Narrow Results

The main motivation behind this numerical analysis is to disclose the salient magneto-thermo characteristic features of two-dimensional viscous incompressible magnetized Soret and Dufour effects on the boundary layer flow of Walter’s-B fluid over a stretching sheet under the influence of viscous dissipation. The novel physical effects such as nonuniform heat source/sink and magnetic Ohmic heating are included in the governing equations. Further, prescribed surface temperature condition is introduced in the boundary conditions to describe the thermal transport features. However, the deployed non-Newtonian Walter’s-B fluid rheology model finds its innumerable applications in numerous areas of science and engineering including electronic cooling, polymer processing, nuclear reactor cooling, extraction of polymer sheet, plastic sheet drawing, chemical engineering, metallurgy, injection molding and many more. Therefore, authors have motivated with these applications and advantageous of considered fluid model. Hence, an effort is made to describe the dynamic characteristic features of non-Newtonian Walter’s-B rheology model about a stretching sheet. However, present physical flow model produces highly nonlinear coupled two-dimensional partial differential equations and which are not acquiescent to available analytical methods. Owing to this, a robust MATLAB-based BVP4C technique is deployed to produce the appropriate numerical solutions through suitable similarity transformations. The graphical representations of velocity, temperature and concentration profiles along with skin-friction coefficient, Nusselt and Sherwood numbers are presented. Magnifying magnetic number decays the velocity profile and enhances the thermal and concentration fields. Rising viscoelastic parameter diminishes the thermal and concentration fields and magnifies the velocity field. Rising the radiation parameter diminish the thermal field. Magnifying Soret number raises the concentration field. Rising the space and temperature dependent heat source/sink coefficient amplifies the thermal diffusion field. Magnifying Dufour and Eckert numbers amplifies the thermal field. Finally, the guarantee and accuracy of the investigated problem is presented through a comparison with previous studies.

This study incorporates the impact of shape factor and slip conditions on a radiative hybrid magnetic nanofluid over slanted sheet being convectively heated within a porous medium, providing valuable insights for enhancing thermal management systems in manufacturing techniques such as the extrusion of plastic films, cooling of metallic plates, and the drawing of polymer fibers. The effect of viscous dissipation, thermal radiation, aligned magnetic field, velocity slip, heat generation, buoyancy force, porosity, and thermal slip on the dynamics of fluid movement are comprehensively discussed. The governing equations were simplified into nonlinear ordinary differential equations through similarity variables and Bvp4c solver in MATLAB was utilized to observe the effects of pertinent parameters on temperature and velocity profiles, alongside the local Nusselt number and skin friction coefficient. It was determined that the hybrid nanofluid’s effective thermal conductivity was most significantly enhanced by blade-shaped nanoparticles. The local Nusselt number enhanced with upsurge of thermal radiation parameter and Biot number whereas opposite trend was observed with incrementation in other parameters. The augmentation in thermal slip and velocity slip resulted in lowering local skin friction coefficient. This research highlights the complex interplay between various physical factors and their influence on the dynamics of hybrid nanofluids, offering potential strategies for optimizing performance of thermal systems comprising hybrid nanofluids.

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

Understanding and optimizing heat transfer processes in complex fluid systems is the driving force behind studying the magnetohydrodynamic (MHD) flow of ${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$–$\mathrm{\text{Cu}}∕{\mathrm{\text{H}}}_2\mathrm{\text{O}}$ nanofluid across a radiative moving wedge, taking into account the impacts of viscous dissipation and Joule heating. Nanofluids, such as ${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$–$\mathrm{\text{Cu}}∕{\mathrm{\text{H}}}_2\mathrm{\text{O}}$, increase heat transmission and thermal efficiency. However, the complicated challenges caused by fluid characteristics and radiative heating need a thorough investigation. This study examines MHD hybrid nanofluid heat transfer via a permeable wedge using joule heating, mass suction, viscous dissipation, variable viscosity, thermal radiation, variable thermal conductivity, and variable Prandtl number. We use similarity transformation to solve the ordinary differential equations that follow from the governing partial differential equations. We then check the results for correctness and dependability. To ensure the reliability and validity of the outcomes, source parameters are crucial to the validation process. The consequence of changing these parameters on the heat transmission properties of the MHD hybrid nanofluid is studied for both the scenario without and with thermal radiation by methodically analyzing the percentage increase or reduction. The validation process also includes a comparison of the computed values, such as the heat transfer rate and skin friction factor, with established theoretical predictions. This examination guarantees that the numerical solution, executed using the bvp4c technique in MATLAB, corresponds to the anticipated physical behavior of the system being studied. In addition, the findings exist using both graphical and tabular forms, which allows for a clear and succinct illustration of how different physical limitations affect flow characteristics.

In this paper, we investigate the Bödewadt boundary layer flow of ferrous oxide-based electrically non-conducting Nanofluid considering the influence of thermal radiation and viscous dissipation over a permeable disc with slip conditions. Here, viscosity is taken as a function of temperature and depth. The equation of energy incorporates the radiative heat flux as described by the Rosseland approximation. The Von Kármán Model alters the constitutive nonlinear coupled partial differential equations of motion, which include slip boundary conditions. The final system of equations in PDE is solved computationally using a shooting approach in MATLAB with ode45, and the results are elucidated, through graphs and tables. The effects of all the above-considered physical entities including the geothermal viscosity on the velocity profile and temperature distribution over the disc are examined. An exhaustive analysis of all the above-investigated results is presented for the record. It is observed that the geothermal viscosity with considered boundary conditions retards the motion of the fluid causing decay in the net molecular movement and the thermal diffusion.

In this work, we examine the oblique flow and heat transfer properties of a micropolar ternary hybrid nanofluid flowing over a lubricated surface while accounting for a convective boundary condition. Ternary hybrid nanofluids are a latest concept in the field of research that offer higher rates of heat transfer than both hybrid and conventional nanofluids. The study also considers the effects of the slip condition and heat radiation. When set to 0.5, the power-law index yields similar results. Through a similarity transformation, the system of partial differential equations is transformed into ordinary differential equations, and the BVP4C technique is used to achieve the numerical solution. Outcomes are shown for ordinary $\text{A}{\text{l}}_2{\text{O}}_3$-water and trihybrid SiC-MWCNT$\setminus$water nanofluids. The primary aim of this study is to investigate how lubrication influences the movement of the stagnation point and the reduction of shear stress, particularly in comparison to viscous fluids. These findings may be beneficial for polymeric processing applications. The study results presented in this publication demonstrate good agreement and consistency with other findings and are closely related to the previously published research.

The medical industry extensively uses nanoparticles for applications such as wound dressing, artificial organ components, drug delivery, tissue engineering, and cardiovascular disease treatment. The incorporation of nanoparticles into the base fluid enhances the rate of heat transmission and additionally decreases blood pressure. This study aims to examine the effects of a new tetra-hybrid nanofluid model, which includes nanoparticles, on the flow of blood through a stenosed artery with a circular shape. Model partial differential equations (PDEs) incorporate phenomena such as thermal radiation and viscous dissipation. Furthermore, we transform these modeled PDEs into dimensionless ordinary differential equations (ODEs) using self-similarity variables and numerically solve the proposed ODEs using the well-established Lobatto IIIa numerical technique. The impact of several dimensionless parameters on the heat transfer rate, skin friction, velocity, and temperature fields has been computed and analyzed using figures and tables. Moreover, we conducted a computational fluid dynamics (CFD) investigation on a tetra-hybrid nanofluid, using blood as the base fluid. The results indicate that heat transmission is higher in tetra-hybrid nanoparticles compared to tri-hybrid and di-hybrid nanofluids. The volume fraction of nanoparticles in the base fluid increases, resulting in a decrease in the surface drag coefficient and a decrease in the heat transport phenomenon. Amplification in the thermal radiation parameter improves heat transfer, helping to remove toxins and plaque from blood flowing through arteries. An increase in thermal radiation generates excess heat that dilates inflexible arteries, facilitating blood flow. From CFD analysis, it is observed that thermal conduction k and heat transfer coefficient h amplify by improving Reynolds number. Pressure at the outlet interface of the tube decreases from 3058 Pa to 2996 Pa for the case of a 10% volume fraction of nanoparticles. Velocity boundary layer thickness decreases from 1.46 to 1.37 with an increase in the volume fraction of nanoparticles from 1% to 10%. Heat deliverance rate amplifies in the case of tetrahybrid nanofluid 2.5394–2.6147 in contrast to trihybrid nanofluid 2.4008 to 2.4711 by amplifying Rd from 0.7 to 1.1. The surface drag coefficient amplifies by magnifying Re but the Nusselt number diminishes by improving the volume fraction of nanoparticles.

Swirling flows are important in rheological devices, spin coatings and lubrication, so we set out to investigate what makes chemically reactive non-Newtonian spinning flows across a disk with a radially applied magnetic field so interesting. Nanofluids are thermally enhanced working fluids with many interesting physical properties. This study takes its inspiration from rotating disk oxidations used in the medical techno industry and builds a mathematical model of a continuous convective von Kármán swirling flow including Jeffrey, magnetic, Joule/ohmic and chemical reactions. The wall anisotropy slips and the concentration-induced blowing effects are included. By using the bvp4c approach, the transformed boundary conditions (BCs) are addressed. Graphical representations of the effects of involved parameters on the density distribution of motile microorganisms, concentration, temperature and dimensionless velocity components are shown. Supporting evidence from prior research is included. Novel bioreactors, membrane oxygenators, bio-chromatography and food processing should take note of the study’s findings. As Jeffrey’s parameter upsurges, there is a decrease in radial velocity. As the Jeffrey parameter increases, there is a decrease in the circumferential velocity. Radial flow is significantly enhanced near the wall as the radial slip parameter ($\delta u)$ increases. As the Eckert number grows, the quantity of temperature increases. Concentration distribution closer to the disk to grow as Le increases. The concentration and diffusivity of microorganisms drop as the number of motile microorganisms thickens.

Recent studies indicate that nanofluids are crucial for solar heat exchange operations and solar energy collectors. Furthermore, the importance of energy and mass transfer in entropy creation is significantly increased in a number of industrial and engineering processes, such as mechanical power collectors, air conditioning, food processing, refrigeration, and heat exchangers. As a result of this advancement, this research is aimed to explore the comparative study on bioconvective Darcy–Forchheimer flow of an incompressible hydromagnetic Ree–Eyring nanofluid over a chemically activated expanding sheet in suction and injection cases while including the consequences of radiation, energy generation, and convective boundary conditions. Boundary layer approximation is utilized to represent this investigation’s primary partial differential equations (PDE). Then, using the appropriate transformation, the models are rebuilt into nonlinear ordinary differential equations (ODE). Utilizing the BVP5C inbuilt MATLAB package, the numerical solutions for this examination are established. Further, the graphical and tabular representations allow us to analyze the impacts of several relevant features on the microorganism’s density, concentration, entropy creation, velocity, temperature, friction factor, Sherwood, and Nusselt number distribution. The outcomes reveal that the velocity field of the liquid movement is declined by applying positive amounts of the Darcy–Forchheimer and magnetic parameters, respectively. Boosting values of the radiation, thermal ratio parameter, and temperature Biot number assist an increase in the thermal field. It reveals the augmented entropy generation with the rising values of bioconvection Lewis number and Brinkman number. Furthermore, the mass transfer rate increases with larger values of the Brownian parameter and chemical reaction parameter.

This study focuses on examining the magnetized bioconvection flow of Casson ternary nanofluid. The mathematical modeling is developed considering Cattaneo–Christov double diffusion (CCDD), Joule heating, and viscous dissipative effects. The Cattaneo–Christov heat flux model is employed to account for finite thermal relaxation time, which addresses limitations of the conventional Fourier’s law by capturing non-instantaneous heat propagation and magnetic responsive boundary conditions considered. The transformation of the governing equations is done using a group of similarity variables. The reduced nonlinear differential equations flow model is numerically solved using the pseudo-spectral collocating integration method. MAPLE develops a graphical illustration of the involved flow parameters. The obtained outcomes are validated by comparing them to recent investigations in the same field. The most important outcome of the work is that growing the Casson variable improves microorganism fluxing at the wall, whereas increasing the mixed convective parameter decreases it. As the thermal relaxation coefficient grows, the Nusselt numbers fall. Conversely, as the thermophoretic parameter increases, the Nusselt number improves. The Brownian diffusion factor and chemical reactive rate reduce the Sherwood numbers and mass transference in a hybrid ternary nanofluid. The findings provide critical insights into optimizing heat transfer mechanisms in industrial cooling, microfluidic devices, and energy storage systems, where precise control over fluid properties and heat flux is essential.

This study highlights the thermal radiation’s impacts on heat transmission in the presence of reduced effects of gravity using the numerical method. For smooth algorithm and integration, the similarity form of stream functions is employed to transform the system of nonlinear partial differential equations into the system of ordinary differential equations. The shooting approach (BVP4C) is employed to acquire the numerical solution of the current model. The numerical findings are acquired using the MATLAB program and are then displayed in tabular and graph forms. The energy equation in the mathematical model includes the thermal radiation impacts along with the expressions for reduced gravity effects. The physical characteristics of the flow profile and thermal distribution for varying values of reduced gravity parameters ($R_g)$, radiation parameter $(F)$, positive number ($m)$ and Prandtl numbers $(\mathrm{\text{Pr}})$ are shown graphically along with the results for skin friction and thermal transmission influenced by various emerging parameters are displayed in tables. The aspect of reduced gravity provides new insight into thermal management in diverse applications such as aerospace, microgravity, environments and high-altitude operations. Further, the incorporation of both heat source and sink into the prescribed mathematical model gives a more comprehensive understanding of heat transfer dynamics. Moreover, this study focuses on a moving surface introducing a dynamic component to the analysis. By combining principles from fluid dynamics, thermodynamics and applied physics, this paper promotes an interdisciplinary approach, which could pave the way for further research in related fields.

This study investigates the performance of Zinc Oxide (ZnO) and Aluminum Oxide (Al₂O₃) nanoparticles suspended in water (H₂O) in the existence of magnetohydrodynamics (MHD) and Hall current effects. The main objective of this examination is to explore the fundamental mechanisms that influence the drag coefficient and Nusselt number over a curved stretching surface. Governing equations are initially transformed into dimensionless PDEs through the application of non-similarity transformations. Following that, the local non-similarity method is employed to treat this non-dimensional system as ODEs. The resulting system is tackled numerically by applying the BVP4c algorithm. This numerical approach entails a comprehensive analysis of numerous graphical and tabular results. The main aim is to elucidate the influences of various flow parameters on the temperature, axial velocity, skin friction, isotherm contour, pressure profile, heat transfer, and streamlines pattern of hybrid nanoliquid. Based on the obtained results, it is evident that the temperature of the hybrid nanofluid increases for higher values of magnetic number and heat sink/source. The velocity profile diminishes for increasing values of magnetic number. Contour plots depicting isotherms and streamlines disclose opposite trends concerning the Hall parameter and magnetic number. The outcomes of the present study also indicate that the temperature profile improves for growing values of Eckert number and radiation parameter, whereas it decreases for concentration of nanoparticles and magnetic number. It is noted that the local Nusselt number rises with increasing Hall parameter, concentration of nanoparticles, curvature parameter, and heat generation parameter. Furthermore, the Nusselt number decreases for higher values of magnetic number and radiation parameter.

To govern the complex rheological dynamics of fluid simulations, numerous mathematical approaches are being developed. The examination of such mathematical frameworks employs theoretical, iterative, empirical, and analytical methodologies. This work analyzes and evaluates the Laplace transforms to estimate the time-dependent mixed convective flow of hybrid nanofluid in a porous material. A hybrid nanofluid is produced through dispersing molybdenum disulfide (${\mathrm{\text{MoS}}}_2$) and silicone dioxide (${\mathrm{\text{SiO}}}_2$) nanoparticles in carboxymethyl cellulose ($\mathrm{\text{CMC }}-\mathrm{\text{water}}$). The objective of this study is to examine the heat transfer properties of a hybrid nanofluid (${\mathrm{\text{MoS}}}_2-{\mathrm{\text{SiO}}}_2)$/$(\mathrm{\text{CMC }}-\mathrm{\text{water}}$) flowing over a vertical sheet while being subjected to a thermal radiation and heat source and sink. The Laplace transform approach has been used in closed form to solve the resulting partial differential equations governing the flow. This study examines how hybrid nanofluids influence time-dependent flow and heat transmission in the presence of porous medium, heat radiation, and rate of heat generation. The computer program MATHEMATICA is used to emphasize the impact of each flow parameter. Graphs are used to analyze the results of radiation, heat source, magnetic, and nanoparticle volume fraction obtained using the Laplace transform technique for engineering variables like fraction and rate of heat, as well as velocity and thermal distribution. The velocity distribution is an increasing function of mixed convective parameter. Larger values of porosity variable and mixed convection variable result in accelerating the velocity of the fluid. Additionally, we conducted research with various ratios of nanoparticles and discovered several intriguing outcomes that can be used to solve various technical issues, particularly in the cooling process.

Development of thin Casson liquid (CL) film on a heated nonlinear flat stretching surface is examined under influences of thermal radiation and transverse magnetic field. The velocity and temperature at any point of the stretching surface are assumed as the generalized nonlinear functions of the distance of that point. The analytical expressions for velocity components and temperature are obtained using long-wave approximation technique. The numerical solution for nonlinear film evolution equation is incurred by the Newton–Kantorovich method. It is found that initial non-uniform film thickness becomes flat with due course of time. It is further observed that the film thinning rate enhances for larger values of the Marangoni number and radiation parameter. It is also discovered that the rate of film thinning diminishes for the larger Hartmann number and Casson parameter.

This paper examines the three-dimensional flow of a bio-hybrid nanofluid through a porous rotating disk while considering the effects of linear thermal radiation and quadratic thermal radiation and examining entropy generation. The fluid enclosure with blood is taken as base fluid and silver–gold is considered as nanoparticles. The fluid flow phenomenon is characterized by nonlinear coupled differential equations involving two or more independent variables. A suitable numerical technique is used to handle the set of governing equations along with a stability and convergence analysis, followed by applying the homotopy perturbation method for solving stated equations. Through graphical illustrations, the radial and tangential velocity distributions, temperature distributions, entropy production and Bejan number are discussed graphically. The Nusselt number and friction factor results are presented and analyzed. The current finding is validated using the available data in both the numerical and homotopy perturbation methods. The results show that when heat absorption increases on blood/gold–silver hybrid nanofluid, a large heat flux develops on the revolving disk, accelerating the heat-transfer mechanism from that surface in both linear thermal radiation and quadratic thermal radiation cases. Moreover, we have seen that the entropy generation is increasing as the magnetic interaction parameter and heat absorption/generation coefficient in quadratic thermal radiation grow, in comparison with linear thermal radiation. The application of thermal radiation and entropy generation analysis is significantly used in the study of renal artery stenosis (RAS) systems and is an active area of research in the field of biomedical engineering. The model is utilized to compute entropy in physiological systems, such as cancer treatment, heat transfer in tissues, dialysis blood pump, and the efficacy of medical apparatus.

This work analyzed numerically the impacts of viscous dissipation, Joule heating and inclined magnetic field on reactive-diffusion magneto-hydrodynamic radiative mixed convection oscillatory non-Newtonian Casson fluid (CF) fluxing across a slanted semi-infinite vertical plate inserted in a porous medium. The framed dimensional flow controlling partial differential equations were modified to dimensionless partial differential equations by bringing in applicable scaling variables and then numerically solved by imposing the finite difference scheme. The outcomes are established with graphical representations to inspect the flow fields’ performance for diverse flow parameters. At the same time, numerical data of skin friction and heat and mass transferal rates near the surface area are presented in a tabular format. This research study discovered that the viscous dissipation and radiation effects intensify the temperature and velocity fields while heat ingestion has a contrary effect. Both velocity and concentration distributions are diminished by the chemical reaction and Schmidt number while the converse trend was noted with thermo-diffusion effect. The velocity distribution was narrowed by the angled magnetic field, Casson parameter, and magnetic field but the porosity parameter exposed the opposite impact. The influence of the magnetic field and Casson parameters incited to decline the friction. Heat absorption in the flow makes the Nusselt number rise but improving viscous dissipation and radiation effects have pointed to an opposite trend. The chemical reaction parameter increases the Sherwood number but thermo-diffusion decreases it. Further, validation with already published results is accomplished and an excellent agreement is realized.

Nanoparticles such as magnesium oxide (MgO), silver (Ag) and gold (Au) can be used in conjunction with therapeutic agents, including anticancer drugs, gene therapy and antibiotics, to enable precise and controlled delivery. Recently, there has been significant interest in modifying biological fluid flow over arteries, particularly for drug delivery applications. This study aims to develop a comprehensive numerical model to investigate the flow dynamics of a hybrid nanofluid, specifically using pure blood as the base fluid and incorporating magnesium oxide (MgO), gold (Au) and silver (Ag) nanoparticles. The primary focus of this research is to explore the potential applications of this model in drug delivery systems, highlighting its promising capabilities for controlled and targeted drug release. The governing equations were transformed using the comparison transformation approach to address the system of nonlinear ordinary differential equations (ODEs). MATLAB’s BVP4C program was used to mathematically solve this problem and analyze the effects of relevant parameters. The findings show that the tri-hybrid nanofluid (MgO, Au and Ag) is extremely effective for heat control and medication transport within arterial channels. Specifically, under conditions of strong thermal radiation, the heat transfer rate at the lower wall increased by 83.924%, while at the upper wall, it increased by 72.098% for the tri-hybrid nanofluids.

The application of fluid flow through a rotating disk in a solar thermal power plant can help in increasing energy production, reduce costs, and improve the overall efficiency of the system. The concentrated solar power (CSP) technology can help in assisting solar energy for sustainable power generation. This work explores the heat transfer assessment of magnetized tangent hyperbolic fluid flowing over a porous rotating disk under the effects of thermal radiation, convective heating, Ohmic heating and viscous dissipation. The solution of transformed ODEs is obtained by the Legendre wavelet collocation method (LWCM). To visualize the impact of acting variables, the results are portrayed by graphs and tables. From the outcomes, it is noted that the rate of heat transfer is enhanced up to 84.79% with an increase in radiation parameter. Moreover, the radial velocity enhances as the rotation parameter is accelerated. The dual behavior in temperature outlines is obtained due to escalated values of the porosity parameter. For the validation of the present results, a tabular comparison is shown with earlier work.

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}$ particles suspended in $\mathrm{\text{EG}}$. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}/\mathrm{\text{EG}}$-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

The study of molybdenum disulfide, along with iron oxide, has various promising applications due to its thermal, electrical, and magnetic properties. In particular, for the efficient cooling in power devices, enhanced fluid transport in medical devices, chemical processing, and cancer therapy. The utility of both nanoparticles is vital. Hence, with this motivation, this study aims to investigate the characteristics of dissipative heat influenced by the inclusion of viscous and Joule dissipation in the flow of a hybrid nanofluid comprised of molybdenum disulfide $({\mathrm{\text{MoS}}}_2)$ and iron oxide $({\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4)$ in the base liquid, ethylene glycol $({\mathrm{\text{C}}}_2{\mathrm{\text{H}}}_6{\mathrm{\text{O}}}_2)$, within a coaxial permeable disk. The proposed model, encompassing various thermal properties, is transformed into a non-dimensional form by applying appropriate similarity rules. Traditional numerical techniques, such as the shooting-based fourth-order Runge–Kutta method, is employed to obtain solutions. Several profiles are computed for various values of contributing factors within their appropriate ranges employing the numerical scheme implemented in MATLAB. A comparative analysis with previous studies is presented, demonstrating a strong correlation in a specific case and thereby validating the current results.