Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes, radiation effects and chemical reactions. The main aim of this research is to address entropy generation due to magnetic field, nonlinear thermal radiation, viscous dissipation, thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk. The conservation laws of mass and momentum along with the first law of thermodynamics and Fick's law are used to discuss the flow, heat and mass transfer, while the second law of thermodynamics is used to analyze the entropy and irreversibility. The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method. The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks. The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks. Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks. The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion. The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant. It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip. The current results present many applications in the lubrication phenomenon,heating processes, cooling of devices, thermal engineering, energy production, extrusion processes etc.     

Lattice Boltzmann simulation for hydrothermal analysis of free convection within dumbbell-shaped heat exchanger

The lattice Boltzmann simulation of nanofluid flow and heat transfer during natural convection within a dumbbell-shaped heat exchanger is carried out. The heat exchanger is filled with CuO–water. The KKL model is employed to predict the thermo-physical properties of nanofluid. In order to perform a comprehensive hydrothermal investigation, different post-processing approaches such as heatline visualization, total entropy generation, local entropy generation based on local fluid friction irreversibility and heat transfer irreversibility, average and local Nusselt variation are employed. In the present investigation, it is tried to present the impact of different influential parameters like Rayleigh number, solid volume fraction of nanofluid and thermal arrangement of internal fins-bodies on the fluid flow, heat transfer rate and entropy generation.     

Rapid communication: Permeability of hydrogen in two-dimensional graphene and hexagonal boron nitride sheets

This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.     

Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis

This research presents the applications of entropy generation phenomenon in incompressible flow of Jeffrey nanofluid in the presence of distinct thermal features. The novel aspects of various features, such as Joule heating, porous medium, dissipation features, and radiative mechanism are addressed. In order to improve thermal transportation systems based on nanomaterials, convective boundary conditions are introduced. The thermal viscoelastic nanofluid model is expressed in terms of differential equations. The problem is presented via nonlinear differential equations for which analytical expressions are obtained by using the homotopy analysis method (HAM). The accuracy of solution is ensured. The effective outcomes of all physical parameters associated with the flow model are carefully examined and underlined through various curves. The observations summarized from current analysis reveal that the presence of a permeability parameter offers resistance to the flow. A monotonic decrement in local Nusselt number is noted with Hartmann number and Prandtl number. Moreover, entropy generation and Bejan number increases with radiation parameter and fluid parameter.     

Hydromagnetic Carreau Nanoliquid in Frames of Dissipation and Activation Energy

The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated.Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis.Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon.Concentration by zero mass flux condition is implemented.Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism.Total entropy generation rate and Bejan number is formulated.The utilization of transformation variables reduces the PDEs into non-linear ODEs.The obtained nonlinear complex problems are computed numerically through Shooting scheme.The impact of involved variables like local Weissenberg number,magnetic parameter,thermal radiation parameter,Brownian motion parameter,thermophoresis parameter,buoyancy ratio parameter,mixed convection parameter,Prandtl parameter,Eckert number,Schmidt number,non-dimensional activation energy parameter,chemical reaction parameter,Brinkman number,dimensionless concentration ratio variable,diffusive variable and dimensionless temperature ratio variable on velocity,temperature,nanoparticles concentration,entropy generation,Bejan number,surface drag force and heat transfer rate are examined through graphs and tables.     

Analytical Analysis of Heat Transfer and Entropy Generation in a Tube Filled with Double-Layer Porous Media

The heat transfer and entropy generation in a tube filled with double-layer porous media are analytically investigated. The wall of the tube is subjected to a constant heat flux. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are analytically derived and validated in limiting case. The analytical solutions of the local and total entropy generation, as well as the Nusselt number, are further derived to analyze the performance of heat transfer and irreversibility of the tube. The influences of the Darcy number, the Biot number, the dimensionless interfacial radius, and the thermal conductivity ratio, on flow and heat transfer are discussed. The results indicate, for the first time, that the Nusselt number for the tube filled with double-layer porous media can be larger than that for the tube filled with single layer porous medium, while the total entropy generation rate for the tube filled with double-layer porous media can be less than that for the tube filled with single layer porous medium. And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.     

Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection

In this communication, an optimization of entropy generation is performed through thermodynamics second law. Tangent hyperbolic nanomaterial model is used which describes the important slip mechanism namely Brownian and thermophoresis diffusions. MHD fluid is considered. The novel binary chemical reaction model is implemented to characterize the impact of activation energy. Nonlinear mixed convection, dissipation and Joule heating are considered. Appropriate similarity transformations are implemented to get the required coupled ODEs system. The obtained system is tackled for series solutions by homotopy method. Graphs are constructed to analyze the impact of different flow parameters on entropy number, nanoparticle volume concentration, temperature and velocity fields. Total entropy generation rate is calculated via various flow variables. It is noticed from obtained results that entropy number depend up thermal irreversibility, viscous dissipation and Joule heating irreversibility and concentration irreversibility. Decreasing behavior of concentration is witnessed for higher estimations of chemical reaction variable. Entropy number is more for higher Hartmann number, Weissenberg number and chemical reaction variable while contrast behavior is noted for Bejan number.     

计及污垢影响的换热器热优化

本文利用熵产生数方法研究了气体和液体传热介质的顺流、逆流换热器的热力学完善性，结果表明，如给定冷、热流体的入口温度，在综合考虑传热、流动阻力和污垢的情况下，可用优化方法确定其它参数。     

Heat transfer analysis for stretching flow over a curved surface with magnetic field

The analysis of a viscous fluid flow and heat transfer is carried out under the influence of a constant applied magnetic field over a curved stretching sheet. Heat transfer analysis is carried out for two heating processes, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF). The equations governing the flow are modeled in a curvilinear coordinate system (r, s, z). The nonlinear partial differential equations are then transformed to nonlinear ordinary differential equations by using similarity transformations. The obtained system of equations is solved numerically by a shooting method using Runge-Kutta algorithm. The interest lies in determining the influence of dimensionless radius of curvature on the velocity, temperature, skin friction, and rate of heat transfer at the wall prescribed by the Nusselt number. The effects of Hartmann number are also presented for the fluid properties of interest.     

Electroosmosis-Optimized Thermal Model for Peristaltic Transportation of Thermally Radiative Magnetized Liquid with Nonlinear Convection

The present study addresses the heat transfer efficiency and entropy production of electrically conducting kerosene-based liquid led by the combined impact of electroosmosis and peristalsis mechanisms. Effects of nonlinear mixed convection heat transfer, temperature-dependent viscosity, radiative heat flux, electric and magnetic fields, porous medium, heat sink/source, viscous dissipation, and Joule heating are presented. The Debye–Huckel linearization approximation is employed in the electrohydrodynamic problem. Mathematical modeling is conducted within the limitations of δ << 1 and Re → 0. Coupled differential equations after implementing a lubrication approach are numerically solved. The essential characteristics of the production of entropy, the factors influencing it, and the characteristics of heat and fluid in relation to various physical parameters are graphically evaluated by assigning them a growing list of numeric values. This analysis reveals that heat transfer enhances by enhancing nonlinear convection and Joule heating parameters. The irreversibility analysis ensures that the minimization of entropy generation is observed when the parameters of viscosity and radiation are held under control. Fluid velocity can be regulated by adjusting the Helmholtz–Smoluchowski velocity and magnetic field strength.     

Entropy generation analysis for peristaltically driven flow of hybrid nanofluid

Present study investigates entropy generation analysis for peristaltic motion of hybrid nanofluid. Hybrid nanofluid is composed of iron-oxide and copper nanoparticles suspended in water. Effects of Hall current, Ohmic heating and mixed convection are taken into account. Governing equations are simplified by utilizing lubrication approach. The numerical solutions for resulting system of differential equations are obtained with the aid of Shooting method. Attention has been given to the analysis of hybrid nanoparticles, Hall parameter and Grashoff number on entropy generation, heat transfer rate, velocity profile and pressure gradient. Outcomes reveal that insertion of nanoparticles decreases the temperature of hybrid nanofluid. It is found that increase in Hall parameter reduces the heat transfer rate at wall. Increment in Hall parameter reduces the entropy generation. Velocity and pressure gradient increases by enhancing Grashoff number. It is believed that the present flow model can prove useful in improving the efficiency of similar thermodynamical systems.     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Second law analysis of the flow of two immiscible micropolar fluids between two porous beds

This work investigates the effect of entropy generation rate within the flow of two immiscible micropolar fluids in a horizontal channel bounded by two porous beds at the bottom and top. The flow is considered in four zones. Zone IV contains the flow of viscous fluid in the large porous bed at the bottom, zone I and zone II contain the free flow of two immiscible micropolar fluids, and zone III contains the flow of viscous fluid in the thin porous bed at the top. The flow is assumed to be governed by Eringen’s micropolar fluid flow equations in the free channel. Darcy’s law and Brinkman’s model are used for flow in porous zones, namely, zone IV and zone III, respectively. The closed form expressions for entropy generation number and Bejan number are derived in dimensionless formby using the expressions of velocity, microrotation and temperature. The effect of physical parameters like a couple stress parameter and micropolarity parameter on velocity, microrotation, temperature, entropy generation number and Bejan number are investigated.     

Analysis for flow of Jeffrey fluid with nanoparticles

An analysis of the boundary layer flow and heat transfer in a Jeffrey fluid containing nanoparticles is presented in this paper. Here, fluid motion is due to a stretchable cylinder. The thermal conductivity of the fluid is taken to be temperature-dependent. The partial differential equations of velocity, temperature, and concentration fields are transformed to a dimensionless system of ordinary differential equations. Nonlinear governing analysis is computed for the homotopy solutions. The behaviors of Brownian motion and thermophoresis diffusion of nanoparticles have been examined graphically. Numerical values of the local Nusselt number are computed and analyzed.     

Entropy Generation Analysis of the Flow Boiling in Microgravity Field

Entropy generation analysis of the flow boiling in microgravity field is conducted in this paper. A new entropy generation model based on the flow pattern and the phase change process is developed in this study. The velocity ranges from 1 m/s to 4 m/s, and the heat flux ranges from 10,000 W/m² to 50,000 W/m², so as to investigate their influence on irreversibility during flow boiling in the tunnel. A phase–change model verified by the Stefan problem is employed in this paper to simulate the phase–change process in boiling. The numerical simulations are carried out on ANSYS-FLUENT. The entropy generation produced by the heat transfer, viscous dissipation, turbulent dissipation, and phase change are observed at different working conditions. Moreover, the Be number and a new evaluation number, E_P, are introduced in this paper to investigate the performance of the boiling phenomenon. The following conclusions are obtained: (1) a high local entropy generation will be obtained when only heat conduction in vapor occurs near the hot wall, whereas a low local entropy generation will be obtained when heat conduction in water or evaporation occurs near the hot wall; (2) the entropy generation and the Be number are positively correlated with the heat flux, which indicates that the heat transfer entropy generation becomes the major contributor of the total entropy generation with the increase of the heat flux; (3) the transition of the boiling status shows different trends at different velocities, which affects the irreversibility in the tunnel; (4) the critical heat flux (CHF) is the optimal choice under the comprehensive consideration of the first law and the second law of the thermodynamics.     

A minimum entropy generation procedure for the discrete pseudo-optimization of finned-tube heat exchangers

This paper presents a novel method which can be helpful in assessing the optimal configuration of finned-tube heat exchangers. The method is an extension of the local irreversibilities method [17], and it is based on the determination on a local basis of the two components of the entropy generation rate: the one caused by viscous dissipations and the one due to thermal irreversibilities. Depending on the engineering purpose for which a technical device was designed, it can be argued that the optimal configuration will be that in which either one (or both) of these two entropy generation rates is minimized. For a heat exchanging device, it is important to minimize thermal irreversibilities, but more important is to minimize the mechanical power lost in achieving a prescribed heat-exchange performance: to this purpose, one can form a relative irreversibility index (named Bejan number here and in [17] because the original seed of this procedure can be found in [1]), and use it to assess the merit of a given configuration.In the procedure presented here, a circular, single-tube, finned heat exchanger configuration is considered: the velocity and temperature fields are computed (via a standard finite-element package, FIDAP) for a realistic value of the Reynolds number and for a variety of geometric configurations (various fin external diameters and fin spacing); then, the entropy generation rate is calculated from the flowfield, and is examined both at a local level, to detect possible bad design spots (ie, locations which correspond to abnormally high entropy generation rates, which could be cured by design improvements), and at an overall (integral) level, to assess the entropic performance of the heat exchanger. Optimal curves are given, and the optimal spacing of fins is determined using alternatively the entropy generation rate and the total heat transfer rate as objective functions: different optima arise, and the differences as well as the similarities are discussed in detail.     

Effect of melting heat transfer and thermal radiation on Casson fluid flow in porous medium over moving surface with magnetohydrodynamics

In this study, the effects of variable fluid properties on heat transfer in MHD Casson fluid melts over a moving surface in a porous medium in the presence of the radiation are examined. The relevant similarity transformations are used to reduce the governing equations into a system of highly nonlinear ordinary differential equations and those are then solved numerically using the Runge–Kutta–Fehlbergmethod. The effects of different controlling parameters, namely, the Casson parameter,melting and radiation parameters, Prandtl number,magnetic field, porosity, viscosity and the thermal conductivity parameters on flow and heat transfer are investigated. The numerical results for the dimensionless velocity and temperature as well as friction factor and reducedNusselt number are presented graphically and discussed. It is found that the rate of heat transfer increases as the Casson parameter increases.     

Models base study of inclined MHD of hybrid nanofluid flow over nonlinear stretching cylinder

Focus of the present analysis is on the stagnation point flow of hybrid nanofluid with inclined magnetic field over a moving cylinder. The extended version of two models (e.g. Xue model and Yamada-Ota model for hybrid nanofluids) are considered in this study). A mathematical model of hybrid nanofluid flow is developed under certain flow assumptions. Boundary layer approximations are also utilized to model a system of partial differential equations. The systems of partial differential equations are further converted to dimensionless systems of ordinary differential equations by means of suitable similarity transformations. A numerical solution is obtained by applying bv4c technique. Effects of variation in physical parameters involved are depicted through graphs. Skin friction coefficient and Nusselt number are highlighted through tables. Our main objective is to investigate the heat transfer rate on the surface of the nonlinear stretching cylinder. The results of Xue model and Yamada-Ota model for the hybrid nanofluid due to nonlinear stretching cylinder are computed for comparison. In both cases, velocity and temperature profiles are best compared to the decay results.     

Entropy generation minimization and statistical declaration with probable error for skin friction coefficient and Nusselt number

Main emphasis of present work is to analyze the novel feature of entropy generation in MHD nanomaterial flow between two rotating disks. Heat transfer process is explored in the presence of Joule heating and thermal radiation. Tiwari–Das nanofluid model is employed in mathematical modeling. Aluminum oxide and copper water nanoparticles are accounted. Statistical declaration and probable error for problem accuracy are computed. Total entropy generation subject to Bejan number is scrutinized. Suitable variables are utilized to transform nonlinear PDEs to ordinary ones. Convergent series solutions are computed. Zeroth and mth order problems are discussed for stability analysis. The impact of physical flow variables like Reynolds number, magnetic parameter, porosity parameter, stretching parameter, rotational parameter, radiation parameter, Eckert number, suction injection parameter, Brinkman number and temperature ratio parameter on velocities, temperature, total entropy generation and Bejan number are examined and discussed through graphs. Velocity and thermal gradients at the surface of disks are computed.