Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids

Energy transfer through third-grade fluid flow across an inclined stretching sheet subject to thermal radiation and Lorentz force

The heat and mass transfer through the third grade fluid (TGF) flow over an inclined elongating sheet with the consequences of magnetic field and chemical reaction is reported. The impact of activation energy, heat source/sink, and thermal radiation is considered on the TGF flow. Fluid that demonstrate non-Newtonian (NN) properties such as shear thickening, shear thinning, and normal stresses despite the fact that the boundary is inflexible is known as TGF. It also has viscous elastic fluid properties. In the proposed model, the TGF model is designed in form of nonlinear coupled partial differential equations (PDEs). Before employing the numerical package bvp4c, the system of coupled equations are reduced into non-dimensional form. The finite-difference code bvp4c, in particular, executes the Lobatto three-stage IIIa formula. The impacts of flow constraints on velocity field, energy profile, Nusselt number and skin friction are displayed through Tables and Figures. For validity of the results, the numerical comparison with the published study is performed through Table. From graphical results, it can be perceived that the fluid velocity enriches with the variation of TGF factor and Richardson number. The heat source parameter operational as a heating mediator for the flow system, its influence enhances the fluid temperature.

Wire coating analysis using Phan-Thien-Tanner fluid subject to Lorentz force as a polymer coating material in a canonical covering die

Wire coating is widely used for electrical insulation to protect the wire from electric shock, prevent electrical leakage, and ensure that the electrical current flows smoothly. In this investigation, a pressurized coating die is used to explore the PTT fluid as a polymer material for wire in a magnetic field. The flow field, flow rate, temperature profile, thickness of the wire coating, volume flow rate, and shear stress are all given exact solutions. Graphs were used to illustrate the effects of certain important technical parameters, including flow rate, wire coating thickness, shear stress, and pressure gradient. It has been noted that as the values of X, Deborah number, and ratio of radii are improved, the volume and thickness of the coated wire rise. The Deborah number has a higher volume flow than the X and radii ratios. A reference to existing literature is made in order to support the validity of the current study.

Entropy Generation and Thermal Analysis on MHD Second-Grade Fluid with Variable Thermophysical Properties over a Stratified Permeable Surface of Paraboloid Revolution

Stratification is used in a wide range of energy storage fields, including solar thermal energy systems. This paper investigates entropy optimization and the effects of heat production, magnetic field, and various fluid parameters on the flow of second-grade fluid through unstratified and stably stratified paraboloids of revolution. In the heat transfer equation, stratification, linear thermal radiation, and Joule dissipation have all been explored. The similarity transformation is used to convert the governing PDEs into nonlinear ODEs. The HAM (homotopy analysis method) is used to solve dimensionless nonlinear ODEs. The impact of significant elements on various profiles is exposed and explored. Graphical results are used to examine the influence of the velocity profile, temperature, concentration, and entropy formation rate using tables to indicate the characteristics of skin friction, Nusselt number, and Sherwood number for numerous parameters. It is noticed that the velocity is enhanced by raising the stratification parameter, while the opposite behavior is observed for temperature distribution. The concentration profile declined as the solute stratification parameter was enhanced. For both the unstratified and stratified regions, incremental values of the Brinkman number and magnetic parameter depict augmentation in entropy production, while entropy production drops for a large value of the temperature ratio parameter.

Heat Transfer Analysis of Nanofluid Flow in a Rotating System with Magnetic Field Using an Intelligent Strength Stochastic-Driven Approach

This paper investigates the heat transfer of two-phase nanofluid flow between horizontal plates in a rotating system with a magnetic field and external forces. The basic continuity and momentum equations are considered to formulate the governing mathematical model of the problem. Furthermore, certain similarity transformations are used to reduce a governing system of non-linear partial differential equations (PDEs) into a non-linear system of ordinary differential equations. Moreover, an efficient stochastic technique based on feed-forward neural networks (FFNNs) with a back-propagated Levenberg–Marquardt (BLM) algorithm is developed to examine the effect of variations in various parameters on velocity, gravitational acceleration, temperature, and concentration profiles of the nanofluid. To validate the accuracy, efficiency, and computational complexity of the FFNN–BLM algorithm, different performance functions are defined based on mean absolute deviations (MAD), error in Nash–Sutcliffe efficiency (ENSE), and Theil’s inequality coefficient (TIC). The approximate solutions achieved by the proposed technique are validated by comparing with the least square method (LSM), machine learning algorithms such as NARX-LM, and numerical solutions by the Runge–Kutta–Fehlberg method (RKFM). The results demonstrate that the mean percentage error in our solutions and values of ENSE, TIC, and MAD is almost zero, showing the design algorithm’s robustness and correctness.

Entropy Optimization on Axisymmetric Darcy–Forchheimer Powell–Eyring Nanofluid over a Horizontally Stretching Cylinder with Viscous Dissipation Effect

The effect of entropy optimization on an axisymmetric Darcy–Forchheimer Powell–Eyring nanofluid flow caused by a horizontally permeable stretching cylinder, as well as non-linear thermal radiation, was investigated in this research work. The leading equations of the current problem were changed into ODEs by exhausting appropriate transformations. To deduce the reduced system, the numerical method bvp4c was used. The outcome of non-dimensional relevant factors on velocity, entropy, concentration, temperature, Bejan number, drag force, and Nusselt number is discussed and demonstrated using graphs and tables. It is perceived that, with a higher value of volume fraction parameter, the skin friction falls down. Likewise, it is found that the Nusselt number drops with enhancing the value of the volume fraction. Moreover, the result reveals that the entropy generation increases as the volume fraction, curvature parameter, and Brinkman number increase.

Entropy Generation in Magneto-Casson Nanofluid Flow Along an Inclined Stretching Sheet Under Porous Medium with Activation Energy and Variable Heat Source/Sink

The current paper deals with the study of magneto-convective and chemically reactive Casson nanofluid flow along an inclined permeable stretching surface embedded in a fluid-saturated uniform porous medium. As a novelty of the work, entropy generation analysis in the presence of multiple slips at the surface and a nonuniform heat source/sink is carried out. Moreover, viscous dissipation, Arrhenius activation energy, Joule dissipation and thermal radiation are included in the investigation. To the best of authors’ knowledge, no such study on Casson nanofluid is reported yet in the literature. Dimensionless similarity transformations have been introduced to convert the regulating model PDEs into ODEs in dimensionless form. As the model equations are highly nonlinear in nature, shooting technique based on the Runge-Kutta Cash-Karp method is used to solve those equations numerically. The updated values of the initial guesses are computed with the help of secant iteration. Profiles for fluid velocity, temperature, nanoparticle concentration and entropy generation have been drawn to explain the impacts of several important parameters on momentum, thermal and mass fields. However, the surface drag force, heat and mass transport rates at the solid wall are illustrated using numerical data displayed in tabular form. Also, a linear regression model is derived for the local Nusselt number and the related physical parameters. Moreover, a comparison table is presented to confirm the correctness of the obtained results. A fantastic correlation of the present results with the existing results is reported. Graphical results reveal that for the rising values of the angle of inclination parameter and magnetic parameter velocity profiles are declined, but for the growing values of Eckert number and thermal radiation parameter temperature profiles are enhanced.

MHD Stagnation Point on Nanofluid Flow and Heat Transfer of Carbon Nanotube over a Shrinking Surface with Heat Sink Effect

This study is to investigate the magnetohydrodynamic (MHD) stagnation point flow and heat transfer characteristic nanofluid of carbon nanotube (CNTs) over the shrinking surface with heat sink effects. Similarity equations deduced from momentum and energy equation of partial differential equations are solved numerically. This study looks at the different parameters of the flow and heat transfer using first phase model which is Tiwari-Das. The parameter discussed were volume fraction nanoparticle, magnetic parameter, heat sink/source parameters, and a different type of nanofluid and based fluids. Present results revealed that the rate of nanofluid (SWCNT/kerosene) in terms of flow and heat transfer is better than (MWCNT/kerosene) and (CNT/water) and regular fluid (water). Graphically, the variation results of dual solution exist for shrinking parameter in range λc<λ≤-1 for different values of volume fraction nanoparticle, magnetic, heat sink parameters, and a different type of nanofluid. However, a unique solution exists at -1<λ<1, and no solutions exist at λ<λc which is a critical value. In addition, the local Nusselt number decreases with increasing volume fraction nanoparticle when there exists a heat sink effect. The values of the skin friction coefficient and local Nusselt number increase for both solutions with the increase in magnetic parameter. In this study, the investigation on the flow and heat transfer of MHD stagnation point nanofluid through a shrinking surface with heat sink effect shows how important the application to industrial applications.

Entropy Generation Analysis of Radiated Magnetohydrodynamic Flow of Carbon Nanotubes Nanofluids with Variable Conductivity and Diffusivity Subjected to Chemical Reaction

The purpose of this article is to analyze the entropy generation and heat and mass transfer of carbon nano-tubes (CNTs) nanofluid by considering the applied magnetic field under the influence of thermal radiation, variable thermal conductivity, variable mass diffusivity, and binary chemical reaction with activation energy over a linearly stretching cylinder. Convective boundary conditions on heat and mass transfer are considered. An isothermal model of homogeneous-heterogeneous reactions is used to regulate the solute concentration profile. It is assumed that the water-based nanofluid is composed of single and multi-walled carbon nanotubes. Employing a suitable set of similarity transformations, the system of partial differential equations is transformed into the system of nonlinear ordinary differential equations before being solved numerically. Through the implementation of the second law of thermodynamics, the total entropy generation is calculated. In addition, entropy generation for fluid friction, mass transfer, and heat transfer is discussed. This study is specially investigated for the impact of the chemical reaction, and activation energy with entropy generation subject to distinct flow parameters. It is found that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with higher radiation parameters and thermal Biot number. Entropy and Bejan number are found to be an increasing function of solid volume fraction, magnetic field, and curvature parameters. Binary chemical reaction and activation energy on concentration profile have opposite effects.

Heat Transfer and Entropy in a Vertical Porous Plate Subjected to Suction Velocity and MHD

This article presents an investigation of heat transfer in a porous medium adjacent to a vertical plate. The porous medium is subjected to a magnetohydrodynamic effect and suction velocity. The governing equations are nondepersonalized and converted into ordinary differential equations. The resulting equations are solved with the help of the finite difference method. The impact of various parameters, such as the Prandtl number, Grashof number, permeability parameter, radiation parameter, Eckert number, viscous dissipation parameter, and magnetic parameter, on fluid flow characteristics inside the porous medium is discussed. Entropy generation in the medium is analyzed with respect to various parameters, including the Brinkman number and Reynolds number. It is noted that the velocity profile decreases in magnitude with respect to the Prandtl number, but increases with the radiation parameter. The Eckert number has a marginal effect on the velocity profile. An increased radiation effect leads to a reduced thermal gradient at the hot surface.

Entropy Generation Incorporating γ-Nanofluids under the Influence of Nonlinear Radiation with Mixed Convection

Nanofluids offer the potential to improve heat transport performance. In light of this, the current exploration gives a numerical simulation of mixed convection flow (MCF) using an effective Prandtl model and comprising water- and ethylene-based γγ−Al2O3 particles over a stretched vertical sheet. The impacts of entropy along with non-linear radiation and viscous dissipation are analyzed. Experimentally based expressions of thermal conductivity as well as viscosity are utilized for γγ−Al2O3 nanoparticles. The governing boundary-layer equations are stimulated numerically utilizing bvp4c (boundary-value problem of fourth order). The outcomes involving flow parameter found for the temperature, velocity, heat transfer and drag force are conferred via graphs. It is determined from the obtained results that the temperature and velocity increase the function of the nanoparticle volume fraction for H2O\C2H6O2 based γγ−Al2O3 nanofluids. In addition, it is noted that the larger unsteady parameter results in a significant advancement in the heat transport and friction factor. Heat transfer performance in the fluid flow is also augmented with an upsurge in radiation.

Hall Effects on Steady Magnetohydrodynamics Flow of Cu-Water Nanofluid Through Porous Medium

It is examined the unstable magneto hydro dynamic flows of an incompressible glutinous nano fluids over a saturated absorbent media. The fluid flow is prompted by a convection temperatured accessible diminishing surfaces as well as captivating Hall impacts into discriptions. The relevant alterations abridge the systems of non-linearly partially differential equation to the syatem of ordinarily differential equation. The flow as well as temperature dissipation peculiarities were cogitated by making use of Homotopy-Analysis methodology. The momentum, temperature as well as Nusselts numbers were assessed also arithmeticaly referred with several non dimensionalized boundaries. This corresponds to observed that greater nano particle volume segments shrinks a momentum field. In addition the temperature together with heat dissipation rate were exacerbated for higher quantities of Biot number.

Entropy generation and dissipative heat transfer analysis of mixed convective hydromagnetic flow of a Casson nanofluid with thermal radiation and Hall current

The present article provides a detailed analysis of entropy generation on the unsteady three-dimensional incompressible and electrically conducting magnetohydrodynamic flow of a Casson nanofluid under the influence of mixed convection, radiation, viscous dissipation, Brownian motion, Ohmic heating, thermophoresis and heat generation. At first, similarity transformation is used to transform the governing nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations, and then the resulting highly nonlinear coupled ordinary differential equations are numerically solved by the utilization of spectral quasi-linearization method. Moreover, the effects of pertinent flow parameters on velocity distribution, temperature distribution, concentration distribution, entropy generation and Bejan number are depicted prominently through various graphs and tables. It can be analyzed from the graphs that the Casson parameter acts as an assisting parameter towards the temperature distribution in the absence of viscous and Joule dissipations, while it has an adverse effect on temperature under the impacts of viscous and Joule dissipations. On the contrary, entropy generation increases significantly for larger Brinkman number, diffusive variable and concentration ratio parameter, whereas the reverse effects of these parameters on Bejan number are examined. Apart from this, the numerical values of some physical quantities such as skin friction coefficients in x and z directions, local Nusselt number and Sherwood number for the variation of the values of pertinent parameters are displayed in tabular forms. A quadratic multiple regression analysis for these physical quantities has also been carried out to improve the present model's effectiveness in various industrial and engineering areas. Furthermore, an appropriate agreement is obtained on comparing the present results with previously published results.

Entropy optimization in CNTs based nanomaterial flow induced by rotating disks: A study on the accuracy of statistical declaration and probable error

BACKGROUND

CNTs (Carbon nanotubes) being allotropes of carbon, made of graphene and diameters of single and multi-walls carbon nanotubes are typically 0.8 to 2 nm and 5 to 20 mn, although diameter of MWCNTs can exceed 100 nm. Carbon nanotubes lengths range from less than 100 nm to 0.5 m. Their impressive structural, electronic and mechanical attributes subject to their small size and mass, their high electrical and thermal conductivities, and their strong mechanical potency. CNTs based materials are successfully applied in medicine and pharmacy subject to their huge surface area that is proficient of conjugating or adsorbing with a wide variety of genes, drugs, antibodies, vaccines and biosensors etc. Therefore, we have presented a theoretical study about mathematical modeling of CNTs based viscous material flow between two rotating disks. Both types of nanotubes i.e., SWCNTs and MWCNTs are considered. Xue model is used for the mathematical modeling. Fluid flow is due to rotating disks. Main focus here is given to probable error and statistical declaration. Entropy is calculated for both single and multi-walls nanotubes.

METHOD

Nonlinear PDEs are first converted into ODEs and then computed for homotopy convergent solutions.

RESULTS AND CONCLUSION

Statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at both disks surface for higher values of Reynolds number, lower stretching parameter and porosity parameter while it decays for both of disks versus larger rotation parameter. Nusselt number or heat transfer rate also enhances at both disks in the presence of radiation and Reynolds number while it decays against Eckert number.

Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects

BACKGROUND

In last few decades, a new class of working materials which comprises from two solid materials dispersed in a continuous phase liquid was established and deeply scrutinized. These materials are called hybrid nanomaterials. This research article aims to investigate entropy optimization in hybrid nanomaterial flow through a rotating peristaltic channel walls. Flow behavior is analyzed between the channels which is caused by propagation of sinusoidal waves. Viscosity of fluid is considered variable instead of constant characteristics. Fluid saturates through porous attributes of channel walls. Nonliear radiative flux and convective condition are considered. Slip conditions are imposed at the boundary of walls.

METHODS

Built-in-Shooting technique is employed to obtain the numerical outcomes for the considered flow problem.

RESULTS

Impacts of sundry variables on the entropy, temperature and velocity are scrutinized through different graphs. Numerical result presents that the axial velocity escalates with the inclusion of hybrid nanomaterial. The temperature of fluid enhances through higher estimations of hybrid nanoparticles.

CONCLUSIONS

Here the flow behavior is discussed between the channels which are caused by propagation of sinusoidal waves with speed c. Entropy generation rate is minimum for variable viscosity and maximum for hybrid nanoparticles. Hybrid nanoparticles increase the temperature of fluid. Bejan number presents the similar impact for variable viscosity and thermal slip parameters. Temperature field decays through higher values of Brinkman number.

Theoretical and mathematical analysis of entropy generation in fluid flow subject to aluminum and ethylene glycol nanoparticles

BACKGROUND

Here we have conducted a magnetohydrodynamic (MHD) flow of viscous material with alumina water and ethylene glycol over a stretched surface. The flow is discussed with and without effective Prandtl number. MHD liquid is considered. Electric field is absent. Effect of uniform magnetic field is taken in the vertical direction to the surface. Influence of thermal radiation as well as Joule heating are taken into account for both aluminum oxide-water and aluminum oxide-Ethylene glycol nanofluids. Velocity slip and melting heat effects are considered.

METHODS

The nonlinear flow expressions are numerically solved via ND-solve technique (built-in-Shooting).

RESULTS

The physical impacts of flow variables like mixed convection parameter, magnetic parameter, Reynold number, Eckert number, melting parameter and heat source/sink parameter are graphically discussed. Moreover, entropy generation (irreversibility) and Bejan number are discussed graphically through various flow variables. Physical quantities like skin friction coefficient and Sherwood and Nusselt numbers are numerically calculated and discussed through Tables.

CONCLUSIONS

Impact of magnetic and slip parameters on the velocity field show decreasing behavior for both effective and without effective Prandtl number. Temperature field increases for both effective and without effective Prandtl number for higher values of magnetic and radiative parameters. Entropy number is an increasing function of Reynolds number while Bejan number shows opposite impact against Reynolds number. Moreover, heat transfer rate upsurges versus larger melting and radiative parameter.

Entropy Analysis of 3D Non-Newtonian MHD Nanofluid Flow with Nonlinear Thermal Radiation Past over Exponential Stretched Surface

The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and convective heat and mass boundary conditions. Apposite transformations were considered to transform the presented mathematical model to a system of differential equations. Analytical solutions of the proposed model were developed via a well-known homotopy analysis scheme. The numerically calculated values of the dimensionless drag coefficient, local Nusselt number, and mass transfer Nusselt number are presented, with physical insights. The graphs depicting the consequences of numerous parameters on involved distributions with requisite deliberations were also a part of this model. It is seen that the Bejan number is an increasing function of the thermal radiation parameter.