MHD flow and heat transfer near stagnation point over a stretching/shrinking surface with partial slip and viscous dissipation: Hybrid nanofluid versus nanofluid

A numerical study of heat and mass transfer characteristic of three-dimensional thermally radiated bi-directional slip flow over a permeable stretching surface

Within fluid mechanics, the flow of hybrid nanofluids over a stretching surface has been extensively researched due to their influence on the flow and heat transfer properties. Expanding on this concept by introducing porous media, the current study explore the flow and heat and mass transport characteristics of hybrid nanofluid. This investigation includes the effect of magnetohydrodynamic (MHD) with chemical reaction, thermal radiation, and slip effects. The nanoparticles, copper, and alumina are combined with water for the formation of a hybrid nanofluid. Using the self-similar method for the reduction of Partial differential equations (PDEs) to the system of Ordinary differential equations (ODEs). These nonlinear equation systems are solved numerically using the bvp4c (boundary value solver) technique. The effect of the different physical non-dimensional flow parameters on different flow profiles such as velocity, temperature, concentration, skin friction, Nusselt and mass transfer rate are depicted through graphs and tables. The velocity profiles diminish with the effect of magnetic and slip parameters. The temperature and concentration slip parameters reduce the temperature and concentration profile respectively. The higher values of magnetic factor lessened the skin friction coefficient for both slip and no-slip conditions. An elevation in the thermal slip parameter reduced the boundary layer thickness and the heat transfer from the surface to the fluid. The Nusselt number amplified with the climbing values of the radiation parameter. The mass transfer rate depressed with the solutal slip parameter. Comparison is made with the published work in the literature and there is excellent agreement between them.

Non-similar bioconvective analysis of magnetized hybrid nanofluid (Ag + TiO2) flow over exponential stretching surface

Scientists have studied fluid flow over a stretching sheet to explore its potential applications in industries. This study investigates the exponential stretching flow of a bioconvective magnetohydrodynamic (MHD) hybrid nanofluid in porous medium taking into consideration thermal radiations, heat generation, chemical reaction, porosity, and dissipation. Moreover, microorganisms are present in the fluid, so the fluid is more stable, which is crucial in biotechnology, biomicrosystems, and bio-nano coolant systems. Silver and titanium dioxide in a water-based medium are the prototypical nanoparticles. The present study involves a transformation of the governing system into a set of dimensionless, coupled and nonlinear partial differential equations (PDEs) using nonsimilar techniques. The local non-similarity (LNS) technique is used to truncate these equations to ordinary differential equations (ODEs). This technique is also used to estimate transformed equations numerically until the second level of truncation takes place via the bvp4c algorithm, which is a built-in MATLAB solver. Furthermore, tables are provided that presents the drag coefficients, Nusselt numbers, Sherwood numbers, and densities of motile microorganisms. Results show a negative correlation between the velocity and the magnetic field parameter as well as the porosity parameter, as evidenced by a decrease in velocity corresponds to rises in these parameters. The temperature distribution exhibits a positive correlation with the rising values of both radiation parameter and Eckert number. The concentration profiles also exhibit a negative correlation with the increasing values of Lewis and bioconvection Lewis number, chemical reaction parameter, Peclet number and the differences in microbial concentration. This study will improve the future research on hybrid nanofluid regarding industrial applications. There haven't been any previous publications that have investigated the use of this model with the local non-similarity method. The main objective of this article is to enhance the heat transfer performance in a hybrid nanofluid.

Effect of non-uniform heat rise/fall and porosity on MHD Williamson hybrid nanofluid flow over incessantly moving thin needle

In this work, a novel enhanced model of the thermophysical characteristics of hybrid nanofluid is introduced. An innovative kind of fluid called hybrid nanofluid has been engineered to increase the heat transfer rate of heat and performance of thermal system. A growing trend in scientific and industrial applications pushed researchers to establish mathematical models for non-Newtonian fluids. A parametric study on theheat transfer and fluid flow of a Williamson hybrid nanofluid based on AA7075-AA7072/Methanol overincessantly moving thin needle under the porosity, Lorentz force, and non-uniform heat rise/fallis performed. Due to similarity variables, the partial differential equations governing the studied configuration undergo appropriate transformation to be converted into ordinary differential equations. The rigorous built-in numerical solver in bvp4c MATLAB has been employed to determine the numerical solutions of the established non-linear ordinary differential equations. It is worthy to note that velocity declines for both AA7075/Methanol nanofluid and AA7075- AA7072/Methanol hybrid nanofluid, but highervelocitymagnitudes occur for theAA7075/Methanol whilethe Williamson fluid parameters increased. It is alsoconcluded that as the porosity parameter isincreased, the flow intensity decreases gradually. It is worthy to note that for both non-uniform heat-rise and fall parameters, the temperature of the fluid gets stronger. Mounting valuesof needle thickness parameter leads to reduction in fluid speed and temperature. It is noticedthat as volume fractions of both types of nanoparticles are augmented then fluidvelocity and temperature amplify rapidly. A Comparison of current and published results is performed to ensure the validity of the established numerical model.

Computational investigation of magnetized hybrid nanofluids heat transport and flow through elongational surface with thermal radiation and wall slip

The improved thermal performance of recently discovered hybridized nanofluids has become essential in large scale thermal processes. In fact, this is highly efficient technique to introduce the thermal efficiency of tranditional heat transferring fluids. The behavior of the nanofluid can be significantly impacted by the unsteady heating and magnetic field effects that may be present in many applications. Therefore, the current study investigat the unsteady magnetized flow of hybrid nanofluid with heat transport characteristics subject to thermal radiation and slip at the surface wall. The shrinking/stretching surface is chosen as a flow source, which is frequently occure in polymer technology, which deals with the deformability of elastic sheets, and in metallurgy, where continued strips are cooled. The novel form of shrinking surface flow is fundamentally a reverse flow and exhibits physical characteristics that differ significantly from the channel flow scenario. The distinctive features of this scruinity is the use of empirical relations to approximate the optimum thermophysical attributes of a C u - A l 2 O 3 / water hybrid nanofluid in order to model the 2-dimensional flow past a flat shrinking/stretching sheet under the action of radiation, Lorentz forces and realastic boundary condition responses. The governing system of modelled equation are assembled using the Tiwari-Das model in conjunction with a hybrid mass-based nanofluid model. The bvp4c algorithm is employed within the computer MATLAB programme. The hybrid nanofluid flow shows conclusive improvement in the frictional coefficient and heat transport performance. However, the effectiveness the unsteadiness parameter deteriorates the heat transmission. In the contiguity of a suction parameter, multiple outcomes appear to arise for both stretched and shrinking instances. The coefficient of energy transport improves as the magnetic factor is augmented, however the skin coefficient of friction exhibits dual behavior for the second solutions. A time-dependence investigation is undertaken to figure out the reliability of the twin solutions, and it is discovered that merely one of them remains stable and aesthetically credible.

Unsteady Ohmic dissipative flow of ZnO-SAE50 nanofluid past a permeable shrinking cylinder

The laminar boundary layer flow of a Zinc Oxide-Society of Automotive Engineers 50 alias nano-lubricant (ZnO-SAE50) past a permeable shrinking cylinder is investigated. The flow is unsteady, incompressible, and Ohmic dissipative. The present study holds immense significance in different engineering as well as scientific domains. It combines research on nanoparticle effects, unsteady flows, and solid surface interactions. The study claimed that the use ofZnO-SAE50nanofluid in the unsteady flow past a permeable shrinking cylinder led to significant heat transfer enhancement. The acquired results from the study would be fruitful in the fields of thermal engineering and heat transfer. The findings of the study can aid in optimizing cooling systems, heat exchangers, and energy-efficient designs. A governing model has been achieved for the flow and heat transfer by using conservation laws related to mass, momentum, and energy. Governing system of partial differential equations is solved to a nonlinear system of ordinary differential equations by using similarity transformation, which is later on solved with the help of the Shooting method and RK-Fehlberg duos. Plots are shown for both velocity and temperature profiles, to display the impacts of involved dimensionless parameters. Additionally, graphs for Nusselt Number have also been represented which shows the local rate of heat transfer. It is examined that the Ohmic dissipation as well as the volumetric ratio of the nanoparticles greatly influence the overall thermal performance of the system.

Enhancing heat transfer in solar-powered ships: a study on hybrid nanofluids with carbon nanotubes and their application in parabolic trough solar collectors with electromagnetic controls

The aim of this research is to explore the use of solar-powered ships (SPS) as a means to reduce greenhouse gas emissions and fossil fuel dependency in the maritime industry. The study focuses on improving the heat transfer efficiency in SPS by employing hybrid nanofluids (HNF) containing carbon nanotubes (CNTs). Additionally, a novel approach utilizing renewable energy and electromagnetic control is proposed to enhance the performance of SPS. The research implements the non-Newtonian Maxwell type and Cattaneo-Christov heat flux model in parabolic trough solar collectors used for ships. The study conducts theoretical experiments and simulations to evaluate the thermal conductivity and viscosity of the CNT-based HNF. Various properties, including solar thermal radiation, viscous dissipation, slippery velocity, and porous media, are assessed to determine the effectiveness of thermal transport in SPS. The research employs similarity variables to simplify the complex partial differential equations into ordinary differential equations and solves them using the Chebyshev collocation spectral method. The results indicate that the MWCNT-SWCNT/EO hybrid nanofluid significantly improves the thermal conductivity, thereby enhancing heat transfer. The HNF exhibits an efficiency rate of approximately 1.78% with a minimum efficiency rate of 2.26%.

Multiple solutions for non-linear radiative mixed convective hybrid nanofluid flow over an exponentially shrinking surface

Hybrid nanofluids have gained too much attention due to their enhanced thermophysical properties and practical applications. In comparison to conventional nanofluids, their capacity to enhance heat transport is impressive. The simultaneous numerical calculations of hybrid and mono nanofluids across an exponentially shrinking surface in a porous medium are taken into consideration here. The analysis of the thermal energy distribution is carried out by using the convective boundary conditions. Shrinking, permeability, and magnetohydrodynamic controlled the motion of the flow. The objective of this research is to conduct stability analysis and identify the existence of dual solutions in the presence of heat source/sink and nonlinear Roseland thermal radiation. The technique, bvp4c, a collocation method is used to achieve numerical results. It is noted that the energy transport is enhanced immensely due to the presence of a mixture of nanoparticles (hybrid) in comparison to mono nanofluids. The stability analysis shows that the solutions for the upper branch were stable, while the solutions for the lower branch were unstable. Moreover, shrinking parameter contributes significantly to exhibit the dual nature of the solutions. Due to the increment in the heat generation/absorption and temperature ratio, the kinetic energy is inclined, which causes the temperature distribution to rise for both branches. For stable branches, an increase in wall stress values is evident as a result of permeability and stretching of sheet, whereas unstable branches show the opposite trend.

Magnetized mixed convection hybrid nanofluid with effect of heat generation/absorption and velocity slip condition

Through a vertically shrinking sheet, a two-dimensional magnetic nanofluid is numerically analyzed for convection, heat generation and absorption, and the slip velocity effect. In this research, Al₂O₃-Cu/water composite nanofluid is studied, where water is deemed the base liquid and copper (Cu) and alumina (Al₂O₃) are the solid nanoparticles. Modern composite nanofluids improve heat transfer efficiency. Using the Tiwari-Das model, the current study examines the effects of the solid volume fraction of copper, heat generation/absorption, MHD, mixed convection, and velocity slip parameters on velocity and temperature distributions. Introducing exponential similarity variables converts nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). MATLAB bvp4c solver is used to solve ODEs. Results showed dual solutions for suction with 0%-10% copper nanoparticles and 1%-500% heat generation/absorption. As copper (Cu) solid volume percentage increases from 0% to 10%, reduced skin friction f ″ ( 0 ) boosts in the first solution but falls in the second. When Cu is added to both solutions, heat transport - θ ' ( 0 ) decreases. As heat generation/absorption increases 1%-500%, - θ ' ( 0 ) decreases in both solutions. In conclusion, solution dichotomy exists when suction parameter S ≥ S c i in assisting flow case, while no fluid flow is possible when S < S c i .

Assessment of thermal distribution through an inclined radiative-convective porous fin of concave profile using generalized residual power series method (GRPSM)

The thermal distribution in a convective-radiative concave porous fin appended to an inclined surface has been examined in this research. The equation governing the temperature and heat variation in fin with internal heat generation is transformed using non-dimensional variables, and the resulting partial differential equation (PDE) is tackled using an analytical scheme, generalized residual power series method (GRPSM). Moreover, a graphical discussion is provided to examine the consequence of diverse non-dimensional variables including the parameters of convection-conduction, ambient temperature, radiation, heat generation, and porosity effect on the thermal field of the fin. Also, a graph is plotted to analyze the variations in unsteady temperature gradient using the finite difference method (FDM) and generalized residual power series method (GRPSM). The major result of this investigation unveils that as the convection-conduction parameter scale upsurges, the distribution of temperature in the fin diminishes. For the heat-generating parameter, the thermal distribution inside the fin increases.

Radiative Heat Transfer of Hybrid Nanofluid Flow Over an Expanding Surface with the Interaction of Joule Effect

The current research examines the characteristic of dissipative heat energy owing to the inclusion of a magnetic field here on the two-dimensional flow of an electrically conducting hybrid nanofluid past an expanding surface. Additionally, the free convection of hybrid nanofluid thermal properties is enhanced with the inclusion of the Joule heating effect as well as the thermal radiation in the heat transfer phenomenon. These physical properties were influenced as a result of the combination of the nanoparticles Al2O3 and Cu into the base liquid ethylene glycol. The novelty arises due to the interaction of thermal conductivity employing the Mintsa model and the viscosity using the Gharesim model. The transformed governing set of nonlinear equations obtained with the assistance of suitable similarity transformations are solved numerically using the Runge-Kutta fourth-order shooting base technique. A good correlation between the earlier studies is obtained in specific cases showing the convergence criteria of the present procedure. Further, the physical significance of the contributive parameters is presented through graphs and tables. The observation shows that the particle concentration for the hybrid nanofluid augments the fluid velocity. Moreover, the inclusion of dissipative heat favors enhancing the fluid temperature for the involvement of the particle concentration.

Pulsating Hydromagnetic Flow of Chemically Reactive Oldroyd-B Nanofluid in a Channel with Brownian Motion, Thermophoresis, and Joule Heating

In the present study, the magnetohydrodynamic pulsating flow of chemically reacting Oldroyd-B nanoliquid via channel with the impressions of Ohmic heating, radiative heat and viscous dissipation is studied. The ruling PDEs (partial differential equations) are changed into ODEs (Ordinary differential equations) by utilizing the perturbation procedure and numerically deciphered by adopting the 4th order Runge-Kutta approach with the aid of the shooting process. The novelty of the current work is to inspect the pulsating flow of Oldroyd-B nanoliquid via channel in the occurrence of an applied magnetic field by deploying the Buongiorno nanofluid model. The application of the proposed physical model is energy production, heating and cooling processes, thermoelectric devices, bio-medical applications like brain tumours, cancer treatment, drug targeting. Detailed analysis on the impacts of several pertinent parameters for velocity, temperature, nanoparticles concentration, rates of heat and mass transfer is done. The outcomes predict that the velocity of nanoliquid is improved with augmenting frequency parameter while it is reduced with acceleration in Hartmann number. The temperature rises with an improvement of thermophoresis, viscous dissipation, and Brownian motion while it falls for a given rise in Hartmann number and thermal radiation. Further, the nanoparticle concentration rises with an increasing Brownian motion while it falls over rising chemical reaction, thermophoresis, and Lewis number.

An MHD Marangoni Boundary Layer Flow and Heat Transfer with Mass Transpiration and Radiation: An Analytical Study

This examination is carried out on the two-dimensional magnetohydrodynamic problem for a steady incompressible flow over a porous medium. The Cu−Al2O3 nanoparticles are added to the water base fluid in order to improve thermal efficiency. The transverse magnetic field with strength B0 is applied. The governing equations formed for the defined flow form a system of partial differential equations that are then converted to a system of ordinary differential equations upon applying the suitable similarity transformations. On analytically solving the obtained system, the solutions for velocity profile and temperature distribution are obtained in terms of exponential and Gamma functions, respectively. In addition, the physical parameter of interest, the local Nusselt number, is obtained. The results are analyzed through plotting graphs, and the effect of different parameters is analyzed. Furthermore, we observe that the suction/injection parameter enhances the axial velocity. The porous and radiation parameters enhance the temperature distribution, and the suction/injection parameter suppresses the temperature distribution.

Exact Solutions for Wall Jet Flow of Hybrid Nanofluid

Hybrid nanofluid wall jet problem of Glauert type has been investigated under effects of the thermal radiation, suction parameter, moving parameter, slip velocity and temperature jumps. Via similarity variables governing equations are converted to system of ODEs. Then, resulted equations are solved exactly for velocity and temperature field in the view of gamma and hypergeometric functions. Further, to confirm the similarity solutions, a relationship between the free stream velocity, slip parameter along with suction parameter, moving parameter and solid volume fractions were introduced. In addition, we discussed the physical existence of the slip parameter and asymptotic behavior in a relation with the moving and suction parameters. Further, the obtained outputs are matched with the previous works. It is seen that adding the copper nanoparticles to the nanofluid titanium dioxide/water has effective part in the velocity behavior. Moreover, they warm the hybrid nanofluid on increasing the thermal radiation parameter. However, effects of suction and temperature jump parameters lead to cooling the hybrid nanofluid temperature. Furthermore, for enlarging the wall velocity, the hybrid nanofluid is much better rather than the classical nanofluid. The current analysis has important applications; such as liquid crystal solidification and polymer process.

Heat transfer analysis on Engine oil-based hybrid nanofluid past an exponentially stretching permeable surface with Cu/Al2O3 additives

The flow characteristic of the two-dimensional conducting hybrid nanofluid past an exponentially stretching permeable surface is analyzed. Flow through variable thicker surface for the free convective flow associated with transverse magnetic field in the flow phenomenon that enriches the study. The specialty of the model is the use of effective conductivity property considering the Mintsa model and the effective viscosity with the help of the Gharesim model for the enhancement of heat transport properties. Depending upon the recent applications related to industrial products, engineering as well as bio-medical science nanofluids are used as the best coolant. A comparative study is carried out for the transformed governing equations using both approximate analytical, that is, “ Variational Iteration Method” (VIM), “ Homotopy Perturbation Method” (HPM), and numerical techniques such as the in-build MATLAB command bvp5c. The simulated result in connection to the behavior of the physical parameters is deployed through graphs. The current outcomes validate the earlier established results in particular cases showing the conformity and the convergence of the methodology adopted. However, the observation shows that, shear rate retards with the significant enhancement in the particle concentration of the metal nanoparticles as well as the suction further the heat transfer rate enhanced. The fluid velocity profile boosts up for the increasing thermal buoyancy parameter whereas the reverse impact is rendered in the fluid temperature.

Blasius Flow over a Permeable Moving Flat Plate Containing Cu-Al2O3 Hybrid Nanoparticles with Viscous Dissipation and Radiative Heat Transfer

This study examines the Blasius flow with Cu-Al2O3 hybrid nanoparticles over a moving plate. Additionally, the effects of viscous dissipation and radiation are considered. Similarity transformation is employed to convert the respective model into similarity equations. The results are generated by using bvp4c in MATLAB. Findings reveal that two solutions are attained when both the free stream and the plate move in opposite directions. Moreover, the domains of the velocity ratio parameter are extended when suction is available. Besides, the upsurge of radiation and hybrid nanoparticles lead to the heat transfer enhancement. The rise in radiation heat energy incorporated in radiation parameter leads to the development of fluid temperature as well as the thermal boundary layer. Meanwhile, hybrid nanoparticles offer good thermal characteristics because of synergistic effects. However, the effects reduce with the rise in Eckert number. The first solution is stable and acceptable based on the temporal stability analysis. Furthermore, the critical/separation values of the physical parameters are also reported. With these findings, the optimized productivity will be achieved as well as the processes on certain products can be planned according to the desire output. This significant preliminary study provides future insight to the engineers and scientist on the real applications.

Analytical Study on Sodium Alginate Based Hybrid Nanofluid Flow through a Shrinking/Stretching Sheet with Radiation, Heat Source and Inclined Lorentz Force Effects

This study investigated the flow and heat transfer of sodium alginate-based hybrid nanofluids with a stretching/shrinking surface. The heat source/sink, Joule heating, inclined magnetic field, and thermal radiation influences are also examined in the designed model. The mixers of non-magnetic and magnetic nanoparticles are utilized, such as Cu and Fe3O4. The Casson fluid model is applied to determine the viscoplastic characteristics of sodium alginate (SA). The necessary governing SA-based hybrid nanofluid flow equations are solved analytically by hypergeometric function. SA-based hybrid nanofluid velocity, temperature, skin friction, and Nusselt number results are discussed in detail with various pertinent parameters, such as radiation, heat source/sink, inclined angle, magnetic field, Eckert number, and Casson parameters. It is noted that the dimensions of both Cu and Fe3O4 hybrid nanoparticles and Casson parameters are minimized by the momentum surface layer thickness. The magnetic field, radiation, heat source and Casson parameters serve to enhance the thermal boundary layer thickness. Finally, the current result was verified with previously published works.

Flow and Heat Transfer Past a Stretching/Shrinking Sheet Using Modified Buongiorno Nanoliquid Model

This paper studies the boundary layer flow and heat transfer characteristics past a permeable isothermal stretching/shrinking surface using both nanofluid and hybrid nanofluid flows (called modified Buongiorno nonliquid model). Using appropriate similarity variables, the PDEs are transformed into ODEs to be solved numerically using the function bvp4c from MATLAB. It was found that the solutions of the resulting system have two branches, upper and lower branch solutions, in a certain range of the suction, stretching/shrinking and hybrid nanofluids parameters. Both the analytic and numerical results are obtained for the skin friction coefficient, local Nusselt number, and velocity and temperature distributions, for several values of the governing parameters. It results in the governing parameters considerably affecting the flow and heat transfer characteristics.

Flow and heat transport phenomenon for dynamics of Jeffrey nanofluid past stretchable sheet subject to Lorentz force and dissipation effects

Survey of literature unveils that nanofluids are more efficient for heat transport in comparison to the traditional fluids. However, the enlightenment of developed techniques for the augmentation of heat transport in nanomaterials has considerable gaps and, consequently, an extensive investigation for aforementioned models is vital. The ongoing investigation aims to study the 2-D, incompressible Jeffrey nanofluid heat transference flow due to a stretchable surface. Furthermore, the effect of dispersion of graphene nanoparticles in base liquid ethylene glycol (EG) on the performance of flow and heat transport using the Tawari-Das model in the existence of Ohmic heating (electroconductive heating) and viscous heat dissipation is contemplated. The boundary-layer PDEs are reconstituted as ODEs employing appropriate similarity transformation. Keller-Box Method (KBM) is utilized to determine the numerical findings of the problem. Graphene conducts heat greater in rate than all of the other materials and it is a good conductor of electrical energy. Graphene/EG nanofluid is employed to look out the parametric aspects of heat transport flow, drag coefficient, and heat transference rate phenomena with the aid of graphs and tables. The numerical outcomes indicate that concentration and magnetic field abate the shear stresses for the nanofluid. An increase of Graphene nanoparticle volume fraction parameter can boost the heat transport rate. The effect of Prandtl Number is to slow down the rate of heat transport as well as decelerate the temperature. Additionally, the rate of heat transportation augments on a surface under Deborah's number. Results indicate that the temperature of the graphene-EG nanofluid is greater than the convectional fluid hence graphene-EG nanofluid gets more important in the cooling process, biosensors and drug delivery than conventional fluids.

Mathematical modeling and thermodynamics of Prandtl-Eyring fluid with radiation effect: a numerical approach

Main concern of current research is to develop a novel mathematical model for stagnation-point flow of magnetohydrodynamic (MHD) Prandtl-Eyring fluid over a stretchable cylinder. The thermal radiation and convective boundary condition are also incorporated. The modeled partial differential equations (PDEs) with associative boundary conditions are deduced into coupled non-linear ordinary differential equations (ODEs) by utilizing proper similarity transformations. The deduced dimensionless set of ODEs are solved numerically via shooting method. Behavior of controlling parameters on the fluid velocity, temperature fields as well as skin friction and Nusselt number are highlighted through graphs. Outcome declared that dimensionless fluid temperature boosts up for both the radiation parameter and Biot number. It is also revealed that the magnitude of both heat transfer rate and skin friction enhance for higher estimation of curvature parameter. Furthermore, comparative analysis between present and previous reports are provided for some specific cases to verify the obtained results.

Convective Heat Transfer of a Hybrid Nanofluid over a Nonlinearly Stretching Surface with Radiation Effect

The flow of the hybrid nanofluid (copper–titanium dioxide/water) over a nonlinearly stretching surface was studied with suction and radiation effect. The governing partial differential equations were then converted into non-linear ordinary differential equations by using proper similarity transformations. Therefore, these equations were solved by applying a numerical technique, namely Chebyshev pseudo spectral differentiation matrix. The results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that the rising of the mass flux parameter slows down the velocity and, hence, decreases the temperature. Further, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases.

Shifted Legendre Collocation Method for the Solution of Unsteady Viscous-Ohmic Dissipative Hybrid Ferrofluid Flow over a Cylinder

A numerical treatment for the unsteady viscous-Ohmic dissipative flow of hybrid ferrofluid over a contracting cylinder is provided in this study. The hybrid ferrofluid was prepared by mixing a 50% water (H2O) + 50% ethylene glycol (EG) base fluid with a hybrid combination of magnetite (Fe3O4) and cobalt ferrite (CoFe2O4) ferroparticles. Suitable parameters were considered for the conversion of partial differential equations (PDEs) into ordinary differential equations (ODEs). The numerical solutions were established by expanding the unknowns and employing the truncated series of shifted Legendre polynomials. We begin by collocating the transformed ODEs by setting the collocation points. These collocated equations yield a system of algebraic equations containing shifted Legendre coefficients, which can be obtained by solving this system of equations. The effect of the various influencing parameters on the velocity and temperature flow profiles were plotted graphically and discussed in detail. The effects of the parameters on the skin friction coefficient and heat transfer rates were further presented. From the discussion, we come to the understanding that Eckert number considerably decreases both the skin friction coefficient and the heat transfer rate.

Entropy Generation Analysis of Hybrid Nanomaterial through Porous Space with Variable Characteristics

Salient features of hybrid nanofluid (MoS₂-SiO₂/water) for Darcy–Forchheimer–Brinkman porous space with variable characteristics is examined. Heat transfer analysis subject to viscous dissipation, nonlinear thermal radiation, and heat generation/absorption is carried out. Disturbance inflow is created by an exponentially stretching curved sheet. Relevant equations are simplified by employing boundary layer theory. Adequate transformations lead to a set of dimensionless equations. Velocity, temperature, and entropy generation rate are analyzed graphically. Comparative results are obtained for hybrid (MoS₂-SiO₂/water) and nanofluid (MoS₂-water and SiO₂-water). Physical quantities are analyzed through numerical data.

Hybrid Nanofluid Slip Flow over an Exponentially Stretching/Shrinking Permeable Sheet with Heat Generation

An investigation has been done on the hybrid nanofluid slip flow in the existence of heat generation over an exponentially stretching/shrinking permeable sheet. Hybridization of alumina and copper with water as the base fluid is considered. The mathematical model is simplified through the similarity transformation. A numerical solver named bvp4c in Matlab software is utilized to facilitate the problem-solving process and dual solutions are attained. The influences of several pertinent parameters on the main physical quantities of interest and the profiles are scrutinized and presented in the form of graphs. Through the stability analysis, only the first solution is considered as the physical solution. As such, the findings conclude that the upsurges of volume fraction on the copper nanoparticle could enhance the skin friction coefficient and the local Nusselt number.

Numerical investigation for rotating flow of MHD hybrid nanofluid with thermal radiation over a stretching sheet

This research investigates the heat and mass transfer in 3-D MHD radiative flow of water based hybrid nanofluid over an extending sheet by employing the strength of numerical computing based Lobatto IIIA method. Nanoparticles of aluminum oxide (Al₂O₃) and silver (Ag) are being used with water (H₂O) as base fluid. By considering the heat transfer phenomenon due to thermal radiation effects. The physical flow problem is then modeled into set of PDEs, which are then transmuted into equivalent set of nonlinear ODEs by utilizing the appropriate similarity transformations. The system of ODEs is solved by the computational strength of Lobatto IIIA method to get the various graphical and numerical results for analyzing the impact of various physical constraints on velocity and thermal profiles. Additionally, the heat transfers and skin friction analysis for the fluid flow dynamics is also investigated. The relative errors up to the accuracy level of 1e-15, established the worth and reliability of the computational technique. It is observed that heat transfer rate increases with the increase in magnetic effect, Biot number and rotation parameter.

Radiation and Mixed Convection Magnetohydrodynamics Boundary Layer of Hybrid Cu–Al2O3/Water Nanofluid Flow Over a Wall Jet

The mixed convection MHD boundary layer flow of the hybrid nanofluid (copper–titanium dioxide/water) over a permeable wall jet surface subject to thermal radiation was studied with the effects of suction/injection and thermal energy. The governing PDEs were converted into non-linear ODEs by using the proper similarity transformations. Then, these equations were numerically solved applying the method of Chebyshev pseudo spectral differentiation matrix (ChPDM). The results were deduced for the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number. It was found that the hydrodynamic and thermal boundary layers decreases and increases, respectively, as the strength of the magnetic field increases. Further, in the industrial applications, the normal angle is to be applied if low velocity and high temperature is needed. Moreover, as the mixed convection parameter rises, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can control the thermal boundary layer. Finally, the Cu-nanoparticles volume fraction plays a very important role in the velocity variation.