Magnetohydrodynamic chemically reactive viscoelastic fluid flow through an inclined porous layer

Analysis of a time-independent magnetohydrodynamic viscoelastic fluid flow in a deformable inclined porous layer with first-order chemical reaction has been investigated. Walters' fluid model has been used to study viscoelastic fluid. The walls are suctioned/injected at a constant rate. The expression representing the solution for solid displacement, fluid velocity, temperature, and concentration distribution is obtained. The effect of applicable parameters on solid displacement, fluid velocity, temperature, and concentration are discussed graphically, while skin friction, heat transfer, and mass transfer are revealed in a tabular structure. It is noticed that solid displacement, fluid velocity, and temperature profiles decrease when the viscoelastic parameter increase. Solid displacement enhances and the velocity of the fluid reduces owing to the influence of increasing drag parameter, whereas the reverse effect is seen for the volume fraction parameter. Nusselt number at the walls shows the opposite behavior for the viscoelastic parameter and Eckert number. Sherwood number at the walls shows opposite behavior for Reynolds number, Schmidt number, and radiation parameter. Also, the entropy generation number rises as a result of the influence of viscoelasticity and Eckert number.     

Finite difference analysis for entropy optimized flow of Casson fluid with thermo diffusion and diffusion-thermo effects

Heat transportation is a novel prospective in many thermal processes and presents dynamic applications in industrial and thermal polymer processing optimization. The importance of heat transportation is noted in heat exchangers, production of crude oils, combustion, petroleum reservoirs turbine systems, thermal systems, porous media, modeling of resin transfer nuclear reactions etc. In view of such thermal applications the main objective here is to examine entropy in unsteady magnetohydrodynamic of Casson fluid flow. Radiation in addition to dissipation and ohmic heating are analyzed. Entropy is scrutinized employing thermodynamic second law. Characteristics of Soret and Dufour are also examined. Main objective here is to examine irreversibility. Dimensionless version of differential system is obtained through suitable variables. The obtained partial differential system is solved through numerical scheme (Finite difference method). Physical features of fluid flow, temperature, entropy optimization and concentration have been explained. Variations of parameters on drag force, Nusselt number and solutal transfer rate are graphically discussed. Higher fluid parameter leads to improve in velocity and entropy rate. Larger values of radiation parameter boost up thermal field. Entropy rate and velocity have reverse trend for magnetic field. An intensification for concentration is found through Soret number. Higher approximation of Reynold number enhances skin friction and velocity. Thermal transfer rate is augmented versus radiation and magnetic variables.     

Flow and thermal analysis of Oldroyd 8 constant fluid in a porous channel

The present research is based on the thermal and flow properties of the viscoelastic Oldroyd 8 constant fluid in an upright microchannel. The energy and momentum equations were solved with the support of temperature Jump and velocity slip boundary conditions. To measure the irreversibility rate of the flow system, the acquired results of velocity and thermal equations were used. To crack the current mathematical model problem, the numerical Runge–Kutta–Fehlberg method was used. With the aid of graphs, the effect of physical parameters such as thermal radiation, thermal-dependent heat source, Joule heating, fluid parameters, velocity slip, and temperature Jump parameters on the fluid flow, thermal energy, and system entropy generation was discussed. Fluid parameters have different effects on the velocity profile. The Grashof and Hartmann numbers demonstrate opposite effects on the momentum field. The thermal energy of the system reduces with thermal radiation and temperature Jump factor. The thermal radiation, Hartmann number, and temperature Jump parameters reduce the system's irreversibility rate. With the Brinkman number and temperature Jump parameter, the irreversibility ratio increases.     

Flow and heat transfer analysis of MHD third-grade fluid flow through a vertical microchannel subjected to entropy generation

This paper analyses the generation of entropy in an electrically conducting third-grade fluid through a vertical channel considering the variable thermal conductivity. Aspects of radiation, viscous dissipation, porous medium, Joule heating, convective boundary condition, and heat generation are studied. Nonlinear systems of ordinary differential equations are obtained via applying suitable dimensionless variables. After that, the system is solved with the aid of using the Runge–Kutta–Fehlberg method. The numerical solutions are used to characterize the irreversibility and irreversibility ratio. It is established that the entropy is enhanced with accelerating estimations of the third-grade material parameter, Brinkman number, magnetism, Biot number, porous parameter, and the impact is decelerated with elevating values of the radiation. The rate of heat transfer is higher for the Brinkman number, and a similar impact on drag force is noticed for magnetic and Grashof numbers. All the parameters on flow, temperature, fluid irreversibility and irreversibility ratio are discussed through graphical illustration.     

Confined swirling jet impingement onto an adiabatic wall

Impinging swirling jets generate interesting flow fields and depending on the magnitude of the swirl velocity, circulation cells develop in the region close to the solid wall. Moreover, axial momentum of the jet is influenced by the magnitude of the swirl velocity. This, in turn, results in considerable entropy generation in the flow field. In the present study, confined swirling jet impingement onto an adiabatic wall is investigated. The flow and temperature fields are computed numerically for various flow configurations. Different jet exit velocity profiles are considered and their effects on the flow field are examined. The entropy production due to different flow configurations is computed and the irreversibility ratios due to fluid friction and heat transfer are determined. It is found that the jet axis tilts towards the radial direction as swirl velocity increases and reducing the velocity profile number enhances the entropy generation due to heat transfer. The irreversibility ratio variation with the velocity profile number behaves opposite for the fluid friction and heat transfer.     

A study on entropy generation and heat transfer in a magnetohydrodynamic flow of a couple-stress fluid through a thermal nonequilibrium vertical porous channel

The effect of local thermal nonequilibrium (LTNE) on the entropy generation and heat transfer characteristics in the magnetohydrodynamic flow of a couple-stress fluid through a high-porosity vertical channel is studied numerically using the higher-order Galerkin technique. The Boussinesq approximation is assumed to be valid and the porous medium is considered to be isotropic and homogeneous. Two energy equations are considered one each for solid and fluid phases. The term involving the heat transfer coefficient in both equations renders them mutually coupled. Thermal radiation and an internal heat source are considered only in the fluid phase. The influence of inverse Darcy number, Hartmann number, couple-stress fluid parameter, Grashof number, thermal radiation parameter, and interphase heat transfer coefficient on velocity and temperature profiles is depicted graphically and discussed. The entropy generation, friction factor, and Nusselt number are determined, and outcomes are presented via plots. The effect of LTNE on the temperature profile is found to cease when the value of the interphase heat transfer coefficient is high, and in this case, we get the temperature profiles of fluid and solid phases are uniform. The physical significance of LTNE is discussed in detail for different parameters' values. It is found that heat transport and friction drag are maximum in the case of LTNE and minimum in the case of local thermal equilibrium. We observe that LTNE opposes the irreversibility of the system. The corresponding results of a fluid-saturated densely packed porous medium can be obtained as a limiting case of the current study.     

Influence of Viscous Dissipation on non‐Darcy Mixed Convection Flow of Nanofluid

In this paper, the steady fully developed non‐Darcy mixed convection flow of a nanofluid in a vertical channel filled with a porous medium with different viscous dissipation models is analyzed. The Brinkman‐Forchheimer extended Darcy model is used to describe the fluid flow pattern in the channel. The transport equations for a nanofluid are solved analytically using the seminumerical‐analytical method known as differential transformation method, and numerically with the Runge‐Kutta shooting method. Finally, the influence of pertinent parameters, such as solid volume fraction, different nanoparticles, mixed convection parameter, Brinkman number, Darcy number, and inertial parameter on the velocity and temperature fields are shown graphically. The results show that velocity and temperature are enhanced when the mixed convection parameter, Brinkman number, and Darcy number increases whereas solid volume fraction and inertial parameter decreases the velocity and temperature fields. The obtained results show that the nanofluid enhances the heat transfer process significantly.     

Soret–Dufour effects on chemically reacting non-Darcian MHD flow around a plate

Here, a study of steady, magnetohydrodynamic flow of incompressible, cold fluid around a moving plate with a non-Darcian porous medium in existence of heat source and nth-order chemical reaction incorporating Soret and Dufour effects is considered. MATLAB bvp4c technique is used to solve the prevailing equations. Variations in velocity, temperature and concentration are analysed. It is observed that the applicable parameters such as non-Darcy, Soret, Dufour, chemical reaction play a significant role in controlling the flow. Chemical reaction parameter reduces skin friction, heat transfer, and mass transfer while Eckert number enhances the mass transfer and skin friction.     

Pulsating hydromagnetic flow of Casson fluid in a vertical channel filled with non-Darcian porous medium

This paper analyzes the Joule heating, Dufour number, and Soret number effects on hydromagnetic pulsatile flow of a Casson fluid in a vertical channel filled with a non-Darcian porous medium. The governing partial differential equations (PDEs) of the Casson fluid flow are transformed to ordinary differential equations (ODEs) using perturbation technique and solved by employing shooting method with Runge–Kutta (R–K) fourth-order technique using MATHEMATICA function NDSolve. The influence of Forchheimer number, Casson fluid parameter, Dufour number, radiation parameter, and Soret number on flow variables has been studied and the numerical results obtained are presented. The results reveal that the velocity rises with the rise of Darcy number, whereas it decreases for a given rise in the Forchheimer number. Furthermore, the temperature distribution enhances by increasing the Dufour number.     

Second law analysis and heat transfer in a cross-flow heat exchanger with a new winglet-type vortex generator

In this paper a second law analysis of a cross-flow heat exchanger (HX) is studied in the presence of a balance between the entropy generation due to heat transfer and fluid friction. The entropy generation in a cross-flow HX with a new winglet-type convergent–divergent longitudinal vortex generator (CDLVG) is investigated. Optimization of HX channel geometry and effect of design parameters regarding the overall system performance are presented. For the HX flow lengths and CDLVGs the optimization model was developed on the basis of the entropy generation minimization (EGM). It was found that increasing the cross-flow fluid velocity enhances the heat transfer rate and reduces the heat transfer irreversibility. The test results demonstrate that the CDLVGs are potential candidate procedure to improve the disorderly mixing in channel flows of the cross-flow type HX for large values of the Reynolds number.     

Entropy generation in a porous channel with hydromagnetic effect

An analytical work has been performed to study the First and Second Laws (of thermodynamics) characteristics of flow and heat transfer inside a vertical channel made of two parallel plates embedded in a porous medium and under the action of transverse magnetic field. Combined free and forced convection inside the channel is considered. Flow is assumed to be steady, laminar, fully developed of electrically conducting and heat-generating/absorbing fluid. Both vertical walls are kept isothermal at the same or different temperatures. Governing equations in Cartesian coordinate are simplified and solved analytically to develop expressions for velocity and temperature, entropy generation number and irreversibility distribution ratio. Velocity, temperature and entropy generation profiles are presented graphically.     

Influence of conjugate heat transfer on the minimization of entropy generation for forced convective flow through parallel plate channel filled with porous material

A fluid–solid conjugate heat transfer model is developed to analyze the characteristics of entropy generation for forced convective steady hydrodynamically fully developed laminar flow of a Newtonian fluid through a parallel plate channel filled with porous material by modulating the following parameters: substrate thickness, the ratio of thermal conductivity of wall to fluid, Biot number, the axial temperature gradient in the fluid, and Peclet number. The exteriors of both the walls are subjected to the thermal boundary conditions of the third kind. The mass and Brinkman momentum conservation equations in the fluidic domain and the coupled energy conservation in both the solid and fluidic domain are solved analytically using the local thermodynamic equilibrium model, so as to derive closed-form expressions for the velocity in the fluid and the temperature both in the fluid and solid walls in terms of relevant parameters. Suitable combinations of influencing factors, namely the geometric parameters of the system, fluid, flow, and substrate properties are identified for which global entropy generation rate is minimized. The findings may be helpful in the design of thermal systems frequently used in diverse engineering applications having heat transfer in the solid wall being a crucial parameter.     

The second law analysis in fundamental convective heat transfer problems

Second law characteristics of heat transfer and fluid flow due to forced convection of steady-laminar flow of incompressible fluid inside channel with circular cross-section and channel made of two parallel plates is analyzed. Different problems are discussed with their entropy generation profiles and heat transfer irreversibility characteristics. In each case, analytical expression for entropy generation number (N_S) and Bejan number (Be) are derived in dimensionless form using velocity and temperature profiles.     

Mixed convection flows of tangent hyperbolic fluid past an isothermal wedge with entropy: A mathematical study

The nonlinear, steady, and mixed convective boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian fluid over an isothermal wedge in the presence of magnetic field are analyzed numerically using the implicit Keller-Box finite-difference technique. The entropy analysis due to MHD flow of a tangent hyperbolic fluid past an isothermal wedge and viscous dissipation is also included. The numerical code is validated with previous Newtonian studies available in the literature. Graphical and tabulated results are analyzed to study the behavior of the fluid velocity, temperature, concentration, shear stress, heat transfer rate, entropy generation number, and Bejan number for various emerging thermophysical parameters, namely Weissenberg number (We), power-law index (n), mixed convection parameter (λ), pressure gradient parameter (m), Prandtl number (Pr), Biot number (γ), Hartmann number (Ha), Brinkmann number (Br), Reynolds number (Re), and temperature gradient (Π). It is observed that velocity, entropy, Bejan number, and surface heat transfer rate are reduced with the increase in the Weissenberg number, but temperature and local skin friction are increased. An increase in pressure gradient enhances velocity, entropy, local skin friction, and surface heat transfer rate, but reduces temperature and Bejan number. An increase in an isothermal power-law index (n) is observed to increase velocity, Bejan number, and surface heat transfer rate, but it decreases temperature, entropy, and local skin friction. An increase in the magnetic parameter (Ha) is found to decrease temperature, entropy, surface heat transfer rate, and local skin friction, and it increases velocity and Bejan number. The research is applicable for coating materials in chemical engineering, for instance, robust paints, production of aerosol deposition, and water-soluble solution thermal treatment.     

MHD convective rotating flow of viscoelastic fluid past an infinite vertical oscillating porous plate with Hall effects

It is considered the unsteady and incompressible magnetohydrodynamic rotating free convection flow of viscoelastic fluid with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field and taking Hall current into account. The governing equations of the flow field are then solved by a regular perturbation method for a small elastic parameter. The expressions for the velocity, temperature, and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction on the boundary, the heat flux in terms of the Nusselt number, and the rate of mass transfer in terms of the Sherwood number are also obtained and their behavior discussed. The resultant velocity enhances with increasing Hall parameter and rotation parameter. The reversal behavior is observed with increasing viscoelastic parameters. The resultant velocity enhances and experiences retardation in the flow field with increasing radiation parameters, whereas the secondary velocity component increases with increasing rotation parameters. The temperature diminishes as the Prandtl number and/or the frequency of oscillations. The concentration reduces at all points of the flow field with the increase in the Schmidt number.     

Numerical study of chemical reaction and heat transfer of MHD slip flow with Joule heating and Soret–Dufour effect over an exponentially stretching sheet

A study of Soret–Dufour effects along with chemical reaction, viscous dissipation combining on MHD Joule heating for viscous incompressible flow is presented. It is assumed that fluid is flowing past an angled stretching sheet saturated in porous means. The slip conditions of velocity, concentration, and temperature are accounted for at the boundary. The mathematical expression of the problem contains highly nonlinear interconnected partial differential equations. To convert governing equations into ordinary differential equations, appropriate similarity transformations were utilized. These differential equations with boundary constraints are resolved by homotopy analysis method. Expression for velocity, concentration, and temperature are derived in the form of series. Effects of numerous physical parameters, for example, Schmidt number, Soret number, buoyancy ratio parameter, slip parameter, and so forth, on various flow characteristics are presented through graphs. Numerous values of velocity, concentration, and temperature gradient are tabulated against different parameters. Results show that the fluid velocity increases by enhancing the Soret number, Dufour number, or permeability parameter. The fluid's concentration rises as the Soret number increases, while it falls as the Dufour number, chemical reaction parameter, or permeability parameter increases.     

Entropy generation analysis of natural convective chemically reacting squeezing flow of Casson fluid between parallel disks with Hall and Ion slip currents

This paper concerns the second law analysis of free convective squeezing flow of a chemically reacting Casson fluid confined between two parallel disks with Hall and Ion slip effects. The upper one is impermeable and the lower disk is porous. The linear momentum, energy balance and mass partial differential equations converted as system of ODEs by similarity transformations and tackled with shooting method via fourth order Runge‐Kutta scheme. The impact of various dimensionless geometric and fluid parameters on the velocity fields, temperature and concentration fields, entropy generation and Bejan numbers are studied and presented in the form of pictorially. The present results are correlated with already published outcomes for viscous case and found to be good agreement. The Bejan number of the fluid enhances with Ion slip parameter, whereas the concentration profile of the fluid is decreases with increasing of the Casson fluid parameter. The entropy generation of the fluid is enhanced with Eckert number whereas the Bejan number is decreased with suction/blowing parameter     

Hall effects on MHD couple stress fluid flow through a vertical microchannel subjected to heat generation: A numerical study

The present study analyzes the irreversibility in an electrically conducting couple stress fluid between two vertical channel plates with the aspects of exponential space and temperature-dependent, radiative heat flux, heat generation, and Joule heating. A reduced system of the governing equations is obtained via applying suitable nondimensional variables. To determine the solutions of velocity, thermal field, irreversibility, and irreversibility ratio, the Runge-Kutta-Fehlberg method along with the shooting technique has been employed. The various pertinent parameters that are involved in the problem have been discussed in detail through graphs. The results show that the entropy production can improve with the viscous dissipation, Joule heating, exponential space and temperature-dependent, and radiative heat flux. Furthermore, it is clear that the entropy enhances with wall ambient temperature difference, radiation parameter, and the effect is reversed with higher estimations of the fluid wall interaction parameter, couple stress parameter, and rarefaction. The present numerical results are compared with the existing results that are in good agreement.     

Numerical study of entropy generation in Darcy-Forchheimer (D-F) Bödewadt flow of CNTs

Three-dimensional Bödewadt flow (fluid rotates at a large enough distance from the stationary plate) of carbon nanomaterial is examined. Single walled and multi walled CNTs are dissolved in water and gasoline oil baseliquids. Darcy-Forchheimer porous medium is considered. Stationary disk is further stretched linearly in radial direction. Heat transfer effect is examined in presence of radiation and convection. Effect of viscous dissipation is accounted. Entropy generation rate is studied. By using adequate transformation (von Kármán relations), the flow field equations (PDEs) are transmitted into ODEs. Solutions to these ODEs are constructed via implementation of shooting method (bvp4c). In addition to Entropy generation rate, Bejan number, heat transfer rate (Nusselt number), skin friction and temperature of fluid are examined through involved physical parameters. Axial component of velocity intensifies with increment in nanoparticles volume fraction and ratio of stretching rate to angular velocity parameter while it decays with higher porosity parameter. Higher nanoparticles volume fraction and porosity parameter lead to decay in radial as well as tangential component of velocity. However it enhances with higher ratio of stretching rate to angular velocity parameter. Temperature of fluid directly varies with higher ratio of stretching rate to angular velocity parameter, radiation parameter, Eckert number, Biot number and nanoparticles volume fraction. Rate of Entropy generation is reduced with higher estimations of porosity parameter, nanoparticles volume fraction and radiation parameter. Skin friction coefficient decays with higher porosity parameter and ratio of stretching rate to angular velocity parameter. Intensification in porosity parameter, nanoparticles volume fraction and Biot number leads to higher Nusselt number. Prominent impact is shown by multiple-walled CNTs with gasoline oil basefluid than single-walled CNTs with water basefluid.     

On inherent irreversibility in a reactive hydromagnetic channel flow

This study is devoted to investigate the inherent irreversibility and thermal stability in a reactive electrically conducting fluid flowing steadily through a channel with isothermal walls under the influence of a transversely imposed magnetic field. Using a perturbation method coupled with a special type of Hermite-Pade＂ approximation technique, the simplified governing non-linear equation is solved and the important properties of overall flow structure including velocity field, temperature field and thermal criticality conditions are derived which essentially expedite to obtain expressions for volumetric entropy generation numbers, irreversibility distribution ratio and the Bejan number in the flow field.