Thermal Stratification Parameter Research Articles

MHD Casson Fluid Flow over a Stretching Surface with Suction, Double Stratification, and Heat and Mass Transfer Effects

Abstract In this article, we investigated the flow of a magnetohydrodynamic Casson fluid across an extending surface with exponential permeability in a double-stratified medium. Thermal radiation, suction, heat sources, viscous dissipation, and chemical reactions drive the stream field. We converted the flow describing partial differential equations into terms of ordinary differential equations by applying appropriate transformations. Next, we utilised the bvp4c package in Matlab to obtain numerical solutions for these equations. We explored and graphically showed the implications of different non-dimensional governing parameters for temperature, concentration, and velocity profiles. After analysis, we provide a tabular presentation of the friction factor, Nusselt, and Sherwood numbers. The Casson fluid temperature shows a rising trend for the solutal stratification parameter and a decreasing trend for the thermal stratification parameter, while the Casson fluid velocity shows a declining trend towards both of these parameters. The Casson fluid concentration also behaves differently depending on the stratification parameter; for example, it increases for thermal stratification and decreases for solutal stratification. We notice that an increase in the Casson parameter's value suppresses the velocity field. However, as the Casson parameter increases, both the temperature and the concentration improve. Furthermore, comparisons with previously published findings also support the current results. \sethlcolor{yellow}\hl{The study of MHD Casson fluid flow that includes suction, dual stratification, and the effects of heat and mass transfer is very useful in many areas, such as polymer processing, metallurgical engineering, biomedical applications, environmental sciences, and advanced cooling technologies.

Significance of tri‐hybrid nanoparticles on the dynamics of Ellis rotating nanofluid with thermal stratification

AbstractThe fluids flow containing nano size particles is essential in industrial applications, especially in nuclear cooling system and nuclear reactor to increase the energy performance. In connection to this, a trihybrid Ellis rotating nanofluid flow through a stretching surface for increasing the heat transportation is presented. By suspending three different types of nano size particles the trihybrid nanofluid is formed with distinct chemical and physical connection into base liquid. In this article, the nano size particles , and are mixed in (water). This type of mixture helps in degradation of noxious substances, cleaning environmental and many other appliances that requires the cooling effect. In addition, the linear thermal radiation is also considered. The governing equations of the flow and fluid temperature are minimized to ordinary differential equations and these equations are solved by Runge Kutta order fourth (RK45) approach. The approximate results are analyzed via graphs and the results reveal that thermal conductivity of trihybrid nano type fluid is more valuable as compared to hybrid and single nanofluid. Higher values of magnetic and rotational parameter have aggrandized the fluid temperature and opposite trend has observed for Ellis and thermal stratification parameter. Moreover, the results are compared with previous literature and found an excellent agreement.

Bioconvective three-dimensional flow of Sutterby nanoliquid due to moving plate with activation energy applications

Owing to enhanced features of nanomaterials, various applications of such materials have been suggested in the thermal systems, heat exchanges, electronic cooling systems, coolant processes, energy production etc. Following to such motivated applications, the objective of current analysis is to presents the bioconvective double stratification flow of Sutterby nanofluid due to bidirectional moving surface. The thermal interpretation of problem is subject to utilization of radiative effects, activation energy and heat source. The observations for heat, mass and microorganism's assessment are performed by using the convective boundary conditions. Shooting numerical simulations are performed for modeled problem. It is noticed that heat transfer enhances due to thermal stratification parameter. An increment in mass transfer is subject to larger values of mass stratification Biot number. The claimed results offer significance in controlling the heating and cooling processes, thermal devices, energy generation, manufacturing developments, solar systems etc.

Impacts of thermally stratified medium on transient convective heat transfer between co‐axial horizontal fixed pipes: Applications of the thermal stratification

AbstractThermal stratification improves coaxial pipe systems’ efficiency and stability. Thermal stratification enables accurate temperature maintenance, reduces thermal stress, optimizes heat transmission performance, and minimizes usage of energy to guarantee the system's long‐term performance. The main aim of the current study is to investigate the impacts of thermal stratification on buoyancy force flow and thermal transmission between coaxial fixed pipes. In the present research, the applications of thermally stratified medium on transient convective heat transfer between two coaxial fixed pipes are studied. A two‐dimensional mathematical formulation in terms of mutually nonlinear partial differential equations is used to analyze the unsteady flow and temperature field between the co‐axial pipes, when the internal pipe is uniformly heated and the outer wall of the external pipe is placed at infinity from the surface of the inner fixed pipe. Flow is assumed along the axial direction of the internal pipe and stationary boundary condition is assumed at the surface of the inner pipe. The coupled equations of the simulated model are solved numerically by applying the Implicit Finite Difference Technique. The computed outcomes in the form of geometrical interpretation are highlighted by using the technically advanced software TECHPLOT‐360. Comprehensive detail of the obtained results for the non‐dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time‐dependent surface shearness and time‐dependent energy shearness in results and discussion section of the manuscript. The emphasis is placed on the thermal stratification parameter in the above mentioned chief quantities. From the obtained results, it is predicted that the fluid flow pattern and thermal distribution are both reduced for rising values of the thermal stratification parameter S = 0.001, 0.03, 0.05, and 0.07. Minimum flow and thermal profile are observed at S = 0.07. Further, the amplitude of the time‐dependent surface shearness is uniformly distributed throughout the medium and the amplitude of the time‐dependent energy shearness is reduced effectively for S = 1.0, 5.0, and 10.0.

Numerical heat transfer analysis of bio convective flow of non-Newtonian nanofluid with Darcy-Forchheimer effect over a curved stretching surface

The main aim of this study is to investigate the behavior of bio-convective flow of 2nd grade micropolar nanofluid with Darcy-Forchheimer law over a curved porous stretching surface. The fluid flow analysis includes novel aspects such as the nonuniform heat source/sink, Joule heating, magnetic field, chemical reaction, and thermal radiation. Furthermore, the boundary of the stretching surface is acquired the stratification conditions. A suitable conversion method is employed to transform the flow model into a collection of ordinary differential equations, characterized by their nonlinearity. The bvp4c technique on the MATLAB is utilized to acquire numerical solutions for this set of nonlinear equations. The characteristics of various influential parameters on the velocity, temperature, concentration, and microorganism density profiles are observed and discussed. In the present problem, it is observed that by the growth of micropolar parameter enhances the angular fluid velocity. Moreover, larger values of the magnetic parameter, Darcy number, and porosity parameter result in a decrease in the fluid’s linear velocity. The temperature profile exhibits a decreasing pattern with the elevation thermal stratification parameter, while the opposite trend shows by the increment of the radiation parameter and Eckert number. Additionally, the concentration of nanoparticles decreases as the Schmidt number and Brownian motion parameter increases.

Stratified numerical heat and mass transport mechanism in MHD Maxwell fluid flow with nonuniform heat source/sink

The present boundary layer flow of Maxwell fluid over a stretching sheet has good number of practical applications in metallurgy, drawing of plastics, polymer sheet extrusion including hot rolling extrusion, glass blowing, spinning of fibers, rubber and plastic sheets, crystal growing and many more. Due to these extensive applications of Maxwell fluid in engineering, medicine and manufacturing industries including the above-mentioned applications, authors have motived, inspired and investigated the present problem. However, in this research paper, the influences of Soret and Dufour effects on the steady-state Maxwell fluid flow past a stretching sheet with nonuniform heat source/sink are considered numerically. The thermal and concentration stratifications impacts are also incorporated. The viscous dissipation and magnetic field effects are also included in the respective governing equations. The main novelty and uniqueness of this numerical research is to generalize the earlier studies and describe the salient features of magneto-thermo visco-elastic dissipative Maxwell fluid motion about a stretching sheet with cross-diffusion effects under the influence of double stratification phenomena. To differentiate the non-Newtonian fluids from those of Newtonian fluids, a well-known Maxwell fluid flow model is used in the present study. The investigated physical problem results the highly nonlinear coupled partial differential equations (PDEs) and which are not amenable to any of the direct methods. Suitable similarity transformations are deployed to reduce the highly complex PDEs into the system of ordinary differential equations (ODEs). A robust BVP4C Matlab function is employed to solve the rendered dimensionless system of ODEs. The numerically generated computed data is plotted in terms of velocity, temperature and concentration profiles including engineering quantities of interest such as skin-friction, Nusselt and Sherwood numbers in the flow region. It is evident from the current analysis that, the amplified magnetic field decreases the velocity field and increases the thermal and concentration distribution fields. Accelerating Maxwell’s number diminished the flow velocity and increased the temperature field. Increasing Soret and Dufour numbers enhances the concentration and temperature fields, respectively. Amplifying Maxwell’s number raises the skin-friction coefficient and enlarging the thermal stratification parameter magnifies the thermal transport rate. The mass transport rate amplified with a raise in concentration stratification number in the flow region. Finally, it is provided that, the current results are excellently matching with earlier published results in the literature and it confirms the accuracy of the used numerical method and the produced similarity solutions.

Computational analysis magnetohydrodynamics natural convection flow round vertical thermally stratified jet: Finite difference method in conjunction with primitive variable formulation

The problem of magnetohydrodynamic free convective heat transfer mechanism across a laminar, round, vertical, and thermally stratified jet is examined. The boundary layer equations are non-dimensionalized, and then, using the primitive variable formulation, the finite difference method is used to find the numerical solution of the problem. The impact of Prandtl number, magnetic parameter, and stratification parameter on velocity distribution, temperature profile, and heat transfer rate is explained graphically and in tabular form. It is found that for increasing values of thermal stratification parameter S, the velocity profile increases while temperature distribution and rate of heat transfer decrease. Similarly, with an increase in the values of Prandtl number, velocity, and temperature distribution decrease, but the rate of heat transfer increases.

Artificial neural computing and statistical analysis of heat and mass transport of nanofluid flow with melting heat and thermal stratification

The melting heat phenomenon in viscous nanofluid MHD flow over a stretching sheet with variable porosity and permeability was utilized. The behavior of magneto-viscous nanofluid flow was scrutinized using the concepts of machine learning and statistics. Thermal stratification, heat source, and activation energy in the solution of tween-20 nanoparticles and an ethyl-acetate base-type fluid are examined. Brownian and thermophoretic phenomena are included. Non-linear partial differential equations (PDEs) are converted into non-linear ordinary differential equations (ODEs) via von Karman similarity variables. Dataset is generated by the 4th-order Runge-Kutta numerical method for the artificial neural network. The ratio parameter and melting parameter enhance the velocity outline, while the melting parameter and thermal stratification parameter reduce the temperature outline. An increase in the concentration outline is seen with the activation energy parameter and Brownian motion parameter both increase the concentration outline. The system's performance using metrics like regression analysis, mean squared error, and error histograms is evaluated. The impact of these factors on significant results, such as the drag coefficient and heat transfer rate, is statistically investigated using multiple linear regressions. The integration of statistical and machine learning methods is deemed crucial for enhancing understanding of complex fluid dynamics in magnetic nanofluid flows.

Effect of Double Stratification on MHD Williamson Boundary Layer Flow and Heat Transfer across a Shrinking/Stretching Sheet Immersed in a Porous Medium

The present study aims to provide a mathematical model of the Williamson fluid flow via a permeable stretching/shrinking sheet in the MHD boundary layer in the presence of a heat source, chemical reaction, and suction. This study is novel because it investigates the physical effects of thermal and solutal stratification on convective heat and mass transport using thermal radiation. The flow’s PDEs are numerically solved using the BVP4c approach and the pertinent similarity variables until a stable solution is found. Through visual analysis, the effects of dimensionless factors on temperature, velocity, and concentration profiles are examined. This encompasses the mass transfer rate, the heat transfer rate, and the coefficient of friction. The results of the present analysis are found to be consistent with those of previously published studies. The findings demonstrate that enhanced temperature and concentration profiles cause the Williamson, magnetic, and permeability parameters to rise in conjunction with a drop in the dimensionless velocity. In relation to temperature, the thermal stratification parameter exhibits the opposite tendency. Regarding the solutal stratification parameter, concentration profiles are seen to show the opposite trend. Lastly, the current work will have important implications for the removal of dust and viruses from viscoelastic fluid in bioengineering, the medical sciences, and medical equipment.

Thermal stratification and heat generation/absorption impacts on stagnation point flow of MHD UCM fluid through a permeable medium

We investigated two dimensional magnetohydrodynamic (MHD) stagnation point upper-convected Maxwell (UCM) fluid flow through a stretch sheet in a porous medium having the effects of heat generation/absorption and thermal stratification. Utilizing suitable similarity transformations, the governing partial differential equations (PDEs) of the fluid flow and heat transfer phenomena are converted to nonlinear dimensionless ordinary differential equations (ODEs). We numerically solved these nonlinear ODEs and compared our results of skin friction and Nusselt number with previous work which demonstrated accuracy of the presented solutions. We also illustrated the graphical behavior of dependent variables that is of the velocity and temperature fields versus the key parameters involved. It showed that velocity field decreases for Deborah number, porosity and magnetic parameters. The temperature of the fluid showed an increasing behavior for Deborah number, magnetic, porosity, and heat source/sink parameters while declining for thermal stratification and velocity ratio parameters.

A Numerical Investigation of the MHD Ternary Hybrid Nanofluid (Cu-Al2O3-TiO2/H2O) Past a Vertically Stretching Cylinder in a Porous Medium with Thermal Stratification

This study focuses on examining the impact of thermal stratification on the magnetohydrodynamics (MHD) flow of water-based nano, hybrid, and ternary hybrid nanofluids past a vertically stretching cylinder in a porous medium. The nanoparticles Cu, Al2O3, and TiO2 are suspended in a base fluid H2O, leading to the formation of a ternary hybrid nanofluid Cu-Al2O3-TiO2 /H2O. The numerical results are calculated with the 3-stage Lobatto IIIa approach, specifically implemented by Bvp4c in MATLAB. The impacts of various parameters are visually depicted through graphs and quantitatively represented in tables. The velocity and temperature of the ternary hybrid nanofluid are lowered by the thermal stratification parameter compared to when there is no stratification. The ternary hybrid nanofluid has a higher heat transfer rate than the hybrid nanofluid, and the hybrid nanofluid has a higher heat transfer rate than ordinary nanofluids.

Sensitivity analysis and response surface methodology for entropy optimization in the exponentially stretching stratified curved sheet for Casson–Williamson nanofluid flow

The current study explains the parametric entropy optimization by using response surface methodology and sensitivity analysis. It also reveals the effects of thermal radiation and exponential heating on Casson–Williamson nanofluid flow over an exponentially stretching curved sheet. The Darcy–Forchheimer model is used and stratification, Navier slip, and suction-injection are used as the boundary constraints. The 4–5th ordered Runge–Kutta Fehlberg approach is enacted to exhibit the modeled flow. Response surface methodology is used to build the statistical design for the Weissenberg number, magnetic parameter, and Brinkmann number. The thermal stratification parameter, according to the findings, lowers temperature. Entropy grows as Brinkmann number and magnetic parameter increase. When the thermal buoyancy factor assumes the minimum value, little shear stress is seen for high Forchheimer number. The squared co-efficient is confirmed to be 99.99 %. The Pareto chart confirms that point 2.2 is the important point. Entropy surface diagrams in three dimensions demonstrate that with high magnetic parameter, high Brinkman number levels and low Weissenberg number levels, high entropy is obtained. For low and medium levels of magnetic parameter, Weissenberg number exhibits positive sensitivity, whereas for high and medium levels of magnetic parameter, it exhibits negative sensitivity.

Thermal energy transport in stratified 2D-Casson fluid flow over an inclined exponentially stretching surface with Soret/Dufour effects: Numerical simulations and applications in energy harvesting

Significance: The thermal energy transfer in nanofluid flow over an exponentially stretching surface has crucial practical configurations in various industrial processes, and it has potential applications in heat exchangers, chemical engineering, energy harvesting, and material processing. Purpose: This study is devoted to exploring the features of free convection in the thermally stratified, unsteady flow of Casson fluid over an inclined, exponentially stretching surface. Moreover, the implications of nonlinear thermal radiation, activation energy, and thermal/salute stratification effects are examined over the thermal energy transport distributions. Diffusion-thermo and thermo diffusion impressions are also taken into consideration. Methodology: By introducing reasonable transformations, partial differential equations are altered into ordinary differential equations. A nonlinear system of differential equations is solved numerically by employing the Midrich numerical technique. Findings: The impacts of diverse fluid parameters like the Soret/Dufour number, temperature difference parameter, radiation parameter, thermal/salute stratification parameter, magnetic parameter, and Prandtal number are assessed and depicted in plots by explaining the physical justifications of each parameter. Also, numerical values of sink friction and local Nusselt and Sherwood numbers are computed and examined for different values of pertinent variables involved in the problems. It is found that the rate of thermal energy transport is significantly enhanced by the larger estimation of the radiation parameter. Furthermore, it is perceived that the escalation in the temperature ratio constant leads to increased thermal convection in the fluid, while the larger thermal stratification constant decays the rate of heat transport in the fluid. Additionally, the rate of thermal transport is de-escalated due to the escalation in the intensity of thermal stratification parameter.

New Analytical and Numerical Solutions for Squeezing Flow between Parallel Plates under Slip

In this article, the effects of physical flow parameters on squeezed fluid between parallel plates are explored through the Darcy porous channel when fluid is moving as a result of the upper plate being squeezed towards the stretchable lower plate, such as velocity slip, thermal slip, solutal slip, thermal stratification parameter, solutal stratification parameter, squeezing number, Darcy number, Prandtl number, and Schmidt number. The governing equations are transformed into a nonlinear ordinary differential equation using the appropriate similarity transformations. The resulting equations are solved by using the perturbation iteration method (PIT) to produce a convergent analytical solution with high accuracy. The phenomena of the squeezing fluid as the plates are moving apart and when they are coming together are illustrated using the resulting analytical solutions. Plots are used to discuss the significant effects of physical parameters on velocity, temperature, and fluid concentration profiles. The skin friction coefficient and Nusselt Sherwood values have graphical interpretations that are listed. For strong velocity slip parameters, the results demonstrate the existence of a minimum velocity profile close to the plate and a growing velocity profile distant from the plate. Additionally, as the slip effects rise, the fluid temperature and concentration both considerably drop. The results of the fourth-order Runge-Kutta method (RK4M) and the presented analytical solutions provided are in excellent agreement.

A numerical study of thermal and diffusion effects on MHD Jeffrey fluid flow over a porous stretching sheet with activation energy

The primary aim of this research work is to develop a mathematical model for the two-dimensional steady incompressible flow of a Jeffrey fluid over a vertical stretching sheet immersed in a Darcy porous medium. The combined effects of Soret and Dufour numbers, activation energy, viscous dissipation, thermal radiation, mixed convection, and Joule heating are included in the energy and concentration equations within this model. Using appropriate similarity variable transformations, the governing partial differential equations were altered into nonlinear ordinary differential equations and then solved numerically using the Runge-Kutta-Fehlberg method along with the shooting technique. The impact of various physical parameters on concentration, velocity, and temperature profiles is deployed through graphs. The velocity increased with a gradual increment in the values of the viscous ratio, thermal, and solutal stratification parameters, whereas the reverse trend was noticed for the magnetic strength. The temperature diminishes as the Prandtl number increases, whereas the opposite scenario exists for Eckert and Dufor numbers and radiation. The fluid concentration rises for a monotonic increment of the Soret number, while it reduces as the Schmidt number, activation energy, and reaction constraint escalate. The amplification of skin friction is observed with an increase in magnetic field strength, while it decreases with an increasing viscous ratio factor. The Nusselt number decreases as radiation increases and the Eckert number rises, but the opposite scenario occurs with increases in the Prandtl number. The Sherwood number is heightened by an increase in the Schmidt number, reaction, and activation energy factors. Moreover, the numerical values of skin friction and the Nusselt number are compared with the previously published work, demonstrating excellent agreement between the results.

Computational analysis of magnetized Casson liquid stretching flow adjacent to a porous medium with Joule heating, stratification, multiple slip and chemical reaction aspects

This article aims to investigate the characteristics of thermo-solutal magnetohydrodynamic (MHD) non-Newtonian smart coating boundary layer flow of a stretching substrate adjacent to a porous medium, considering the influence of chemical reactions and thermal radiation subject to a transverse static magnetic field. A non-Darcy drag force model is deployed to capture both Darcy bulk drag and inertial Forchheimer (quadratic) drag effects. A diffusion flux model is deployed for radiative heat transfer. The Casson viscoplastic model has been utilized to simulate rheological characteristics. Due to polymeric slip effects, three slip phenomena are included at the wall (hydrodynamic, thermal and concentration) in the formulation. Furthermore, viscous dissipation and Ohmic heating (Joule dissipation) are also included. Robust scaling similarity variables are deployed to transform the governing partial differential equations into ordinary differential equations. Subsequently, the emerging dimensionless coupled nonlinear boundary value problem is solved utilizing the Bvp4c method in MATLAB version 2022. This numerical approach allows for a logical parametric examination of all key control parameters on the transport phenomena, enabling a comprehensive understanding of the system behavior. Validation with previous studies is included. Detailed graphical and tabular computations are included for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number, for the influence of Darcian parameter, Forchheimer inertial parameter, mixed convection, velocity (momentum) slip, magnetic number, Casson parameter, nonlinear thermal convection parameter, nonlinear concentration convection parameter, radiation parameter, thermal stratification parameter, Prandtl number, heat source/sink parameter, Eckert number, thermal slip parameter, Schmidt number, chemical reaction, solutal stratification parameter and solutal slip parameter. Detailed interpretation of the physics associated with these multiple effects is included. The simulations provide further insight into the transport characteristics of electromagnetic viscoplastic coating material manufacturing.

Thermophoresis and Brownian motion effect on hybrid nanoparticles flow over a wedge surface by considering double stratification effects

This research looks at the flow of hybrid nanoparticles across a wedge-shaped surface. In addition to this, Brownian motion and thermal stratification are used to model how heat moves through a system. The mass expression also deals with the thermophoresis effect and mass stratification. The governing equations involve the continuity, momentum, energy, and mass equation of hybrid nanofluids that are modified into ODE's by applying similarity transformation. The solutions are obtained from two well-known numerical routines, RKF-45 and the profiles embodying f ′ ( η ) , θ ( η ) , and P ( η ) are interpreted under the influence of several physical parameters. The results showed that as the Prandtl number goes up, temperature profiles of fluid flow go down, and as Brownian motion factors go up, temperature profiles go up. It is found that the fluid’s thermal flow rate slows down as the Brownian motion and thermophoretic elements get stronger. On the other hand, the thermal flow rate of fluid goes up as the thermal stratification parameter goes up.

Double layered combined convective heated flow of Eyring-Powell fluid across an elevated stretched cylinder using intelligent computing approach

This study investigates the possessions of a dual stratified common on the diverse convection barrier layer discharge of an Eyring-Powell fluid (CBLFEPL) induced by an prone extensive barrel. The temperature and concentration at the exterior of the barrel are assumed to be larger than the moving fluid. To solve the resulting flow equations, an brilliant numerical established aggregating solver is employed using the Levenberg-Marquardt neural network scheme (LMNNS). The governing equations of partial differential are converted into interconnected nonlinear ordinary differential equations using appropriate transformations. First, a dataset is generated for two distinct cases, one with a zero curvature parameter (plate) and the other with a non-zero curvature parameter (cylinder). The behaviors of skin-friction coefficient, Sherwood number and Nusselt number are presented over chart obtained using the BVP4C technique. Subsequently, an intelligent computing algorithm nftool, is utilized for training, validation, and testing steps to approximate solutions for various cases. The designed solver, LMNNS, is applied to solve the CBLFEPL problem through regression, mean squared error (MSE), histogram studies, and gradient analysis. The study of double-layered combined convection flow of Eyring-Powell fluid around an elevated stretched cylinder provides insights into heat and mass transfer characteristics, crucial for applications in engineering and fluid dynamics. This study aims to contribute insights that can be applied to engineering and fluid dynamics, aiding in the optimization of relevant processes and applications. The research methodology involves employing numerical technique, three-stage Lobatto IIIa formula, to solve the governing equations of the double-layered combined convection flow of Eyring-Powell fluid around an elevated stretched cylinder, while systematically varying key parameters to analyze their impact on heat and mass transfer phenomena. The speed of the fluid experiences a notable rise with higher values of curvature parameter K, fluid parameter M, mixed convection parameter λm, and the ratio of buoyancy forces N. Conversely, the velocity profile exhibits a contrasting behavior concerning the thermal stratification parameter ϵ1, solutal stratification parameter ϵ2, and an inclination angle α.

MULTI-STRATIFIED EFFECTS ON STAGNATION POINT NANOFLUID FLOW WITH GYROTACTIC MICROORGANISMS OVER POROUS MEDIUM

The present investigation focuses on the intricate interplay of multiple stratified effects on the stagnation point nanofluid flow with gyrotactic microorganisms across a porous medium. The study encompasses a comprehensive numerical analysis, examining the impacts of varying parameters, such as stratification parameters, porosity, etc., on the flow characteristics. The gyrotactic behavior of microorganisms further adds complexity to the analysis. The findings contribute to a deeper understanding of the combined effects and their consequences on heat and mass transfer within the system. Such insights hold relevance in various engineering and environmental applications, including biofuel production and water treatment processes. Numerical solutions are obtained via the fifth order Runge-Kutta-Fehlberg method with shooting technique. A graphical view of the velocity, temperature, concentration, and density of the microorganism-profile-concerned parameters are discussed in detail. A comparison with the local Nusselt number for distinct values of the Prandtl number reveal the validity of current results. The temperature, concentration, and density of microorganism fields lessened with enhancement of thermal, solutal, and motile stratification parameters. Also, concentration field boosts with enhancement of thermophoresis and Brownian motion parameter.

Darcy-Forchheimer flow with viscoelastic Cattaneo-Christov heat flux model and nonlinear thermal radiation: A numerical investigation

Jeffrey fluids have found vast applications in industries and engineering along with their rheological properties. This article investigates the heat and fluid flow within the frame of the nonlinear thermal radiation and non-Fourier heat flux model on Jeffrey nanofluid over an inclined permeable stretched cylinder through saturated porous medium. In addition, non-uniform heat generation/absorption, nonlinear thermal radiation, thermal stratification, and homogeneous/heterogeneous reactions are accounted. Porous medium is characterized through nonlinear Darcy-Forchheimer relation. Shooting method is employed in conjunction with Runge-Kutta-Fehlberg method to solve nonlinear ODEs. The effects of flow variables involved in velocity, temperature and concentration profiles are deliberated through graphs. It is evident from obtained results that the temperature field rises with thermal radiation parameter and space dependent heat generation/absorption parameter. Local Nusselt number has same enhancing attitude towards the thermal relaxation time (0.7443≤−Nˆuz(Rez)−12≤0.7857 for0.2≤δe≤0.6) and thermal stratification parameter (0.7239≤−Nˆuz(Rez)−12≤0.7689for0.2≤S1≤0.6). The exactness of the solution and F′(ξ) variation is verified by comparison with already published literature. The computed results are of great interest in cooling of nuclear reactors. Viscoelastic stuff are generally employed in mats, car shields, computer hard drives and other protective paddings. Synthetic materials can work as the lubricant for an osteoarthritic joint.