Non-dimensional Equations Research Articles

Convective transport in a nanofluid-filled annulus with an eccentric hypocycloid within a square disk

Considering varying cusp numbers, we investigate the time-dependent, incompressible natural convective flow of an iron oxide-water nanofluid within an annulus formed between a square and a concentric hypocycloid. The vertical walls of the annulus are treated as relatively colder walls, while the bottom wall of the square disk and the inner hypocycloid wall act as heat sources. The outer upper wall of the square is considered adiabatic. We transform the dimensional, nonlinear, and strongly coupled fundamental equations of nanofluids in Cartesian coordinates into non-dimensional equations. We utilize the Galerkin finite element method to solve the governing equations. This study comprehensively explores the flow and heat transfer of nanofluids, considering the essential parameters relevant to the problem. The results highlight a remarkable observation, as the ferric oxide-water nanofluid exhibits significantly enhanced heat transfer compared to the conventional fluid. The precise positioning of the hypocycloid in the cusp configuration represents a critical phenomenon that substantially improves the flow and heat transfer rates of the nanofluid. The three cusped hypocycloids positioned on the inner wall of the annulus perpendicular to the horizontal axis result in a nanofluid flow configuration and heat transfer that surpasses other configurations and cusp numbers studied in the analysis. Notably, heat transfer exhibits a discernible increase with an increase in the nanoparticle volume fraction (maximum 3vol%), while it declines with an increase in the nanoparticle diameter. The intricate relationship between the nanoparticle diameter, volume fraction, cusp number, and hypocycloid configuration substantially influences the friction factor and particle-surface interactions. As the number of cusps on the inner surface increases, the velocity magnitude, Nusselt number, and concentration profiles near the boundary layer decrease, while the fluctuations of the middle annulus indicate the combined influence of nanoparticle dispersion and the formation of the annulus boundary layer due to the orientation of hypocycloidal cusps. Furthermore, an increase in the particle diameter and the sharpness of the corners of the hypocycloid lead to a proportional increase in the nanofluid flow resistance within the annulus.

Double diffusive mixed convective flow over a wedge and cone in the presence of Brownian diffusion and thermophoresis parameter

The present article examines the double diffusion mixed convective nanofluid flow over a wedge and cone in which slip effects as Brownian motion and the thermophoretic parameter are considered. Mixed convective flow over wedges and cones is applied in different technical fields such as fiber technology, nuclear cooling systems, surface treatment, spray deposition techniques, and polymer production. Double diffusion is increasingly significant in scientific fields like astronomy, geosciences, oceanography, and chemical processes. Mixed convection occurs in several applications such as electric devices, solar panels, nuclear power plants, heat exchangers, radiators, and atmospheric boundary layer fluxes. The governing equations of the study are highly coupled nonlinear partial differential equations with surface constraints. The process of similarity transformation used to converts partial differential equations into nondimensional ordinary differential equations, which can be resolved using the MATLAB Bvp5c function. The graphical representation and detailed analysis of variations in velocity, temperature, and concentration distributions of nanofluids are presented. As the mixed convection parameter increases, the fluid’s velocity rises, with a more pronounced effect observed in the cone compared to the wedge. As the Brownian diffusion parameter grows, the fluid temperature increases, and velocity is more pronounced in the wedge scenario compared to the cone. Moreover, an increase in the thermophoresis parameter results in an elevation in the fluid’s temperature. Additionally, the wedge has a higher concentration of fluid and nanoparticles compared to the wedge. Fluid concentration falls with increasing Schmidt number, but fluid nanoparticle concentration decreases with increasing Lewis number.

Electromagnetic and Darcy-Forchheimer porous model effects on hybrid nanofluid flow in conical zone of rotatable cone and expandable disc

Primary objective of this examination is to discover hybridized nanofluid flowing and heat transport that flows between a rotatable cone positioned above an expandable disc. Hybridized nanofluid contains Cadmium telluride (CdTe) as first nanoparticle and Silicon carbide (SiC) as second nanoparticle in ethylene glycol as base fluid. Electromagnetic impact and Darcy-Forchheimer model are considered with thermal radiative fluxing. By using appropriate similarity transformation, physical phenomena may be illustrated by a collection of nondimensional equations. An in-depth analysis is conducted to examine how the expansion of the surface affects the motion and temperature layers, as well as the swirl angle from the disc surface, and heat transfers from the cone and disc walls. Results demonstrate that expanding the wall varies flowing and heat dynamics within the conical gap. Boost CdTe nanoparticles without SiC nanoparticles lower disc Nusselt numbers while increasing it in a cone. In absence of CdTe nanoparticles, SiC nanoparticles increase Nusselt numbers in disc and cone. Nusselt numbers peak for rotating cone and expanded disk at φ1=φ2=0.04. When gap angles are modest, faster wall expansion rate cools disk surface and heats cone surface. These findings have important medical and pharmacological implications in blood component separation and drilling machine cooling.

Simultaneous absorption of H2S, MM and COS into a novel SRSG absorbent using a rotating packed bed

In industries, many gases are required to remove hydrogen sulfide (H2S) and organic sulfur. However, it is still a huge challenge to achieve the efficient and simultaneous removal using a single process. Herein, a novel simultaneous removal sulfide gas (SRSG) absorbent is developed to simultaneously absorb H2S, methyl mercaptan (MM) and carbonyl sulfide (COS). The absorption mechanism between the SRSG absorbent and H2S, MM, COS is explored by quantum chemistry calculations (QCC) and controlled experiments in a rotating packed bed (RPB). Results indicate that the interaction between SRSG and H2S, MM belongs to physical absorption while COS absorption in SRSG obeys two molecule reaction mechanism. Furthermore, the effect of different operating conditions, including rotating speed (N), liquid flow rate (L), gas–liquid ratio (G/L) and temperature (T), on the absorption efficiencies (η) and gas volumetric mass transfer coefficient (KGa) of H2S, MM and COS is systematically investigated. It can be found that both η and KGa are dependent on those operating conditions. The optimal η value for H2S, MM and COS is up to 99.99%, 100%, 100%, respectively. Moreover, nondimensional equations for Sherwood number (Sh) are established, and the calculated and experimental values of Sh(H2S), Sh(MM) and Sh(COS) are in agreement with a deviation within ±13%, ±13%, and ±20%, respectively. These results will provide a valuable potential technique for simultaneously removing acidic gas components from industrial gases.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Magnetic williamson hybrid nanofluid flow around an inclined stretching cylinder with joule heating in a porous medium

The study of an inclined stretching cylinder in a porous medium holds significant implications for understanding complex fluid dynamics and heat transfer phenomena, mainly when influenced by a hybrid nanofluid containing Cu and Al2O3, Joule heating, and a magnetic field in the presence of Williamson fluid. The nonlinear ordinary differential equations are derived by applying pertinent similarity transformations to partial differential equations. Subsequently, these non-dimensional ordinary differential equations are transformed into a system of first-order ODEs and numerically solved using Maplesoft's symbolic computation software MAPLE 2023. The influence of governing parameters on dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rates is investigated. This investigation is crucial for various practical applications, including geothermal reservoirs, enhanced oil recovery, and environmental processes involving porous media. It is demonstrated that Biot and Eckert numbers and nanofluid parameters contribute to increased surface temperature, while the Lewis number leads to a decrease in dimensionless concentration. Moreover, the curvature parameter is associated with an increase in dimensionless concentration, and skin friction demonstrates a direct relationship with the magnetic parameter while inversely correlating with the cylinder's curvature.These results contribute to the scientific understanding of these complex interactions and provide valuable insights for engineering applications, such as designing efficient heat exchangers, optimizing cooling systems, and advancing technologies involving fluid flow and magnetic fields.

Comparative simulation of nonlinear radiative nano casson and maxwell fluids with periodic magnetic force and sensitivity analysis

This study investigated cyclic magneto-hydrodynamic radiative effects in Casson and Maxwell fluids, including nonlinear radiation and Arrhenius activation energy. It promotes non-Newtonian fluid use in diverse fields like industry, manufacturing, sciences, medicine, and engineering. Using boundary layer approximations, non-dimensional equations are formulated. For numerical solutions, widely recognized explicit finite difference method (EFDM) has been utilized. To ensure the robustness of EFDM results, stability and convergence tests are performed. Exploration involve a detailed sensitivity analysis by using RSM, offering a thorough understanding of influential parameters. These analyses explore complex interactions among physical parameters, affecting Nusselt number, skin friction, and Sherwood number. Maxwell fluid's velocity is more affected by periodic magnetic force than Casson fluid, during the presence of nonlinear radiation. Additionally, nonlinear thermal radiation has a greater impact on temperature and concentration profiles compared to linear radiation for both fluids. Moreover, Casson fluid has a stronger influence on the average heat transfer rate compared to Maxwell fluid with nonlinear thermal radiation which is 8.6 % greater than the Maxwell fluid. On the other hand, at constant thermal radiation (Ra), due to decrease of Brownian motion (Nb), the rate of heat transfer is reduced by 1.2 % and 0.3 % respectively for Maxwell and Casson fluid. Also, for thermophoresis parameter (Nt), this rate is reduced by 2 % and 1.6 % respectively. The investigation also revealed that the Ra exhibits a positive sensitivity towards average Nusselt number, while Nb and Nt are displayed a negative sensitivity.

Heat Generation/Absorption in MHD Double Diffusive Mixed Convection of Different Nanofluids in a Trapezoidal Enclosure

Numerical simulation of MHD double-diffusive mixed convection flow of different nanofluids in a trapezoidal enclosure is performed with an internal heat generation/absorption source inside the enclosure. The nondimensional momentum, heat and mass equations are solved numerically by using the finite difference method. The present study focused mainly on the increment of the rate of heat and mass transfer using internal heat generation or absorption sources inside a lid-driven trapezoidal cavity. Considering numerous governing parameters (Q = −5 to 5, Ha = 0 to 30, Ri = 0.01 to 100) the flow velosity, temperature and concentration profiles are calculated for various nanofluids. Graphs and numerical tables are utilized to examine how different physical entities affect the distribution of flow, temperature and concentration. It is noted that enhancing values of Ha reduces the mass and heat transfer rate. It is observed that heat generation/absorption significantly affect the heat transfer rate as internal heat generation source increases heat transmission rather than mass transfer. The involvement of heat generation/absorption source significantly affects the heat transfer rate. By considering Al2O3-water nanofluid, the solid volume percentage has an accelerating effect on the Nusselt and Sherwood numbers as compared to the other nanofluids in the study.

Magnetohydrodynamic flow of carbon nanotubes and heat transfer over a moving thin Needle: A numerical and research surface methodology

A steady flow of carbon nanotubes (CNTs) nanofluids and heat transfer past a horizontally moving thin needle are investigated under the influence of magnetohydrodynamic (MHD). Single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) are the two main nanoparticles that represent CNTs. The slender needle moves relative to the flow with parallel velocity in either the same or opposite direction. Using the similarity method, a system of partial differential equations (PDEs) subject to boundary conditions is converted into nondimensional ordinary equations (ODEs). The ODEs are then reduced to a first-order ODEs system and solved using the MATLAB R2022b bvp4c solver. On a numerical scale, the impacts of varying potential parameters, such as the magnetic, CNTs’ volume fraction, and moving parameters, on the velocity and temperature profiles, the skin friction, and heat transfer coefficients are investigated. Utilising response surface methodology (RSM), the optimisation of the response based on numerical experimentation of physical quantities is performed. The outcomes are depicted using tables and a graphical approach. Results indicate the existence of dual solutions when the needle travels in the opposite direction. Moreover, the increase in the magnetic parameter by 100% in the flow will increase both the skin friction and heat transfer coefficients by nearly 30% and 4%, respectively. Furthermore, when the value of the CNTs volume fraction increases by 100%, the heat transfer rate increases substantially by almost 33%.However, doubling the size of the thin needle cansignificantly reduce the skin friction coefficient by nearly 32%. RSM results demonstrate that the maximal heat transfer coefficient is generated at the highest values of the magnetic and CNTs’ volume friction parameters and the lowest value of the needle size parameter. Findings also show that SWCTNs are superior to MWCNTs both in the skin friction and heat transfer coefficients. When comparing the performance of water and kerosene, we find that water is less effective as a base fluid than kerosene.

Non-similar analysis of micropolar magnetized nanofluid flow over a stretched surface

The study of micropolar nanofluids unveils intriguing applications, propelled by their exceptional heat transfer capabilities in comparison to conventional fluids. This investigation focuses on analyzing the behavior of magnetized micropolar nanofluid flow over a stretched surface, taking into account crucial factors such as viscous dissipation and heat source. The chosen base fluid is blood, with Copper [Formula: see text] nanoparticles serving as the selected material. Incorporating the single-phase (Tiwari-Das) model with boundary layer assumptions for micropolar nanofluid flow, we introduce the volume fraction of nanoparticles to assess heat transport. The governing system undergoes transformation into a set of dimensionless non-linear coupled differential equations through appropriate transformations. This transformation involves the utilization of a combination of the local non-similarity technique and bvp4c (MATLAB tool) to derive the system of nondimensional partial differential equations (PDEs) for micropolar nanofluid. Our systematic exploration delves into the consequences of nondimensional parameters on velocity, microrotation, and temperature profiles within the boundary layer, including the Eckert number, micropolar parameter, magnetic field parameter, heat source, Prandtl number, and microorganism parameter. Graphical representations vividly demonstrate that the velocity and temperature of micropolar nanofluid increase with the rise in material parameter values, while the microrotation profile decreases. Increasing the magnetic field parameter leads to a reduction in the velocity profile. Moreover, the micropolar temperature profile shows an increase with the rising Eckert number. Crucially, the research emphasizes that factors like the heat source and Eckert number play a role in decreasing the local Nusselt number. In contrast, an increase in the local Nusselt number is observed for material parameters. Furthermore, the skin friction coefficient decreases as micropolar parameter values increase, whereas an increase in the skin friction coefficient is noted for the magnetic field. The primary focus of this research lies in the development of suitable non-similar transformations for the investigated problem, aiming to yield authentic and efficient results. These results hold substantial promise to make meaningful contributions to future research on nanofluid flows.

Influence of magnetic field-dependent viscosity on Casson-based nanofluid boundary layers: A comprehensive analysis using Lie group and spectral quasi-linearization method

This study examines the effects of magnetic-field-dependent (MFD) viscosity on the boundary layer flow of a non-Newtonian sodium alginate-based Fe3O4 nanofluid over an impermeable stretching surface. The non-Newtonian Casson and homogeneous nanofluid models are utilized to derive the governing flow and heat transfer equations. Applying Lie group transformations to dimensional partial differential equations yields nondimensional ordinary differential equations, which are then numerically solved using the spectral quasi-linearization technique. The analysis primarily focuses on the impacts of the MFD viscosity parameter, nanoparticle volume fraction of Fe3O4, and magnetic parameters on the flow and heat transfer characteristics. The local skin friction and heat transfer rate behaviors influenced by viscosity changes due to the magnetic field are discussed. It is found that MFD viscosity significantly impacts flow and thermal energies, enhancing skin friction coefficients and reducing Nusselt numbers in the boundary layer region.

Derivation of nondimensional rigid-body equation of motion and coupling with flexible body in ANCF

Derivation of nondimensional rigid-body equation of motion and coupling with flexible body in ANCF

An analytical solution and stability analysis of asymmetric non-actuator guided projectiles

PurposeOne of the challenges encountered in the design of guided projectiles is their prohibitive cost. To diminish it, an appropriate avenue many researchers have explored is the use of the non-actuator method for guiding the projectile to the target. In this method, biologically inspired by the flying concept of the single-winged seed, for instance, that of maple and ash trees, the projectile undergoes a helical motion to scan the region and meet the target in the descent phase. Indeed, the projectile is a decelerator device based on the autorotation flight while it attempts to resemble the seed’s motion using two wings of different spans. There exists a wealth of studies on the stability of the decelerators (e.g. the mono-wing, samara and pararotor), but all of them have assumed the body (exclusive of the wing) to be symmetric and paid no particular attention to the scanning quality of the region. In practice, however, the non-actuator-guided projectiles are asymmetric owing to the presence of detection sensors. This paper aims to present an analytical solution for stability analysis of asymmetric decelerators and apprise the effects of design parameters to improve the scanning quality.Design/methodology/approachThe approach of this study is to develop a theoretical model consisting of Euler equations and apply a set of non-dimensionalized equations to reduce the number of involved parameters. The obtained governing equations are readily applicable to other decelerator devices, such as the mono-wing, samara and pararotor.FindingsThe results show that the stability of the body can be preserved under certain conditions. Moreover, pertinent conclusions are outlined on the sensitivity of flight behavior to the variation of design parameters.Originality/valueThe analytical solution and sensitivity analysis presented here can efficiently reduce the design cost of the asymmetric decelerator.

Hybrid nanofluid flow and heat transfer in symmetric porous ducts with CuO nanoparticles and multi-walled carbon nanotubes under peristaltic motion

This study focuses on the analysis of peristaltic transport of a hybrid nanofluid comprising deionized water as a base fluid and the multi-walled carbon nanotubes (MWCNTs) and copper oxide (CuO) as nanoparticles within a sinusoidal wavy porous duct, taking into consideration the influence of heat generation or absorption. The inaugural literature piece addresses the utilization of hybrid nanofluid in the context of peristaltic flow within ducts. To simplify the analysis, we have converted the non-dimensional equations into a two-dimensional (2D) coordinate system using the assumptions of a very long wavelength [Formula: see text] and low Reynolds number (Re). The non-dimensional equations governing the behavior of the hybrid nanofluid are then solved numerically using the finite volume method. Numerical solutions for temperature and the 2D peristaltic flow are obtained with the assistance of the Mathematics software MATLAB. These solutions are subsequently represented graphically using MATLAB software. The graphical results highlight several key findings for important parameters. First, it is observed that the pressure rise, temperature profile, and pressure gradient in the hybrid nanofluid (CuMWCNTs/H2O) flow increases as heat generation increases. Furthermore, an increase in the nanoparticle volume fraction of both nanoparticles leads to a decrease in the pressure rise and pressure gradient in the hybrid nanofluid flow. Additionally, the widening of the channel reduces the pressure gradient and pressure rise in the CuMWCNTs/H2O hybrid nanofluid. The analysis also includes the visualization of streamlines for peristaltic transport. These streamlines reveal that an increase in amplitude results in larger bolus sizes, while heightened heat generation has the opposite effect, decreasing bolus sizes. The results of this investigation can be found in various cooling devices as flows in the ducts are very frequently utilized for the cooling process of engines. A further topic is common in applications related to microfluidics, heat exchangers, and biomedical devices where peristaltic pumping is employed. Our results are in 100% agreement with the existing literature in special cases.

Heat generation effects on the MHD Nimonic 80A-Fe3O4 water hybrid nanofluid flow over a wedge with influence of shape factor of nanoparticles

This study reports both MagnetoHydroDynamics (MHD) and heat generation aspects of a water-based hybrid nanofluid flow with various shapes of the nanoparticles involving Nimonic 80A and [Formula: see text], over a moving wedge. Similarity transformations were adapted to obtain non-dimensional equations and solved using MATLAB bvp4c code. All the results and graphs were formulated after a positive outcome of our results with that available in existing literature. Nusselt number, which signifies the heat transfer rate in a flow, increased with an increase in empirical shape factors of the nanoparticle with a contrasting decrease in the drag experienced during the flow, represented by the skin friction coefficient. The velocity profile decreased at a rate of 0.75% for [Formula: see text] to [Formula: see text] due to the augmenting Lorentz forces while it augmented by 18.9% for an augmenting velocity ratio parameter from [Formula: see text] to [Formula: see text] due to the no-slip boundary conditions. Both the Nusselt number and skin friction coefficients decreased with an increase in magnetic parameter. An increase in the nanoparticle concentration resulted in an incrementing streamline value along with increasing temperature profile due to increasing thermal conductivity of the fluid flow system. The physical significance of the study involves in its applications in nuclear, steel industries, MRI scanning for its anti-corrosive and high thermal conductivity properties.

Numerical investigation of mixed convective Williamson nanofluid flow over a stretching/shrinking wedge in the presence of chemical reaction parameter and liquid hydrogen diffusion

The numerical simulation of mixed convective Williamson nanofluid flow over a stretching/shrinking wedge with chemical reaction parameters and liquid hydrogen diffusion is studied. The usage of Williamson fluid in industry has had a considerable impact on industrial processes. Chemical reactions substantially impact heat and mass transfer in hydrometallurgical industries and chemical technology. The governing equations of the inquiry are nonlinear partial differential equations with surface constraints. The similarity transformation transforms partial differential equations into nondimensional ordinary differential equations that may be solved with the MATLAB bvp5c function. Variations in nanofluid velocity, temperature, and concentration patterns are graphically represented and thoroughly examined. In the case of a stretching/shrinking wedge, the liquid velocity decreases as the Williamson nanofluid parameter values increase. The dual nature solution for the skin friction coefficient is obtained when the Williamson nanofluid parameter increases. The liquid’s temperature rises proportionately to the thermophoresis and Williamson nanofluid parameters. As the Schmidt number increases, the fluid concentration improves while the chemical reaction parameter decreases.

Parameter influence analysis of stochastic resonance and stochastic P-bifurcation for the shape-memory alloy laminate

This paper investigates the transverse vibration of an axially moving shape-memory alloy (SMA) fiber hybrid laminations under the combined action of transverse harmonic excitation and stochastic disturbance. Considering the shape memory alloy (SMA) fiber volume fraction random field, the kinetic energy and strain potential energy of SMA laminates are solved, and the axial motion equation of SMA laminates is derived according to Hamilton principle, a non-dimensional differential equation of the transverse vibration of the axially moving SMA laminated plates is obtained by adopting the Galerkin integral method. Considering the volume-fraction stochastic field, the stochastic natural vibration of a SMA laminate is analyzed. Considering the stochastic resonance of the SMA laminate under the action of Gaussian white noise and harmonic excitation, the effects of geometric parameters, physical parameters of materials, and temperature on the stochastic resonance behavior of the SMA laminate is analyzed. Finally, the effect of the stochastic P-bifurcation phenomenon of the parameters on the steady-state response of the SMA laminate is analyzed.

Enhancing energy efficiency and heat transfer performance of engine oil flow through hybrid nanoparticles in convergent/divergent channel

Engine oil (EO) is employed as a lubricant in various machinery engines. Efficient heat transfers are a fundamental requirement for all processes. To improve heat transfer rates and reduce the energy loss caused by high temperatures, this study focuses on incorporating Iron Oxide (Fe3O4) and Cupper Oxide (CuO) into the engine oil as suspended particles. However, the focus of this research paper is to analyze entropy generation in a convergent/divergent channel that contains a hybrid nanofluid. Mathematical modeling is utilized to present the continuity, momentum, and energy equations. Using the resemblance transformation variables, the governing dimensional partial differential equations (PDEs) are transformed into a system of non-dimensional ordinary differential equations (ODEs), which are then resolved in ascending order through the BVP4c scheme. The graphical results illustrate the effects of various parameters on fluid velocity, temperature, entropy generation, and Bejan number. The study explores changes in velocity profiles under different Hartmann numbers, revealing opposing variations in divergent and convergent channels. Velocity profiles exhibit similar patterns when varying the porosity parameter. In the convergent passage, a higher porosity parameter results in a higher temperature field. Entropy rises against Eckert and Hartmann numbers in both Convergent and Divergent cases. These insights aid in designing and optimizing machinery engines.

Flow and thermal characteristics of Jeffrey nanofluid in the fixed and moving frames of reference with newly developed Reynolds model

Nanofluids with their excellent thermophysical properties strengthen the thermal performance of an ordinary fluid. Due to the efficacious thermophysical characteristics of nanofluids, the aim of the present study is to discuss the three distinct viscosity models for an incompressible Jeffrey nanofluid relative to its oscillatory oblique stagnation point flow. Three different viscosity models namely Brinkman model, Einstein model, and Reynolds model are discussed to scrutinize the thermophysical attributes of (TiO2-Kerosene oil) nanofluid. The unsteady magnetized flow problem of Jeffrey nanofluid is deliberated over an oscillatory medium corresponding to different frames of references namely fixed frame and moving frame. The thermal analysis is evaluated with the involvement of heat absorption/generation and radiation effects. In both frames of reference, the non-dimensional equations are numerically handled via an efficient technique of bvp4c. The fluid velocity and temperature distribution are graphically compared regarding three distinct viscosity models with numerous pertinent parameters. In the context of all viscosity models, both the distributions of velocity and temperature exhibit excellent behavior in the fixed and moving frame of reference. This study exhibits that the parameter that portrays the ratio of relaxation to retardation times deteriorates the flow field in the fixed frame for all viscosity models.

Thermophoretic particle deposition in a nanofluid flow across a disc with non-fourier heat flux: An investigation using tangent hyperbolic model

Non-Newtonian nanofluids are attracting the attention of researchers and academics due to the high heat transmission rates that they possess. To improve thermal devices and exchangers, the researchers come up with innovative and expense-effective methods. One of the advanced technological approaches that can be utilized to enhance the thermal performance of devices is the utilization of nanofluids. This non- Newtonian nanofluid possesses the advanced properties of increasing heat transfer and destroying harmful bacteria. For this purpose, the present theoretical work is to explore the heat and thermophoretic particle deposition analysis on the tangent hyperbolic nanofluid flow over the rotating porous disk with presence of non-Fourier heat flux model and nanoparticle aggregation effect. Darcy-Forchheimer fluid model is adopted to develop the fluid flow system. Furthermore, the nanofluid’s viscosity and thermal conductivity are expressed through advanced modeling, employing the modified Krieger-Dougherty model for viscosity and the Maxwell-Bruggeman model for thermal conductivity. The nanoparticles and base fluid involved in this context are Molybdenum disulfide ( Mo S 2 ) and Water/carboxyl-methyl cellulose (CMC) respectively. The mathematical representation of the fluid flow and energy propagation involves a system of coupled partial differential equations (PDEs). The system of partial differential equations (PDEs) is transformed into non-dimensional ordinary differential equations (ODEs), which are then solved both analytically and numerically using the Homotopy Analysis Method(HAM) and Runge-Kutta-Fehlberg (RKF) method along with shooting technique. Exploring the graphical representation reveals a comprehensive analysis of key factors influencing velocity, temperature, and concentration. Through innovative visualization, these parameters take center stage, providing insights into their intricate interplay and dynamic relationships. The heat transfer rate is enhanced 0.24% and 1.4% by rising the values of thermal relaxation parameter and Weissenberg number. Also, the mass transfer rate is accelerated 0.8% and 0.14% due to enhancing the values of thermophoretic coefficient and thermophoresis parameter.