Narrow Results

Recent studies indicate that nanofluids are crucial for solar heat exchange operations and solar energy collectors. Furthermore, the importance of energy and mass transfer in entropy creation is significantly increased in a number of industrial and engineering processes, such as mechanical power collectors, air conditioning, food processing, refrigeration, and heat exchangers. As a result of this advancement, this research is aimed to explore the comparative study on bioconvective Darcy–Forchheimer flow of an incompressible hydromagnetic Ree–Eyring nanofluid over a chemically activated expanding sheet in suction and injection cases while including the consequences of radiation, energy generation, and convective boundary conditions. Boundary layer approximation is utilized to represent this investigation’s primary partial differential equations (PDE). Then, using the appropriate transformation, the models are rebuilt into nonlinear ordinary differential equations (ODE). Utilizing the BVP5C inbuilt MATLAB package, the numerical solutions for this examination are established. Further, the graphical and tabular representations allow us to analyze the impacts of several relevant features on the microorganism’s density, concentration, entropy creation, velocity, temperature, friction factor, Sherwood, and Nusselt number distribution. The outcomes reveal that the velocity field of the liquid movement is declined by applying positive amounts of the Darcy–Forchheimer and magnetic parameters, respectively. Boosting values of the radiation, thermal ratio parameter, and temperature Biot number assist an increase in the thermal field. It reveals the augmented entropy generation with the rising values of bioconvection Lewis number and Brinkman number. Furthermore, the mass transfer rate increases with larger values of the Brownian parameter and chemical reaction parameter.

The purpose of this paper is to study the peristaltic dusty fluid flow where dust particles are distributed uniformly. The passage of flow is asymmetric. Slip conditions have been incorporated into both momentum and thermal profiles. The mathematical model is constructed using the laws of momentum and energy conservation. The resulting coupled equations are solved using small wavenumber approximation. Impacts of important quantities on temperature and velocity profiles of fluid along with solid particles have been debated through graphs. Entropy generation analysis has been carried out for influential parameters. An enhancement is observed in temperature irreversibility as Brinkman and thermal slip are increased. Bejan number is studied for various values of Brinkman number, wavenumber and thermal slip. The analysis of peristaltic flow of particle fluid with slip has a vital role in biomedical sciences and industry.

The impact of nanoliquid in the evolution of various industries and electronic devices is very remarkable. Motivated by these uses, this exploration describes the second law analysis in the Maxwell two-phase nanoliquid subject to the Lorentz force due to axisymmetric heated convective rotating flow with microorganisms and slip conditions. Thermal radiation, thermal variable conductivity, and chemical reaction are examined in the heat and concentration equation. The mass equation has been accounted for through the chemical reaction. Additionally, the physical properties of the entropy rate are considered. The constitution equations have been transformed into dimensionless form through the suitable transformation. The reduced system of equations has been solved analytically by the homotopy analysis method (HAM). The physical variables on Bejan number, entropy minimization, microorganism, concentration, velocity, and temperature distributions have been presented in graphical form. Computational results of moment coefficient, heat, mass, and motile density versus other factors are examined. The Maxwell fluid and slip variable display a reduction in radial velocity. An increase in the stretching parameter. The thermal layer is enlarged against the larger values of variable thermal conductivity, thermal radiation, and Biot number. Entropy generation and Bejan number are escalated due to the augment in the temperature difference variable, Brikamann number, and magnetic field.

Here the Cattaneo–Christov double diffusion model explores the mixed convective flow of third-grade nanoliquid on a stretchable surface with Riga device diverging from the traditional Fourier and Fick’s law. The model incorporates entropy optimization and Soret–Dufour effects, offering a unique perspective on heat and mass transfer phenomena. By employing relevant transformations, the complex partial differential equations are converted into more manageable ordinary differential systems. An optimal analysis method is then applied to solve the resulting nonlinear differential system, shedding light on the intricate interplay of various physical variable. Through the utilization of plots, the study delves into the impact of these physical variable, providing insights into the behavior of the system under different conditions. This comprehensive approach not only enhances our understanding of the underlying mechanisms governing the convective flow of nano-liquids, but also highlights the significance of considering nonclassical models in thermal and mass transport studies. The key finding of this study is that fluid velocity enhances for material parameters due to low viscosity. Temperature and nanoparticle concentration enhance for higher values of Dufour and Soret numbers, respectively. For higher estimations of Reynold number, entropy of the system decreases.

In the current study, the DSMC method is utilized to obtain the entropy, entropy generation and the local gradient length Knudsen number in the rarefied flows. Two particular geometries, cavity and flat plate, are considered to study the departure from equilibrium state in the presence of sudden expansion/contraction, bend in the velocity profile, boundary flow and shock waves. The entire slip regime is considered to investigate small and large nonequilibrium effects on the entropy and entropy productions. Our investigation reveals that the distribution of entropy in the rarefied flow is very similar to the temperature contour. The entropy generation distribution in the micro cavity indicates that the two top corners are the regions around which departure from equilibrium state takes place. The study of entropy generation over the flat plate reveals that the entropy production is maximized along the shock wave. Moreover, increasing the rarefaction effects thickens the nonequilibrium shock wave. We also observed that increasing the nonequilibrium effects reduces the level of entropy generation in the rarefied flow. As the flow density decreases in the nonequilibrium regime, the level of shear stress and heat flux reduces, which subsequently lower the level of entropy generation in the rarefied flows. Furthermore, it was found that although the level of entropy generation in the flow reduces as the Knudsen number increases, the boundaries of the maximum entropy production region extends under large rarefaction effects.

Flow patterns and heat transfer inside mini twisted oval tubes (TOTs) heated by constant-temperature walls are numerically investigated. Different configurations of tubes are simulated using water as the working fluid with temperature-dependent thermo-physical properties at Reynolds numbers ranging between 500 and 1100. After validating the numerical method with the published correlations and available experimental results, the performance of TOTs is compared to a smooth circular tube. The overall performance of TOTs is evaluated by investigating the thermal-hydraulic performance and the results are analyzed in terms of the field synergy principle and entropy generation. Enhanced heat transfer performance for TOTs is observed at the expense of a higher pressure drop. Additionally, the secondary flow generated by the tube-wall twist is concluded to play a critical role in the augmentation of convective heat transfer, and consequently, better heat transfer performance. It is also observed that the improvement of synergy between velocity and temperature gradient and lower irreversibility cause heat transfer enhancement for TOTs.

Our paper is consecrated to show the influence of variable fluid properties in EMHD non-Newtonian power-law fluid along a moving Riga plate. Slip velocity phenomenon is considered at the surface which is convectively heated. Entropy analysis is elaborated employing thermodynamic second relation. The governing nonlinear PDEs are altered into ODEs through adequate propinquity transformations which have been solved numerically via the shooting method with the fourth-order Runge–Kutta algorithm through Mathematica software (bvp4c). Characteristics of different basic parameters on velocity, temperature, entropy generation and Bejan number are highlighted through graphs. The outcomes exhibit that the minimum entropy rate in the flow system can be obtained either with rising viscosity parameter and slip parameter or declining dimensionless parameter and thermal conductivity parameter. The entropy rate is minimal for dilatant fluid when compared to pseudo plastic fluid with the most governing parameters. Contrast behavior on the thermal field is noticed for larger values of viscosity parameter and thermal conductivity parameter.

The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, $\mathrm{\text{Ha}}=0-20$, Rayleigh number, $\mathrm{\text{Ra}}=10^4-10^6$, PL indices, $n=0.6$–1.4, Prandtl number, $\mathrm{\text{Pr}}=6.2\mathrm{\text{(water)}}$, to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio $\mathrm{\text{AR}}=2.0$. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, $\mathrm{\text{Ra}}$ and decreasing the PL index, $n$. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, $\mathrm{\text{Ha}}=0$, fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing $n$ and $\mathrm{\text{Ra}}$, respectively. In the presence of the magnetic field, $\mathrm{\text{Ha}}>0$, the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility.

In this study, we investigate the effect of entropy generation on a Casson hybrid nanofluid over a stretching cylinder in the presence of linear thermal radiation and Cattaneo–Christov heat flux. We assumed ${\mathrm{\text{Fe}}}_2{\mathrm{\text{O}}}_3$ and ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$ to be the nanoparticles suspended in the blood’s basic fluid for our model. Targeted drug delivery is one of the most proficient ways to diagnose and treat cancer. This is because attractive nanoparticles can be used as beneficial agents in the occurrence of both heat and an angled magnetic field. In addition, several form aspects have been taken into account. By making sure that the self-similarity transformations are accurate, the fundamental Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs). The Runge–Kutta fourth-order and firing approach are used to solve the ODEs. For the situations of cylinder and plate, homotopy perturbation method (HPM) and numerical method (NM) solutions on behalf of the nonlinear structure are obtained to compare one another. In this model, we compared the shapes of the sphere, the cylinder, the blade, the platelet and the lamina, which are all graphically represented. Additionally, the results are compared to those that have already been published and are found to be in great agreement. The performance of biological applications, particularly Radio-Frequency Identification (RFA), cancer therapy, MRI, tumor therapy and malaria disease, is improved by this kind of theoretical research.

This study aims to investigate the magnetoconvection of an electrically conducting fluid within a rectangular enclosure through a comprehensive three-dimensional computational analysis. The enclosure has a hemispherical block for bottom heating and incorporates two elliptical sources with differing temperatures along its vertical sidewalls. The primary focus is to optimize heat transfer and fluid flow characteristics within this thermal system by analyzing various control parameters. The simulations were carried out with the relevant parameters of the problem, including the Rayleigh number $(10^3\le \mathrm{\text{Ra}}\le 10^6)$, Hartmann number $(0\le \mathrm{\text{Ha}}\le 100)$, the inclination of the magnetic field $(0^{\circ }\le \chi \le 90^{\circ })$, and the radius of the hemispherical block $(0.2\le \mathrm{\text{HR}}\le 0.5)$. Three distinct scenarios represent different positions for the localized heat sources. Among these configurations, the Middle–Middle (MM) arrangement is the most favorable, with the specific value for the radius $\mathrm{\text{HR}}$ yet to be determined. The findings highlight the effective control of heat transfer rate and irreversibility effects by manipulating the parameters $\mathrm{\text{Ha}}$, $\mathrm{\text{HR}}$ and $\chi$. It is demonstrated that selecting $\mathrm{\text{HR}}$ and $\mathrm{\text{Ha}}$ values of $0.4$ and 15 allows for optimal thermal system configuration. A correlation with two variables $(\mathrm{\text{Ha}},\mathrm{\text{HR}})$ expressing the rate of heat transfer through the cavity was established and verified. The analysis of the helicity confirms the predicted optimal case.

Entropy optimization or entropy plays vital roles in our understanding of numerous various diverse phenomena running from cosmology to science. Their significance is shown in regions of immediate practical interest like provision of global energy as well as in others of a progressively essential flavor, such as the source of order and unpredictability in nature. The purpose of this communication is to investigate some of ongoing and significant outcomes in a way that not only appeals to the entropy expert but also makes them available to the nonexpert looking for an outline of the field. This communication addresses the entropy optimized flow of hybrid nanofluid between two plates accounting Darcy–Forchheimer porous medium. Energy equation is developed through implementation of first law of thermodynamics subject to radiative flux, dissipation and Joule heating. MHD fluid is rotating with angular frequency $\mathrm{\Omega }$. Total entropy rate obtained is subject to thermal irreversibility, friction or dissipation irreversibility, magnetic or Joule heating irreversibility and Darcy–Forchheimer irreversibility via second law of thermodynamics. The nonlinear ordinary system (differential equations) is tackled via homotopy method for series solutions. Behaviors of sundry variables on the velocity, skin friction, temperature, Nusselt number and entropy generation rate are discussed and presented through various plots. Schematic flow diagram is presented. Furthermore, skin friction (drag force) and Nusselt number are discussed numerically. Obtained results analyzed that the entropy rate increases subject to higher radiation parameter and Hartmann and Brinkman numbers.

This motivating analysis aims to present the thermal mechanism for mixed convection flow of Reiner–Philippoff nanofluid with assessment of entropy generation. The thermal performances of nanomaterials have been modified by utilizing the nonuniform heat source/sink, Ohmic dissipations and thermal radiation consequences. The assumed surface is assumed to be porous with non-Darcian porous medium. The modified Cattaneo–Christov relations are followed to modify the mass and heat equations. The invoking of similarity variables results in differential equations in nonlinear and coupled form. A MATLAB-based shooting algorithm is employed to access the numerical simulations. The physical aspect of thermal model is graphically addressed for endorsed flow parameters. The importance of entropy generation is visualized with associated mathematical relations and physical explanations. The numerical values are obtained for the assessment of heat and mass transfer phenomenon.

In this research, thermal radiation, entropy generation and variable thermal conductivity effects on hybrid nanofluids by moving sheet are analyzed. The liquid is placed by stretchable flat wall that is flowing in a nonlinear pattern. Thermal conductivity changes with temperature governed by thermal radiation and MHD is incorporated. Approximations of boundary layer correspond to a set of PDEs which are then changed into ODEs by considering suitable variables. The resulting ODEs are solved using the bvp4c method. The implication with considerable physical characteristics on temperature, entropy generation and velocity profile is graphically represented and numerically discussed. Entropy generation increases for increasing Reynolds number, velocity slip parameter, Brinkman number and magnetic parameter. Scientists have recently established a rising interest in the importance of nanoparticles due to their numerous technical, industrial and commercial uses. The provided insights can be used in extrusion application areas, macromolecules, biomimetic systems, energy production and industrial process improvements.

The flow of non-Newtonian liquids and their heat transfer characteristic gained more importance due to their technological, industrial and in many engineering applications. Inspired by these applications, the magnetohydrodynamic (MHD) flow of non-Newtonian liquid characterized by a power-law model is scrutinized. Further, viscous dissipation, Marangoni convection and thermal radiation are taken into the account. In addition, the production of entropy is investigated as a function of temperature, velocity and concentration. For different flow parameters, the total entropy production (EP) rate is examined. The appropriate similarity transformations are used to reduce the modeled equations reduced into ordinary differential equations (ODEs). The Runge–Kutta–Fehlberg 45-order procedure is then used to solve these reduced equations numerically using the shooting technique. Results reveal that the escalating values of radiation parameter escalate the heat transference, but the contrary trend is portrayed for escalating values of power-law index. The augmented values of thermal Marangoni number decline the heat transference. The gain in values of radiation parameter progresses the entropy generation.

This study aims to investigate the thermodynamic analysis for electroosmotic flow of ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–${\mathrm{\text{Cu/H}}}_2\mathrm{\text{O}}$ hybrid nanofluid in the presence of peristaltic propulsion. Hybrid nanofluid is an aqueous solution of copper and iron oxide nanoparticles. Effects of electric field, Ohmic heating, magnetic field, viscous dissipation, heat sink/source and mixed convection are also considered. The Debye–Hückel and lubrication approach has been adopted to perform mathematical modeling. The resulting differential equations are numerically solved by employing the Shooting method. Analysis has been presented for irreversibility rate and heat transfer for the flow of hybrid nanoliquid. Results reveal that the addition of nanoparticles reduces the temperature and entropy generation of hybrid nanoliquid. Heat transfer rate enhances by improving Joule heating and electroosmotic parameters. An increase in Helmholtz–Smoluchowski velocity and Hartmann number decrease the velocity of fluid. Thermal performance of hybrid nanofluid (${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–${\mathrm{\text{Cu/H}}}_2\mathrm{\text{O}}$) is more noticeable in comparison with conventional mono nanofluid (${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–${\mathrm{\text{H}}}_2\mathrm{\text{O}}$) and base fluid (${\mathrm{\text{H}}}_2\mathrm{\text{O}}$).

This paper deals with the study of an incompressible electro-magneto-hydrodynamic (EMHD) Jeffrey fluid flow over a vertical nonlinear stretching surface of variable thickness. Heat and mass transfer effects are analyzed by considering different source terms like viscous dissipation, Ohmic heating, thermophoresis, Brownian motion, thermal heat source, exponential heat source and activation energy. Governing equations for the flow system are converted into dimensionless forms using appropriate similarity transformations. The solution for the resulting governing equations is obtained by using the shooting technique with RK-4 method. The effects of various physical parameters such as magnetic field parameter $(M)$, Grashof number (Gr), solutal Grashof number $(G_c)$, Brownian diffusion parameter $(N_b)$, thermophoresis diffusion parameter $(N_t)$, thermal heat source parameter $(Q_t)$, exponential heat source parameter $(Q_e)$, Prandtl number (Pr) and Lewis number (Le) are presented with the help of graphs. It is observed that the heat transfer effects increase by increasing thermal and exponential heat sources, and mass transfer effects enhance by increasing the activation energy. Entropy generation for this flow system is also analyzed. Entropy decreases with an increase in the electric field parameter. In contrast, the Bejan number initially increases with an increase in the electric field parameter. After some particular value of electric field parameter, it changes its behavior in the boundary layer and decreases with an increase in the electric field parameter. Entropy and Bejan number increase with an increment in the concentration difference parameter. The accuracy of the results is validated by those of published literature and found in reasonable justification. The present results may be helpful in many engineering and industrial applications like manufacturing lubrication, natural gas networks, cooling nuclear reactors and spray processes.

Recent advancements in nanotechnology have created a tremendous platform for the development of the improved performance of ultrahigh coolants known as nanofluids for several industrial and engineering technologies. The present research peruses an inspection of irreversibility analysis of mixed convective flow near a stagnation point provoked by ternary hybrid nanoparticles through a vertical heated flat plate with the Hall effects. Water conveying alumina (Al₂O₃), silver (Ag) and titanium oxide (TiO₂) nanoparticles experiencing convectively heated as appropriate in the engineering or industry are investigated. The leading equations are non-dimensionalized using relevant similarity variables and then numerically cracked via utilizing the bvp4c solver. The impressions of different pertinent parameters on the axial velocity, transverse velocity and temperature profile along with heat transfer and drag force are discussed carefully. Double solutions are observed in the opposing flow; however, a single solution is obtained for the assisting flow. Also, the results indicate that due to nanofluid, the velocity boundary layer thicknesses decrease and the thermal boundary layer width upsurges. Further, the flow and the characteristics of heat transfer can be controlled using a magnetic field.

This research explored the influences of entropy generation on bioconvected nanoliquid flow through the porous cavity filled with nanofluid and gyrotactic microbes. The porosity term in the momentum equation is summarized by the implementation of Darcy’s formula through Boussinesq estimation. The novelty of this study is to investigate entropy generation in cavity by augmenting the convection generated by the phenomenon of Brownian motion, thermophoresis of nanofluid flow and the bioconvection due to swimming of microorganisms. The governing partial differential equations (PDEs) are highly nonlinear and are nondimensionalized through the suitable similarity constraints. The transformed PDEs are tackled via implementation of finite difference method (FDM). The reaction of entropy generation and Bejan number against various quantities like bioconvection Rayleigh number ($\mathrm{\text{Rb}}=1$–100), Rayleigh number ($\mathrm{\text{Ra}}=1$–100), Peclet number ($\mathrm{\text{Pe}}=0.1$–0.9) and ratio of buoyancy ($\mathrm{\text{Nr}}=0$–1) are reported and visualized. The entropies by theliquid friction, heat transportation, mass transmission and microorganisms are focused. Upsurge in Nr (0.3–0.5) and Pe (0.1–0.15) accelerated the maximum of entropy due to microorganism by 7% and 44%, respectively. Here, an increment in Ra, Rb, Pe and Nr affects the distribution pattern of total entropies and Bejan number consistently. The higher Lewis number caused a decrement in the total entropy by liquid friction.

In this research work, the two-dimensional (2D), incompressible fluid flow has been taken into consideration. The flow is supposed to be steady and laminar. By considering the water-based nanoparticles of SWCNTs and MWCNTs in the presence of thermal radiation, the rate of heat transferring and entropy generation effects in a regenerative cooling system of a rocket engine are evaluated. The effects of the length and radius of the nanomaterials on the problem are also considered. Solutions for temperature, velocity profile, irreversibility (entropy generation) and the Bejan number are discussed graphically, and the effects of various significant factors are considered on these profiles. The modeled physical problems in current exploration are dependent upon governing laws which appear in terms of PDEs. These PDEs are reformed into a system of nonlinear ODEs. We used numerical scheme known as (RK-4) in combination with the shooting iteration technique to obtain the solutions to transformed fluid flow equations, because the resultant ODEs are extremely nonlinear and finding the exact solution is very difficult. It is investigated that the Eckert number, nanoparticles volume fraction and radiation parameter upsurge the thermal field as well as the irreversibility of the system. Furthermore, the dual behavior of nanoparticles volume fraction and viscosity parameter on velocity profile is observed. Bejan number shows increasing effects in response to nanoparticles volume fraction and radiation parameter, whereas a reverse impact of Bejan number is noticed for the rising values of Eckert number.

The applications of nanofluids (NFs) have been comprehensively explored in current years, as they have abundant potential for technical progress and more prominently offer assistances that can be associated with the applications of NFs for several determinations. Nanotechnology can be applied in various technological fields such as medicine, information technologies, food safety and novel materials. Here, novel properties of entropy generation in a mixed convective magneto flow of a Sutterby nanomaterial to an extended surface is scrutinized. Nanofluid model comprises Brownian motion and thermophoresis aspects. The expression of energy depends upon the phenomenon of viscous dissipation and thermal radiation. We formulated the Bejan number and entropy generation. To reduce PDEs into nonlinear ODEs, we use transformation of variables and then the resultant system is solved by bvp4c technique. The influence of the parameters involved, such as thermal radiation, chemical reaction parameter, diffusive variable, magnetic parameter, thermophoresis parameter and Schmidt number for temperature, concentration as well as Bejan number, entropy generation are inspected through tables and graphs.