Search

This study numerically investigated the entropy production in nanofluids’ dissipative unsteady oscillatory flow characterized by variable electric conductivity and magnetic heating effects. The imposition of the non-isothermal boundary condition on the oscillatory stretching sheet plays a crucial role in establishing the self-similar solution in the presence of viscous heating. An external magnetic field (uniform in space and time) is imposed perpendicular to the plane of the oscillating stretched boundary. The energy equation, incorporating viscous dissipation effects and momentum equation, is reduced to nonlinear coupled partial differential equations and numerically solved using the Gear-generalized differential quadrature scheme.Additionally, to ensure the precision and reliability of the outcomes, the numerical code undergoes a thorough validation process that involves comparing its outputs to the findings of previous available studies. The Corcione model is implemented to describe the nanofluid’s effective viscosity and thermal conductivity. Furthermore, expressions for entropy production and relative irreversibility parameter (Bejan number), considering variable electric conductivity, are derived and computed based on solutions obtained from momentum and energy equations. The impacts of parameters such as magnetic parameter, variable electric conductivity parameter, Eckert number, Strouhal number, Prandtl number and temperature difference parameters on flow, heat transfer, entropy generation, and Bejan number are systematically illustrated and examined. We observed that increasing the variable electric conductivity parameters reduces the velocity profiles while improving the thermal fields. Similar behavior is found when the strength of a magnetic field is increased. The skin friction coefficient exhibits an augmentation in response to the Eckert number, dimensionless time, Strouhal number, nanoparticle volume fraction, magnetic parameter, and variable thermal conductivity parameter. Conversely, the Nusselt number increases concerning the Strouhal number and nanoparticle volume fraction. At the same time, it declines in association with the magnetic parameter, dimensionless time, Eckert number, and variable electric conductivity parameter.This comprehensive investigation enhances our understanding of nanofluid dynamics and provides valuable insights for optimizing thermal management systems across various engineering disciplines.Graphical Abstract

The failure to consider thermal radiation in addition to free convection heat transfer in many cases such as heat exchangers will cause an unavoidable error in the flow analysis. Due to the complexity of volumetric radiation modeling in solving various problems, it is difficult to simulate this issue, especially through computer coding. The reason for this numerical study is the lack of extensive investigation of the effect of volumetric radiation on non-Newtonian nanofluid flow under magnetic field and heat absorption. By using the LBM and simulating the natural convection phenomenon, the cooling of a square-shaped component within a sector of a ring containing a non-Newtonian nanofluid has been modeled in the present research. The findings indicate that the presence of radiation increases the average value of the Nusselt number for the shear thickening, the Newtonian, and the shear thinning fluids by about 17%, 11%, and 8.5%, respectively. The growth of the thermal performance index and the mean Nusselt Number value is observed via the enhancement of the fluid power-law index, especially in the absence of heat absorption. In most cases, the presence of nanoparticles improves the heat transfer rate, especially in cases where thermal conduction dominates convection. There is the lowest cooling performance index and magnetic field effect for the cavity placed at the angle of 45°. By designing the system in such a way that the magnetic field is imposed on the system at different angles and positions, the thermal performance can be improved to a great extent.

In this article, von Kárman MHD viscoelastic fluid flow with second-grade model through a heated permeable disk on electric field is examined thoroughly. The effects of viscous dissipation and elasticity on fluid motion around the disk, temperature and space-dependent heat source/sink are also examined. Governing partial differential equations are transmitted into ordinary differential equations with similarity functions. Later, nonlinear system of ordinary differential equations was solved with the help of Galerkin finite element method. Accuracy and validity of the method were noticed by comparing our results with the previous literature. Simulations are performed in order to capture the dynamics of the physical situations against the variation of the pertinent parameters. Nature of heat flux and stresses of the physical parameters are discussed. Physical influence of heat flux, heat transfer is exhibited graphically at the surface of disk and increases when the values of Prandtl number are increased, whereas there is a decreasing trend in the rate of heat transfer when the value of Eckert number is increased.

This review explores machine learning approaches for predicting ignition delay in combustion processes. Ignition delay is a vital parameter in optimizing the engine design, fuel formulations, and combustion efficiency. The review examines the applications of artificial neural networks (ANNs) and convolutional neural networks (CNNs) in various combustion processes and equipment, such as engines, boilers, and rapid compression machines. The differences between ANNs and CNNs are discussed, highlighting their capabilities and limitations. Numerous studies are presented, demonstrating the successful application of neural networks in predicting ignition delay for different fuels and engines. Overall, machine learning approaches show great promise in accurately predicting the ignition delay and advancing energy utilization.

The hydrothermal performance of a hybrid nanofluid made of graphene, gold/polydimethylsiloxane between two squeezing plates is discussed in this study. In the investigation of thermal transport of the flow, both linear and nonlinear thermal radiation's effects are taken into account. Bejan numbers are used to determine the system's energy efficiency. Viscous and thermal radiation effects on Maxwell hybrid nanofluid flow in a squeezing channel are incorporated to explore the outcomes. By applying similarity transformations, the set of ordinary differential equations in this case is transformed into the governing equations. With the use of the Runge–Kutta–Fehlberg technique converted system is solved numerically. Skin friction and heat transfer rates under the influence of certain oriented parameters are numerically analysed and presented in tabular form. The impacts of different factors on the temperature and velocity profiles are illustrated graphically and briefly described. Important findings include that the Bejan number raises as the radiation parameter Rd rises, but that it falls with respect to the Eckert number effect. Additionally, the skin friction values and Nusselt number in the hybrid nanofluid case are larger than in the nanofluid case. Furthermore, it has been found that the Deborah number-described stress relaxation phenomenon causes the flow field and thermal energy transfer to be less efficient when fluids are moving. There is surprisingly little research on the hybrid fluid integrated into their issues.

The hydromagnetic dissipative, heat-absorbing, chemically reactive and optically thick radiative flow of nanofluid over a stretchable surface together with heat and mass transport phenomena is investigated. The prevailing partial differential equations (PDE) of the mathematical model are changed by incorporating apt similarity variables in the form of nonlinear similarity equations. Further, these similarity equations are solved numerically utilizing the Runge-Kutta Fehlberg technique in conjunction with the shooting method. For the numerical explorations, three kinds of nanofluids are prepared by disseminating very fine nanoparticles of titanium oxide (TiO2), aluminium oxide (Al2O3) and copper (Cu) into water. The significance of numerous regulatory flow parameters on the nanofluid velocity, nanofluid temperature, local Nusselt number, species concentration, wall velocity gradient and mass flow rates are examined through different graphical results. Additionally, a quadratic regression approximation analysis is accomplished to analyze the connection between the heat transport rate and regulatory flow parameters. The numerical results reveal that the temperature of Cu-water based nanofluid temperature gets enhanced owing to improvement in the strength of radiation, viscous dissipation and magnetic effects. Further, regression approximation analysis unveils that a slight change in the velocity slip parameter leads in the optimal perturbation in both the shear stress values and heat transfer rate at the stretchable surface. Finally, the validation of numerical results and the developed algorithm of employed computational technique have been done by making a comparison of computed results with the available results under restricted situations.

The paper presents the boundary layer flow of mass transfer on a continuous flat plate moving in parallel or reversely to a free stream with a chemical reaction. By using suitable similarity transformations, the boundary-layer equations are transformed into coupled nonlinear ordinary differential equations (NODEs) over semi-infinite interval. These equations have been analysed using a novel semi-numerical method, viz. spectral method. The dual solutions for velocity and concentration distributions are determined using Chebyshev collocation method (CCM) and the results are presented in the form of tables and graphs. The obtained spectral solutions are compared with previously published results and are comparable. Many interesting physical properties of the problem are observed and verified through both theoretical as well as semi-numerical approach. The derived quantities show that the mass transfer rate is established to be increased as the Schmidt number increases for the solution of the upper branch and reduces for the solution of lower branch.

The viscoelastic characteristics of an incompressible, axisymmetric Casson–Maxwell nanoliquid flow between two stationary discs were examined in this paper. Two porous discs are constrained for uniform injection. The Christov model is used in conjunction with the Buongiorno model. In an energy equation with a nonlinear form, thermal radiation characteristics are used. In the current continuation, the impact of chemical reactions is taken into account, making the work more adaptable. Using appropriate transformations, the constructed model was transformed into a dimensionless form. The solution is obtained by employing the FEM technique. The related parameters are described using physical results. The radial velocity distribution at the center line was reduced using a magnetic parameter and a Casson parameter. When the Brownian motion constant and radiation parameter are increased, the temperature distribution of nanoparticles enhances. Furthermore, the rate of the reaction increases in the presence of a chemical reaction. Pearson's correlation coefficient was used to discover a relationship between the Sherwood and Nusslet numbers. To determine the linear relationship between variables, the t-test method is used.

This article discusses a mathematical model for the electrokinetic and Darcy’s resistance of Williamson fluid in an electroosmotic pumping environment. The zeta potential at walls aids in peristaltic movement, and porous dissipation is incorporated into this modulation by the Williamson fluid’s material parameters. Through the use of Debye-Huckel approximations, long wavelengths, and low Reynolds numbers, the model equations are simplified. Mathematica software is used to produce analytical and numerical results, and plots and analyses are done using the included parameters on physical quantities of interest. This study has various practical applications, such as modifying belt resistance in laboratory drainage testing and improving pipeline design. It could also potentially aid in the development of blood filtration and purification techniques and optimize drug delivery systems that utilize fluids. It is observed that the modified Darcy’s law is more accurate for porosity effects in electroosmotic peristaltic channels and results in higher shear stress at the channel wall compared to Darcy’s law.

This research mainly focuses to study hydrothermal characteristics of magnetohydrodynamic nanofluid flow over a slippery permeable bended surface which is rotated in a circular cross-section with radius R1. In this nanofluid model, a nanoparticle concentration gradient is taken due to Brownian motion and thermophoretic force. Thermal conductivity and viscosity of nanofluid are a function of the local volume fraction of the nanoparticle. The system includes the most important parameters such as viscous dissipation and internal heat absorption (or) generation. For the supposed flow governing equations are formulated and then converted to a nonlinear system and resulted system is numerically evaluated with bvp4c in Matlab package. Multiple streamlines and three-dimensional graphics are provided to improve the results. The results obtained show that as the magnetic parameter values increase, the magnitude of the velocity field decreases and the pressure in the boundary layer decreases. Further, the parameters Brownian motion and thermophoresis increase the fluid temperature tends and the concentration should increase as the value of the slip parameter increases.

In this paper, the mechanism of radiative Walter's B nanofluid on a rotational cone under magnetic regime is examined. Time-dependent fluid flow caused by cone rotation includes implication theoretically and practically in engineering and applied sciences. Additionally, interesting characteristics of thermophoresis, Brownian motion, and chemical reactions are examined. Self-similar solutions are obtained by treating angular velocity as an inverse linear function of period toward too far from the cone. The Runge–Kutta–Fehlberg fourth–fifth procedure was used to replicate the performance of the course visually and obtain the numerical result of a reduced nonlinear system. Comparing the acquired result to previously published material is another significant aspect of the current investigation that serves to verify the outcome. The Brownian motion parameter is found to have conflicting influences on heat and mass transfer rates, along with temperature and concentration fields. The existence of chemical reactions, according to the research, may be more beneficial in developing reaction processes.

•Thermomicropolar nanofluid flow upon a perpendicular permeable sheet is studied.•First derivation of angular momentum equation is obtained by mass-based model.•Results are compared with formerly reported cases to validate computational method.•Shear stress, microrotation gradient, and heat transfer are analyzed.•Mass-based model can be used for thermomicropolar nanofluid flow with confidence.

This article elucidates the impact of activation energy on magnetohydrodynamic (MHD) stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions. Negative activation energy is scarce in practice, but the impact of negative activation energy could not be neglected as it is noticed in chemical processes. The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies, such as exothermic binding of urea or water. In some processes, the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies. The present mathematical model is solved with successive linearization method (a spectral technique). A comparison of results is made for negative and positive values of activation energy. Apart from it, the quadratic multiple regression model is discussed briefly and explained with bar diagrams. It is observed that with rise in unsteadiness parameter from 0 to 1 (taking positive activation energy), skin friction and Sherwood number are increased by 9.36%and 19%respectively, and Nusselt number is decreased by 26%. However, for negative activation energy, 9.36%and 112%enhancement is observed in skin friction and Sherwood number, respectively.

This present study is intended for a CFD analysis of hydrodynamic and thermal characteristics of water-based fluid containing TiO2 or CuO nanoparticles flowing in laminar regime in a 3D uniformly heated horizontal annulus utilizing several. Four distinct models have been developed using various combinations (A, B, C and D) of the available theorical-based and experimental-based thermal conductivity and viscosity correlations. A CFD-Fortran code based on the finite volume technique was elaborated for the numerical solution of the mathematical model of the problem. The implications of Grashof number, volume fraction, and type of nanoparticle on isovelocity, isotherms, mean and wall temperatures, Nusselt number, heat transfer coefficient, pressure drop, and thermal performance evaluation criteria are explored using these different models. The results demonstrate that the Nusselt number and heat transfer coefficient of all developed models improve with the addition of nanoparticles. For 2% of nanoparticles’ concentration, the largest enhancement was reached for model D by about 23.5% with respect to the based liquid, while the smallest enhancement was obtained for model B by about 1.16%. The highest Performance Evaluation Criteria (PEC) are attained by employing model D by about 1.263, followed by model C by about 1.074.

•A Y-shaped obstacle in a nanofluid-filled cavity enhances heat transfer substantially.•An optimal magnetic field angle of 75° maximizes overall heat transfer.•Entropy generation analysis reveals system irreversibilities.•Higher reynolds numbers improve fluid mixing and heat transfer.•Complex interplay between forced convection, buoyancy, and MHD effects.

The current study explores the aspects of unsteady stagnation point flow of hybrid nanofluid (Cu-Al2O3/H2O) over a continuously moving and convectively heated stretching cylinder under the influence of oblique Lorentz force. The impacts of velocity slip, Joule dissipation, thermal radiation, viscous dissipation and internal heat generation are also incorporated into this study. Appropriate thermo-physical relations for the hybrid nanofluid are accomplished by following the Xue model. With the use of suitable similarity transformations, the governing dimensional mathematical equations are converted into dimensionless forms. Numerical solutions are obtained for the velocity and energy fields with the help of a shooting technique based on the Runge–Kutta–Fehlberg method of 5-th order and secant iteration. Graphical and tabular representations of numerical data are used to explore the physical impacts of various pertinent parameters on the hybrid nanofluid velocity and temperature. The stability of this approach and the validity of the obtained results are illustrated by comparing the current findings to previously reported data for a specific case. Further, the multiple (quadratic) regression analysis is performed to show the dominance of physical parameters on local skin-friction coefficient and Nusselt number. The thermal buoyancy force boosts the fluid flow while a reverse trend is observed for the magnetic and the velocity slip parameters. Heat transfer rate at the surface is improved with the enhancement in Biot number, thermal radiation and unsteadiness parameters.

In the present study, the physical features of the bioconvective MHD flow of a couple stress fluid over an upper horizontal surface (i.e. surface shaped like a submarine or any (uhsp) aerodynamical automobile) is analysed by considering radiation and viscous dissipation effects. In the fluid-saturated domain flow is induced due to the reaction of catalytic surface, double diffusion and stretching fluid layers. In fact, couple stress fluid is electrically conducted because non-uniform magnetic field is imposed. With the assistance of appropriate similarity transformations governing equations of the study are reduced to set of ordinary differential equations. Thereafter, built-in MATLAB solver bvp4c is implemented to solve the system numerically. By means of graphs and tables variations of the velocity, temperature, concentration, friction factor, local heat and mass transfer rates are observed thoroughly by varying the flow controlling parameters. From this analysis, main observations are, for rising values of couple stress and magnetic parameter velocity is decline, whereas temperature rises for the same parameters and increase in the thermal boundary layer is noted for the Brinkman number, whereas reverse trend is noted in the concentration boundary layer. Finally, comparison is done and a good correlation is identified between the present analysis and perversely recorded analysis.

Application of partial magnetic field can be useful for controlling thermal convective processes occurring in magneto-thermal devices/systems. The present work aims to demonstrate the implementation of a partial magnetic field using a typical thermal system. This study explores both local transport phenomena and global heat transfer rates. The partial magnetic fields involving multiphysical conditions find many applications in electronic industries, medical, and health science. The paper presents a conceptual finding from the use of a partial magnetic field on a classical porous cavity comprising Cu−Al2O3/water hybrid nanoliquid heated differentially. The partial magnetic field is functional either horizontally or vertically. The finite volume technique is employed to the coupled transport equations subjected to particular boundary situations using a developed computing code. The simulations are accomplished to a great extent with different variables such as the Darcy-Rayleigh number (Ram), Darcy number (Da), Hartmann number (Ha), and hybrid nanoparticles concentrations (φ). The effects of magnetic field widths and their positional variations in horizontal and vertical directions are also analyzed. The study found that the convective transport process could effectively be modulated by setting the appropriate position, widths, directions, and intensity of the imposed magnetic fields. The partial magnetic field causes a decrease in heat transfer ∼17.15% or 9.71% less compared to the whole length horizontal or vertical magnetic field. The application of partial magnetic fields significantly alters local thermo-fluid flow phenomena and advancement in heat transfer characteristics in comparison to the magnetic fields acting over the entire domain. Furthermore, the heatline visualization tools reveal the insight of the heat flow dynamics, which dictates the selection of appropriate parametric values and magnetic field configurations.

•Impact of Fe3O4nanoparticle with water as base fluid is addressed.•Behaviours of thermophoresis and Brownian motion are taken into consideration.•Mass transfer is done with the consideration of binary chemical reaction.•The numerical computations are performed by fourth order finite difference scheme.•The results are well described graphically.

Heat and flow pattern of a vertical free jet impinging on a hot disk were numerically investigated. A cylinder with various thicknesses and materials exposed simultaneously to uniform heat flux on one side and a free impinging jet on the other side is simulated by ANSYS Fluent 19.3. For simulations, the thermal boundary condition on the hot surface might differ due to the nature of the heat flow. The Volume of Fluid (VOF) approach is used to model the free jet heat transfer and fluid dynamics with the presence of air, while only the energy equation is solved in the cylinder. Heatline equation is solved to reveal the heat flow direction and effects of different geometry conditions. The maximum heat flux of 2.5 MW/m2 was obtained at the edge of stagnation region for hot target made of copper, while the value was 1.5 MW/m2 when the material was combined with stainless steel. However, the general thermal and hydrodynamic features of the jet flow were not influenced. It means that hot object condition may only affect the balance between heat flux and temperature, and the ideal uniform heat flux on the impinging wall may not be achieved in any experimental conditions.

•We analyzed the graphene Maxwell nanofluid flow past a linearly stretched sheet.•Runge-Kutta Fehlberg method with shooting technique is used to solve mathematical model.•Multiple regression analysis is done on the numeric data of skin friction and Nusselt number.•Effects of influencing flow parameters on the flow field are obtained.•Obtained results are validated under limiting conditions with previously published results.

Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments. A Casson type incompressible viscous nanofluid passes through the given porous medium via Darcy-Forchheimer relation. Slip boundary conditions are used for velocity, temperature and concentration of the nanoparticles. Brownian diffusion and thermophoresis is attended. An induced magnetic field effect is involved to accentuate the thermo-physical characteristics of the nanofluid. The model incorporates boundary layer formulations and small magnetic Reynolds for practical validity. A fourth order Runge-Kutta (RK) scheme is enforced to solve the system numerically. Graphs are prepared for various progressive values of non-dimensionalized parameters whereas; variation in wall drag factor, heat and mass transfer rates is analyzed through numerical data. Results indicate that momentum boundary layer reduces for stronger inertial impact and the resistance offered by the porous media to the fluid flow. Temperature is found as a progressive function for the Brownian motion factor and thermophoresis. The magnitude of wall drag factor, heat transfer and mass transfer rates shows reduction for progressive values of slip parameters.

We examine the thermo-magnetohydrodynamic effects on nanofluid flow in a porous circular annular region bounded by two rotating cylinders in the presence of a constant radial magnetic field but variable thermal conductivity. The nanofluid consists of a sample liquid (water/ engine oil) along with suspended copper nanoparticles. This physical problem is formulated and analytical solutions for the governing equations are obtained by using the homotopy analysis method in the form of the physical variables such as, the pressure, fluid speed, temperature, shear stress, heat transfer, and the concentration of nanoparticles. The obtained results are compared with the existing results for the clear fluid and are found in excellent agreement. The effects of the field parameters on these physical variables are studied. It is found that the fluid speed (pressure) increases (decreases) with the Forchheirmer coefficient, porosity, applied magnetic field intensity, and the angular speed of the outer cylinder, but it decreases with the angular speed of the inner cylinder for both liquids. The reverse flow exists if the inner and outer cylinders are rotating in the opposite directions for both the liquids. Furthermore, the thermal transfer rate in the engine oil is lower than that in water. If the annulus region is squeezed, then the fluid speed decays while the pressure rises. The temperature and the thermal transfer rate decay if we march from the inner cylinder to the outer one. The porosity and the angular speed of the outer cylinder enhance the viscous dissipation and shear stress.

In this work, the thermal behavior of a turbulent forced-convection flow of air in a rectangular cross section channel with attached W-shaped obstacles is investigated. The continuity, momentum and energy equations employed to control the heat and velocity in the computational domain. The turbulence model of k-ε is employed to simulate the turbulence effects. The finite volume method with SIMPLE algorithm is employed as the solution method. The results are reported temperature, local and average Nusselt numbers, and mean velocity contours. The subject is relevant and important for industrial applications.

Arrhenius condition has been broadly utilized as a model of the temperature impact on the rate compound responses and organic procedure. Hence, our aim of this article is to examine the effects of chemical reaction and activation energy on a Carreau nanoliquid in a permeable surface. For thermal and mass transport curiosities, the cumulative upgrade of convective type condition and zero mass transition have been considered. The overseeing sets of partial differential equations are rendered into coupled nonlinear ordinary differential equations. The arrangement of the subsequent ordinary differential equations is acquired with the assistance of the Runge-Kutta-Fehlberg-fourth-fifth order (RKF-45) procedure. The influence of relevant parameters and physical quantities is investigated. The results show that the presence of reaction rate and energy activation term decelerates the temperature and concentration gradients.

A computational study on the effect of magnetohydrodynamic mixed convection of nanofluid flow in a square split lid driven cavity with a block placed near the bottom wall is undertaken. Two different nanoparticles gold and alumina are considered for the study. The observations for the study are obtained by solving the non-dimensionalized governing equations by Finite Element Method with variational approach as accessible with the FreeFEM++ software. The results for different Prandtl numbers (Pr), Richardson number (Ri), volume fractions of nanoparticles (φ), Reynolds number (Re), and MHD parameters (M) are displayed through graphs and figures. It has been observed that the pressure distribution significantly increases with the increment in Reynolds number but both the nanoparticles behave differently. The magnetic field enhancement (M= 0.1, 0.2, 0.5 and 0.9) decreases the velocity within the cavity. The convective heat transfer is faster in the case of Reynolds number (Re) = 100 than in the case of Reynolds number (Re) = 14 or 21. And also increasing the Richardson Number from 0.1 to 1.0, the average Nusselt number shows increment of ∼9.5% and with Ri= 1.0 to 10.0, an increment of ∼3% whereas decrement with higher Reynolds Number (Re= 21, 100) for Gold and Allumina nanoparticles respectively. The present simulations have various applications for the study of natural phenomenon like climate control, meteorological and geophysical activities and industrial applications like cooling of electronics equipment, heat exchanger.

•Normal mode analysis is used to determine the conditions under which stationary and oscillatory convection occur when analysing linear instability.•This approach facilitates weakly nonlinear stability analysis, resulting in a cubic complex Landau equation that describes amplitude evolution and transfer analysis.•Chemical reaction parameters are crucial in determining the stability of fluids, as they can either delay or accelerate instability depending on their values.•Discovery of the oscillating neutral stability curves.•Study discusses subcritical/supercritical bifurcations.•Detailed analysis of Heat and mass transfer offers control insights in viscoelastic fluids.