion along with first-order chemical reactions. Adequate transformations are introduced to convert the controlling partial differential equations to ordinary differential equations. The three-phase Lobatto solvers (bvp5c) are used to obtain numerical solutions of the transmitted equations. Findings The effects of various factors on temperature, velocity, concentration, Bejan number and entropy rate are shown graphically. The velocity field is enhanced by increasing the melting heat parameter, and it declines for growing magnetic parameters. Temperature is decreased for increasing parametric values of melting heat, porous and Casson parameters. A 7% decrease in the Sherwood distribution is seen when we increase the Brownian motion parameter from 0.1 to 0.2. Similarly, an 11% decrement is found in the Nusselt distribution for increasing the Brinkman number from 0.5 to 1. Originality/value Entropy and Bejan number experience dual tendencies whenever the melting heat parameter increases. Nusselt number and skin friction experience the opposite behavior for the increasing values of melting parameter. Sherwood number decreases for the increasing values of melting parameter. The velocity profile is directly related to the melting parameter and inversely related to porous and magnetic parameters. Thermophoresis and Brinkman parameters boost the temperature profile and it is controlled by melting and porous parameters. Some notable fields where the present study is used inevitably are silicon wafering, geothermal energy recovery and semiconductor manufacturing.

Thermal analysis of Casson nanofluid flow over exponentially/horizontally stretching cylinders with physical conditions

Thermal analysis of Casson nanofluid flow over exponentially/horizontally stretching cylinders with physical conditions

Mixed Convection Flow of MHD Casson Nanofluid over a Vertically Extending Sheet with Effects of Hall, Ion Slip and Nonlinear Thermal Radiation

This manuscript investigates the effects of viscous dissipation, Ohmic heating, nonlinear thermal radiation, chemical reactions, Hall current, and ion slip on the mixed convection flow of magnetohydrodynamic (MHD) Casson nanofluid over a vertically stretching sheet in a spongy medium. The strongly nonlinear ordinary differential equations (ODEs) derived from the governing equations are solved using a sixth-order, seven-stage Runge–Kutta (RK6) method in conjunction with the shooting technique. Numerical simulations are conducted using an open-source Python programming language. The study evaluates temperature, velocity, nanoparticle concentration, skin friction coefficients, Nusselt number (rate of heat transfer), and Sherwood number (rate of mass transfer) based on dimensionless parameters. Key findings reveal that increasing ion slip and Hall currents enhance the velocity profile in the x-direction, while the Casson parameter exerts a diminishing effect. The fluid temperature decreases with higher Hall current, Casson parameter, and ion slip values but increases due to nonlinear thermal radiation, the temperature ratio parameter, and the Eckert number. Furthermore, the chemical reaction parameter and Schmidt number reduce nanoparticle concentration within the boundary layer, with the Casson parameter amplifying this effect. The study also examines the rates of mass, heat, and momentum transfer near the surface under varying parameter influences, presenting results through comprehensive graphs and tables. To validate the numerical method, a comparative analysis is conducted against previous studies, demonstrating excellent agreement and thus confirming the reliability and accuracy of the computational approach.

Analytical and numerical examinations on the stability investigation of Casson nanofluid flow in a permeable layer controlled by vertical throughflow

Purpose The purpose of the study is to analytically as well as numerically investigate the weight of throughflow on the onset of Casson nanofluid layer in a permeable matrix. This study examines both the marginal and over stable kind of convective movement in the system. Design/methodology/approach A double-phase model is used for Casson nanofluid, which integrates the impacts of thermophoresis and Brownian wave, whereas for flow in the porous matrix the altered Darcy model is occupied under the statement that nanoparticle flux is disappear on the boundaries. The resultant eigenvalue problem is resolved analytically as well as numerically with the help of Galerkin process with the Casson nanofluid Rayleigh–Darcy number as the eigenvalue. Findings The findings revealed that the throughflow factor postpones the arrival of convective flow and reduces the extent of convective cells, whereas the Casson factor, the Casson nanoparticle Rayleigh–Darcy number and the reformed diffusivity ratio promote convective motion and also decrease the extent of convective cells. Originality/value Controlling the convective movement in heat transfer systems that generate high heat flux is a real mechanical challenge. The proposed framework proved that the use of throughflow is one of the most important ways to control the convective movement in Casson nanofluid. To the best of the authors’ knowledge, no inspection has been established in the literature that studies the outcome of throughflow on the Casson nanofluid convective flow in a porous medium layer. However, the convective flow of Casson nanofluid finds many applications in improving heat transmission and energy efficiency in a range of thermal systems, such as the cooling of heat-generating elements in electronic devices, heat exchangers, pharmaceutical practices and hybrid-powered engines, where throughflow can play a significant role in controlling the convective motion.

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.

Bioconvective reversible (an esterification process) Casson nanofluid flow over a radiative spinning disc with microorganism

This study describes the Casson (a non-Newtonian fluid) nanofluid bioconvection flow across a spinning disc in the presence of gyrotactic microorganisms, many slips and thermal radiation. Also, the flow is considered as a reversible flow. The esterification process is taken into account. Using the proper variables, a system of extremely nonlinear PDEs is converted into a system of ODEs. To arrive to the solution of such equations, a numerical approach is used. Using the bvp4c approach, nonlinear flow equations can be numerically solved. Investigated are the effects of different numbers on the thermal field, volumetric concentration of nanoparticles and microbiological field. The key characteristics of the parameters in relation to the profiles of the velocity, temperature, concentration and microorganisms are graphically assessed with appropriate physical effects. A graphical explanation is provided for the wall shear stress, local Nusselt number, local Sherwood number and local motile density number. Rate of motile density number shows a prominent difference between reversible and irreversible flows for Brownian motion and Peclet number. The results of the theoretical simulations have dynamic applications in the fields of biotechnology and thermal engineering.

Influence of activation energy and variable thermal conductivity on magneto-convective nonlinear thermo-radiative Casson nanofluid containing motile microorganisms over a sinusoidal surface

The activation energy of convective-radiative nanoliquids with sinusoidal walls has garnered significant academic interest in recent years. This focus arises due to the pivotal applications of nanoparticles in thermal engineering, industrial processes, and medical sciences. This article investigates the magnetohydrodynamic heat transfer characteristics of Casson nanofluids containing microorganisms influenced by an oscillatory surface. The study incorporates temperature-dependent viscosity and utilizes Buongiorno’s mathematical model to account for nonlinear thermal radiation, Brownian motion, and thermophoretic effects from using nanomaterials in Casson fluids. These effects enhance thermal conductivity, improving the heat transportation phenomenon while considering gyrotactic microorganism density distributions. The boundary layer flow problem is formulated using partial differential equations and associated boundary conditions, subsequently numerically simulated using the bvp4c function. The investigation explores the thermal behavior of nanoparticles in the presence of bioconvection phenomena, Lorentz force, chemical reactions, and activation energy. As a result, this model addresses variable thermal conductivity and bioconvection aspects in Casson nanofluids over a sinusoidal surface. Numerically computed results for the Nusselt number, motile density, and Sherwood number provide insights into several essential features. The findings reveal that an increase in the Casson fluid parameter correlates with a decreased velocity profile. The assumptions of variable thermal conductivity and temperature-dependent viscosity prove more effective in raising the temperature of nanoparticles. The nanoparticle concentration profile rises noticeably for smaller Schmidt number Sc values when the activation energy parameter is higher than larger Sc values. Additionally, the presence of microorganisms in Casson nanofluids leads to increased temperatures due to an elevation in the bioconvection Rayleigh number. Moreover, heightened oscillating frequency parameters decrease nanoparticle concentration and microorganism density. Including activation energy and oscillating frequency parameters further enhances the understanding of nanoparticle concentration and microorganism density dynamics, offering valuable contributions to theoretical research and practical applications across multiple interdisciplinary fields.

Radiation, absorption, and Joule heating Influence on MHD Casson fluid flow over an exponentially stretching surface

This work investigates the MHD convective flow through the boundary layer of a Casson nanofluid over an exponentially inclined porous stretched surface in the occurrence of radiation, absorption, and Joule heating. The proper conversions transform the PDEs that specify flow into a series of nonlinear ODEs. The MATLAB in-built solver bvp4c helps one to solve the problem. Graphical findings also show for non-dimensional profiles. For various values of parameters controlling the flow system, the numerical values of the Sherwood number and Nusselt number, friction factor are shown in tabular form. A comparison table is used to confirm the acquired findings.