Convection Flow Of Nanofluid Research Articles

Nanofluid Flow Past a Static Wedge with Velocity Slip Condition

Nanofluids are known for their exceptional thermophysical properties, especially their thermal conductivity, which make them ideal for a number of heat transfer applications. In this study, the mixed convection nanofluid flow past a static wedge with the presence of velocity slip condition is investigated. The problem is governed by a system of partial differential equations which then transformed into a set of nonlinear ordinary differential equations by using an appropriate similarity transformation. The transformed governing equations are then solved numerically by using MATLAB bvp4c solver. Numerical solutions obtained are presented graphically in the form of velocity and temperature profiles for different values of nanoparticles volume fraction, wedge angle and velocity slip. It is found that the increasing values of the wedge angle parameter causes the velocity of the fluid to increase whereas the temperature profile of the nanofluid decreases, additionally it observed that velocity of the fluid increase when velocity slip is increased. The findings of this study provide valuable insights into optimizing heat transfer processes in various engineering applications by leveraging the enhanced thermal properties of nanofluids and considering factors such as wedge angle and velocity slip

Turbulent forced convection flow of water-based nanofluids with temperature-dependent properties over backward-facing step channel with upwardly deflected downstream wall

The heat transfer performances of various water-based nanofluids (NFs) relative to the base fluid in turbulent forced convection flow within a 2-D backward-facing step (BFS) channel with an upwardly deflected downstream wall with a uniform heat flux are analyzed using the package OpenFOAM. The k-ω shear stress transport (SST) model based on the Euler-Euler single-phase framework is used. The performance evaluation criterion (PEC) is defined to assess the relative importance of the enhanced heat transfer and intensified resistance (pressure drop) caused by Cu/water NFs and MWCNT-Fe3O4/water hybrid NFs (low concentration NFs), Fe3O4/water NFs, and Cu-MWCNT/water hybrid NFs (high concentration NFs). At Re = 30215, the maximum enhancement of the average Nusselt number (ANN) is 7% when the copper NPs are added to the water. In addition, the increment of the deflection angle from 0.0 to 1.27 enhances the ANN values by 44 ∼ 45% concerning low-concentration NFs. At Re = 7940, the friction factor increases by 24.3% and 32.1% when copper and MWCNT-Fe3O4 hybrid NPs are dispersed in the base fluid, respectively. The highest PEC value (1.07) is achieved when the copper NPs with ϕ = 0.003 are used in configuration BFS1 at Re = 7940. Using MWCNT-Fe3O4 hybrid NPs is only proposed at lower Re numbers when the downstream wall is deflected and ϕ = 0.001. At Re = 30215, due to the addition of magnetic NPs, the ANN value abates by 28.5% and 30.7%, respectively, in the canonical case and configuration BFS2. Among the high-concentration NFs, the highest PEC (1.05) is obtained using Cu-MWCNT hybrid NPs with ϕ = 0.01 at Re = 30215 when the downstream wall is deflected upwardly. As Mouromtseff (Mo) number-based figure-of-merit (FOM) verifies, the worst scenario (PEC < 1.0) is substituting the base fluid with Fe3O4/water NFs. Cu-MWCNT/water hybrid NFs with ϕ = 0.02 become an effective coolant (PEC > 1.0) when the deflection angle and Re number increase simultaneously.

Mixed convective flow of nanofluid across exponential surface: A numerical assessment of the impact of Darcy-Forchheimer and nanoparticle aggregation

Improving heat transmission is a modern difficulty faced in a multitude of areas, incorporating but not limited to electronics, heat exchangers, biochemical reactors, and other similar areas. In their capacity as cutting-edge heat transfer fluids, nanofluids have the promise of becoming a useful instrument in the pursuit of greater energy transfer efficiency. So, the focus of this work is on how it is possible to enhance heat transmission by using nanofluids. Using a stretched exponentially accelerating surface, this analysis investigates the effect that nanoparticle aggregation with thermal radiation has on the nanofluid of mixed convective stagnation point flow through Darcy-Forchheimer porous surfaces. The aggregation of nanoparticles may be assessed using modified Krieger-Dougherty and Maxwell-Bruggeman models. By using the right similarity transformations, the controlling equations of this problem were turned into a numerical model that can be unraveled. Mathematica was used to resolve the issue numerically by using the shooting with Runge-Kutta (RK-IV) procedure. nanoparticles with base fluid under aggregation effect boost heat transfer performance. A diversity of parameter estimates, including the mixed convection, mass suction, solid volume fraction of nanoparticles, thermal radiation, and stretching, were used to provide solutions for heat transfer and lower skin friction coefficients, as well as velocity and temperature curves. In addition to the findings, there were graphs and tables with explanations. The increase in heat transfer rates was 6.7021% when the suction parameters were set between 2.0 to 2.5 with =0.01. When the amount of nanoparticles volume fraction went from 0% to 1% by volume, the ineptitude of heat transfer went by an average of 4.249%. Aggregation models are often favored over non-aggregation models due to their ability to provide more accurate velocity and skin fraction profiles. Because of their superior precision, they are often used in situations where accuracy is paramount.

Mixed convection simulation of TMPHN by Eringen’s micropolar rules, Tiwari–Das nanofluid model, and mass-based hybridity algorithm

In this study, a combination of the Tiwari–Das nanofluid model, the mass-based hybridity algorithm, and the Eringen micropolar rules are applied to inquire about the mixed convective flow of a thermo-micropolar hybrid nanofluid (TMPHN) over a shrinking perpendicular surface. The working fluid of the TMPHN includes two nanoparticles (alumina and copper) suspended in an aqua-base fluid. The applied methodology considers the masses of base fluid and nanoparticles as an alternative to the first and second nanoparticle volume fractions, which is named the mass-based hybridity algorithm. The transformed ODEs are solved numerically by the shooting-based bvp4c method with MATLAB software. It is significant to mention that the nonlinearity of the pertinent governing equations and the nature of the pertinent boundary conditions both contribute to the duality of similar solutions. The effects of various controlling factors on the velocity, the angular velocity, and temperature, as well as the shear stress, the gradient of micro-rotation, and heat transfer, are graphically depicted. With great confidence, the current algorithm for the modeling of thermo-micropolar hybrid nanofluid can be applied to a variety of issues. Moreover, the numerical outputs reveal that the shrinking parameter range for the occurrence of solution duality increases with the alumina mass and the Richardson number. The findings, in a comprehensive and detailed form, have been presented in the article’s body.

Magneto-convective hybrid nanofluid slip flow over a moving inclined thin needle in a Darcy-Forchheimer porous medium with viscous dissipation

PurposeThe purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.Design/methodology/approachThe first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.FindingsIt is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al2O3 and Fe3O4 are nanoparticles, H2O − C2H6O2 (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.Practical implicationsThe results can be very helpful to improve the energy efficiency of thermal systems.Social implicationsThe hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.Originality/valueThis study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

Heat and Mass Transfer Analysis in An Unsteady Natural Convective Magnet Hydrodynamic Flow of a Nano Fluid under the Presence of Thermal Diffusion and Absorption Radiation

An analysis of unsteady natural convective MHD flow of nanofluid under the presence of thermal diffusion and absorption radiation with the effects of chemical reaction on heat and mass transfer without a porous medium is discussed in the present study. The governing equations were implied and were solved analytically using perturbation technique. The velocity, temperature and concentration fields are obtained. Graphical results were presented for velocity, temperature and concentration profile for various values of parameters.

Turbulent flow of a shear-thinning non-Newtonian CMC-based nanofluid in twisted finned tubes with an elliptical profile

In this article, the forced convective turbulent flow of a shear-thinning non-Newtonian nanofluid through twisted tubes with elliptical cross sections is numerically studied and analyzed at various Reynolds numbers. The base fluid of the studied nanofluid is 0.5% carboxymethyl cellulose solution in water (which has non-Newtonian behavior of shear-thinning), and it contains copper oxide nanoparticles. Two types of twisted tubes are considered: finned tubes and unfinned ones. The finite volume method is utilized, and the two-equation model of k-ε has been applied to analyze the flow characteristics of the turbulent problem. The computational results demonstrate an excellent agreement with respect to already published reports, which is a testament to our reasonable and correct procedure. The effects of pipe wall twisting on the average Nusselt number have been investigated. The achievements demonstrate a powerful secondary and rotating flow is formed with the tube surface twisting. This secondary flow causes better mixing and increases the average Nusselt number. The increase is up to 45% for the unfinned case and 62% for the finned case in comparison with the tube without projections. In addition, the coefficient of friction in these pipes increases to 62% and 104% for the unfinned and finned tubes, respectively. It is also observed that by increasing the length of the fin and adding nanoparticles up to 1.5%, the highest value of the performance evaluation criterion (i.e. 1.78) in the twisted finned tube could be achieved, which occurred at the Reynolds number of 4000. The combination of present geometry and the working fluid of shear-thinning non-Newtonian CMC-based nanofluid is the main novelty of this work, and the results can be applicable and reliable in the relevant industries.

Effect of solid obstacle and thermal conditions on convective flow and entropy generation of nanofluid filled in a cylindrical chamber

PurposeOne of the major challenges in the design of thermal equipment is to minimize the entropy production and enhance the thermal dissipation rate for improving energy efficiency of the devices. In several industrial applications, the structure of thermal device is cylindrical shape. In this regard, this paper aims to explore the impact of isothermal cylindrical solid block on nanofluid (Ag – H2O) convective flow and entropy generation in a cylindrical annular chamber subjected to different thermal conditions. Furthermore, the present study also addresses the structural impact of cylindrical solid block placed at the center of annular domain.Design/methodology/approachThe alternating direction implicit and successive over relaxation techniques are used in the current investigation to solve the coupled partial differential equations. Furthermore, estimation of average Nusselt number and total entropy generation involves integration and is achieved by Simpson and Trapezoidal’s rules, respectively. Mesh independence checks have been carried out to ensure the accuracy of numerical results.FindingsComputations have been performed to analyze the simultaneous multiple influences, such as different thermal conditions, size and aspect ratio of the hot obstacle, Rayleigh number and nanoparticle shape on buoyancy-driven nanoliquid movement, heat dissipation, irreversibility distribution, cup-mixing temperature and performance evaluation criteria in an annular chamber. The computational results reveal that the nanoparticle shape and obstacle size produce conducive situation for increasing system’s thermal efficiency. Furthermore, utilization of nonspherical shaped nanoparticles enhances the heat transfer rate with minimum entropy generation in the enclosure. Also, greater performance evaluation criteria has been noticed for larger obstacle for both uniform and nonuniform heating.Research limitations/implicationsThe current numerical investigation can be extended to further explore the thermal performance with different positions of solid obstacle, inclination angles, by applying Lorentz force, internal heat generation and so on numerically or experimentally.Originality/valueA pioneering numerical investigation on the structural influence of hot solid block on the convective nanofluid flow, energy transport and entropy production in an annular space has been analyzed. The results in the present study are novel, related to various modern industrial applications. These results could be used as a firsthand information for the design engineers to obtain highly efficient thermal systems.

Exploration of entropy analysis and viscous dissipation on radially convective flow of (Cu‐Al2O3:H2O) hybrid nanofluid over a stretching disk

AbstractThe current research work deals with the impact of suction/injection on the thermally radiating convective flow generated by a nonlinear stretched disk. The energy equation is addressed by the presence of thermal radiation and the energy dissipative function. This work was carried out with the help of the Das and Tiwari (single‐phase nanofluid) models and the Maxwell Garnett and Brinkman nanofluid models for the analysis of entropy generation. In the present model, nanoparticles of copper (Cu) and alumina (Al2O3) are being used with water (H2O) as the base fluid. The governing nonlinear partial differential equations are transformed into ordinary differential equations with the assistance of appropriate similarity variables. These transformed equations are then solved using the bvp4c function, a built‐in function in MATLAB software. The investigation examines the influence of various factors on the velocity and temperature fields, entropy generation, skin friction, and heat transfer rate. The findings show that suction decreases velocity and temperature by 6.59%, while injection has the opposite effect. Viscous dissipation increases velocity by 5.13% and temperature by 17.94% in hybrid nanofluids. Higher Prandtl numbers reduce velocity and temperature by 6% in nanofluids but boost them by 5.45% and 18.81% in hybrid nanofluids with radiation growth. As volume fraction rises, Al2O3/H2O nanofluid speed falls by 5.37%, but Cu‐Al2O3/H2O hybrid nanofluid temperature increases by 13.09% and surface drag force increases by 12%. The entropy of the hybrid nanofluid increases by 5.84%, 8.19%, and 14.04% with Eckert number, suction, and Prandtl number but decreases by 10.08% with temperature difference. The Nusselt number of nanofluid decreases by 10.58% and 12.40% with Eckert number and radiation, but hybrid particles increase it by 10.31% with intensified Prandtl number. These findings offer valuable insights for potential applications of hybrid nanofluids in heat transfer and cooling systems.

Numerical study for bioconvection in Marangoni convective flow of Cross nanofluid with convective boundary conditions

The current study investigates incompressible, MHD flow of Cross nanofluid containing of gyrotactic microorganisms and thermophoretic particle deposition over a sheet with activation energy and variable thermal conductivity. The variable characteristic of thermal conductivity is considered as a linear function of temperature. The present study’s insights can optimize the design of nanofluid-based systems, enhance drug delivery methods, improve environmental monitoring, refine materials engineering, advance microfluidics for diagnostics, boost renewable energy technologies, and upgrade electronics cooling solutions. Moreover, this study contribution to scientific understanding will catalyze further research across disciplines, fostering innovation and progress. Cross nanofluid containing iron oxide [Formula: see text] nanoparticles, and based fluid ethylene glycol ([Formula: see text] is used. In the current study, distributions of concentration, temperature, mass, microorganisms, and flow are examined in the presence of nanofluid while also accounting for thermophoretic particle deposition and a heat source. The proposed flow equations are transmuted into ODEs by employing the suitable similarity variables. RKF-45th approach is used to evaluate the reduced equations. Graphs are used to determine the effects of important factors on thermal, microorganism, concentration, and flow profiles. With a rise in the Marangoni ratio parameter, the velocity distribution is enhanced, whereas the temperature distribution exhibit inverse behavior.

Development of an intelligent computing system using neural networks for modeling bioconvection flow of second-grade nanofluid with gyrotactic microorganisms

Nanoparticles are carried in bioconvective fluid flow by convective motion caused by living tissues. This flow has important applications in cell and tissue engineering because it demonstrates the mechanics of particle transfer between cells and fluids. This type of flow is used in medicine delivery systems that particularly target cancer cells in real life. Nanofluids are crucial suspensions that allow nanomaterials to disperse and behave in a homogeneous and stable environment. The bioconvective second-grade nanofluid flow, on the other hand, is distinguished by a more complex process that permits nanoparticle motion to be controlled by external fields and pressures. This type of flow has numerous applications, including biology, the environment, and energy. It is particularly useful in medical imaging, cancer hyperthermia treatment, and nanodrug delivery systems. The primary purpose of this research is to use an artificial neural network to examine the rate of heat, mass, and motile microbe movement in the convective flow of magnetohydrodynamic second-grade nanofluid toward vertical surface. Suspended nanoparticles are effectively stabilized by the action of microorganisms, facilitated through bioconvection. This process is influenced by both nanoparticle attributes and buoyancy forces. In addition to thermophoretic dynamics and Brownian motion, the model considers radiation and Newtonian heating effects. Nonlinear equation systems are obtained using appropriate transformations. The non-linear simplified equations underwent numerical calculations utilizing the fourth-order Runge-Kutta shooting method. The Sherwood number, Nusselt number, and density of motile microorganism coefficient were determined using various parameters, and three distinct artificial neural networks were built employing the findings.

A generalized thermal memory effect of Caputo–Fabrizio fractional integral on natural convection flow of hybrid nanofluid

In this paper, the natural convective flow of hybrid nanofluid over the vertical plate has been examined. Cattaneo law of thermal flux is used to characterize thermal transport. The novel model for fractional constitutive equation is expressed by the time fractional Caputo–Fabrizio integral. The analytical solution of the generalized convective flow of viscous fluid over the vertical plate along generalized conditions is obtained by using the Laplace transform. Mathcad is used to determine numerically the influence of the physical and fractional parameters on the temperature and velocity field to depict the results graphically.

A revised model on three-dimensional hydromagnetic convective flow of nanofluids over a nonlinearly inclined stretching sheet

Theoretical research has been done on the hydromagnetic three-dimensional nanofluid flow across an inclined stretching sheet in the presence of Brownian motion and thermophoresis. It is taken into account that there are two different kinds of water-based nanofluids that contain copper and alumina. Three-dimensional nonlinear-type similarity transformations are used to convert the governing boundary-layer equations into a collection of similarity equations, which are then numerically solved by MATLAB. Further, results obtained in some limiting cases are compared to some results that have already been published, and it is found that there is good agreement. The problem is controlled by a number of physical factors, and the impact of these factors on different flow distributions is thoroughly examined with the help of graphs and tables. It has been observed that the nanofluid has better heat transfer conductivity than the ordinary base fluid.

Magneto-double-diffusive natural convection and irreversibility analysis of a nanofluid flowing in an annular concentric space

In the present article, magneto-double-diffusive density driven convection accompanied by an entropy optimization analysis of Al2O3-water nanofluid filled in a horizontal coaxial annular space is numerically addressed. The double-diffusive natural nanofluid flow which is produced due to the maintaining of constant and different temperature and solute on the inner and outer cylinders is affected by a uniform vertical magnetic field. Dimensionless governed equations which are developed through law of conservation of mass, momentum, and energy are numerically solved via finite volume approach, and parametric control analysis is developed. By using Corcione empirical correlations considering the Brownian diffusion of 4% of Al2O3 nanoparticles in water, the thermal conductivity and viscosity of the mixture nanofluid are determined. Results are performed and interpreted in detail for wide range of relevant variables: Rayleigh (102 ≤ Ra ≤ 105), Hartmann (0 ≤ Ha ≤ 30), Lewis numbers (0 ≤ Le ≤ 10), and Buoyancy ratio (−4 ≤ N ≤ 4) to evaluate the double-diffusive convective nanofluid flow, heat and solute transfer rates as well as entropies produced in the system.

Instability of MHD mixed convection flow of nanofluid in porous channel with thermal radiation, chemical reaction, Dufour and Soret effects

The present paper aims to investigate a stability analysis of the mixed convection of Al2O3/water nanofluid through an anisotropic porous channel heated from below and cooled from above. The effects of the magnetic field, thermal radiation, chemical reaction, mass transfer (Soret effect) and energy transfer (Dufour effect) are taken into consideration. The equations governing the motion of the nanofluid are converted by means of hydrodynamic stability theory into a system of eigenvalue equations which is then solved numerically by the spectral collocation method. The effects of Hartmann number, thermal radiation parameter, volume fraction of nanoparticles, permeability parameter, chemical reaction parameter, Dufour and Soret number are presented and analyzed. The results showed that in presence of nanoparticles the inertia of the working fluid increases, which dampens the disturbances and thus reduces their growth. The Hartman number attenuated the amplitude of the disturbances and thus has a stabilizing effect. The permeability parameter affected the stability of the flow and its growth prevented the redistribution of disturbances within the flow, which reflected its stabilizing character. The numbers of Soret and Dufour showed an important effect on the stability of the convective mixed flow. Their growth increased the transition Reynolds number for which there was a transition to instabilities, which prevented the transition to increasingly turbulent flows. On the other hand, the increase in the chemical reaction parameter decreased the values of transition Reynolds number, thus showing that the chemical reaction maintained the instabilities.

The Mixed of Hybrid Nanofluid GO-MoS2/Engine Oil Over a Shrinking Sheet with Mass Flux Effect: Reiner-Philippoff Model

The mixed convection flow and heat transfer of the hybrid nanofluid over a shrinking sheet are investigated. Molybdenum disulphide (MoS2) and graphene oxide (GO) are employed as two hybrid nanoparticles while engine oil (EO) as the base fluid is considered. In this study, the Reiner-Philippoff model as one of non-Newtonian types is deliberated since it has the ability to function on three distinct types of fluids: viscous, shear thickening and shear thinning. The Reiner-Philippoff relation, the momentum and energy equations under Tiwari and Das model are all employed in the study. Influences from mass flux are also considered in the flow. Before computation using the bvp4c function in MATLAB, the respected equations are first converted into ordinary differential equation form using the similarity transformation. When the established and current models are discovered to be identical in a specific case, a direct comparative investigation is conducted to confirm the correctness of the current model. In addition, the present results are shown graphically and in tabular form. It is hypothesized that the presence of a hybrid nanofluid significantly affects the fluid characteristic and gives more satisfactory results than a single nanofluid. The skin friction coefficient and heat transfer rate of hybrid nanofluids are greater than the nanofluids. In terms of velocity and temperature profile, the reduction in velocity and the enhancement in temperature profile are caused by a rise in the Reiner-Philippoff parameter. The same outcome is also seen when the volume fraction of hybrid nanofluids increases.

An exact analysis of radiation absorption and Dufour effect on MHD convective flow of Cu-water nanofluid with heat generation and chemical reaction

The combined effects of diffusion-thermo and radiative absorption on free convective hydromagnetic heat-generating chemically reactive flow of Cu-water nanofluid past an instantaneously accelerated unlimited vertical plate nested in a porous medium are investigated. A comparative analysis is executed for both isothermal and ramped conditions. The set of transformed domain equations has been obtained using a closed form of the Laplace transform method with the help of the Heaviside step function. Graphical and tabular explanations are provided for the physical characteristics of several flow parameters affecting the problem. Graphs are generated using MATLAB computing software. Findings of the problem manifest that the diffusion-thermo parameter and the radiation absorption parameter intensify the velocity and fluid temperature in the entire fluid area. This augmentation is most prominent for copper nanoparticles. Concentration, temperature, and velocity profiles in the case of ramped conditions are less than in isothermal conditions. Furthermore, the ramped parameter amplifies the heat transfer rate while reversing the mass transfer rate. It is also established that the volume concentration of nanoparticles enhances the heat transfer rate. The present study is of great interest in numerous fields of industry and machine-building applications.

Dual solutions for nanofluid flow past a moving plate embedded in a Darcy porous medium in attendance of heat source/sink

The aim of this study is to present forced convective nanofluid flow over a moving plate embedded in an absorbent medium. Following Darcy law’s for porous medium, the flow analysis is explored in attendance of warmth basis/drop. The main objective of this study is to explore the effects of Brownian motion and thermophoresis. The plate is considered to move in both directions: in the way of movement of fluid and in the opposite route of fluid movement. Similarity alterations have been applied to alter the leading partial differential equations (PDEs) to ordinary differential equations (ODEs). Numerical solutions have been obtained with the help of MATHEMATICA software. Dual solutions have been obtained when the plate and liquid go in reverse ways. Wall shear stress, Nusselt and Sherwood numbers all are found to rise with the rising permeability parameter of absorbent medium. For Nusselt and Sherwood numbers, ranges of dual solutions diminish by the mounting values of permeability parameter K. The critical values for porosity parameter [Formula: see text], 0.02, 0.03 are [Formula: see text], [Formula: see text], [Formula: see text], respectively. For decreasing values of s, range of dual solutions decreases. For [Formula: see text], dual solutions exist in the range [Formula: see text].

Soret Effect with Chemical Reaction on Unsteady MHD Flow of Nanofluid Past an Impulsively Started Infinite Vertical Plate Embedded in a Porous Medium

This article deals with the analysis of the thermal-diffusion effect, chemical reaction and heat generation on the convective hydromagnetic flow of water-based nanofluid past an instantaneously accelerated infinite vertical plate nested in a porous medium. Simultaneous application of ramped temperature, ramped velocity, and ramped concentration has been considered. With the help of Laplace transformation, the set of transformed domain equations has been resolved. The consequences of various flow parameters involved in the study are analysed graphically. The results exhibit that the hydrodynamic and solutal boundary layer elevates for the higher value of the Soret effect Sr. Moreover, the rate of heat transfer hikes and on the other hand, the rate of mass transfer drops on account of the volume concentration of nanoparticles φ. Again, it is observed that the temperature, concentration and velocity field are dominated in the ramped condition by that of the isothermal condition.

MHD Natural Convection Nanofluid Flow between two Vertical Flat Plates through Porous Medium considering effects of viscous dissipation, non-Darcy, and Heat Generation/Absorption

MHD Natural Convection Nanofluid Flow between two Vertical Flat Plates through Porous Medium considering effects of viscous dissipation, non-Darcy, and Heat Generation/Absorption