Entropy analysis in MHD Couette flow of chemically reacting viscoelastic fluid past a deformable porous channel

Here, an investigation of MHD Couette flow of a chemically reacting viscoelastic fluid past a deformable porous layer with entropy generation using Walters liquid model has been considered. A binary, homogeneous, and isotropic mixture of fluid and solid phases in the porous medium is considered. The impact of heat source parameter and Soret effect are taken into account. The governing equations are solved analytically to obtain the expressions for solid displacement, fluid velocity, temperature, and concentration. The impact of relevant parameters on the flow system, temperature, concentration, mass transfer flux, entropy generation number, and Bejan number are discussed graphically. It is observed that solid displacement enhances due to the growth of drag and viscoelastic parameter, while it reduces due to rising volume fraction parameter. Fluid velocity rises when the volume fraction parameter increases. Rising Brinkmann number enhances the temperature, while Brinkmann number and Soret number reduces the species concentration. The irreversibility of heat transfer dominates the flow near the channel plates, while the effect of fluid friction irreversibility can be observed within the channel centerline region.     

Entropy analysis of a flow past a heat‐generated bluff body

Cooling of a bluff body is a topic of interest for many engineers and scientists. Forced convection over the bluff body generates flow separation, which in turn affects the heat transfer characteristics and increases the irreversibilities involved in the system. In the present study, flow over a rectangular solid body with constant heat flux is considered. The governing flow and energy equations are solved in two‐dimensional space numerically using a control volume approach. In order to investigate the effect of the fluid properties on the heating process, three different fluids are taken into account. These are air, ethylene glycol and therminol. To determine the irreversibilities involved in the system, entropy analysis is carried out. It is found that fluid properties have considerable effect on the entropy generation. The entropy generation due to heat transfer well exceeds the entropy generation due to fluid friction. The surface temperature of the solid body highly depends on the cooling fluid employed. Copyright © 1999 John Wiley & Sons, Ltd.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

Entropy analysis of wet-surface cooling system for air flow

A wet-surface heat-exchanger, where the effluent air is moistened, is analysed according to a thermodynamic theory and data of experimental tests. An entropy generation function, which takes into account the changes of temperature and humidity of air, is derived. The analyses show that it is thermodynamically possible, without any cooling machine, to achieve extremely large temperature drops. With certain parameters the system results in a maximum rate of entropy generation which is used to analyse differences between two different methods of spraying the moistening water. Approximal limits for the efficient working fluid mass flow value are also given. © 1998 John Wiley & Sons, Ltd.     

Entropy analysis of conjugate heating in a pipe flow

In the present study, an analytical approach governing the temperature rise in the solid pipe and fluid is presented. The entropy analysis in the fluid system due to heat transfer is introduced to obtain the integrated entropy generation in the system. Coolanol, water and mercury are selected as fluids while copper and steel are considered as pipe materials. In order to simplify the analysis, the heat transfer coefficient at solid–liquid interface is kept constant during the calculations. It is found that the fluid temperature rise in the early heating period and the integrated entropy generation in the fluid system is lower in the case of a copper pipe. Copyright © 2002 John Wiley & Sons, Ltd.     

Entropy generation on MHD peristaltic flow of Cu‐water nanofluid with slip conditions

The current research explores entropy generation and effect of magnetic field on peristaltic flow of copper‐water nanofluid in an asymmetric configuration saturated with porous medium. Slip conditions are invoked for velocity and temperature. Governing flow problem is constructed under the long wave length assumption. Analytical result for the problem is computed by exploiting homotopy analysis methodology. The influences of involved physical parameters are investigated through plots.     

Entropy generation in an unsteady Eyring‐Powell hybrid nanofluid flow over a permeable surface: A Lie group analysis

In thermal processes, the choice of the thermofluid plays an essential role in minimizing entropy generation and thereby improving thermal efficiency. In this study, entropy generation in a viscous hybrid nanofluid described by the Eyring‐Powell model is investigated. The model accounts for the effect of the nanoparticle volume fraction and viscous dissipation on an Eyring‐Powell Cu‐Al₂O₃/ethylene glycol nanofluid. A similarity solution to the time‐dependent model is found using the Lie group symmetry technique. The bivariate spectral quasi‐linearization method is used for the solution of the self‐similar transport equations. We analyze the effects of the nanoparticle volume fraction, suction/injection, and viscous dissipation on the fluid properties. The skin friction and Nusselt number are determined. A comparison between the Nusselt number of a regular nanofluid and a hybrid nanofluid shows that the hybrid nanofluid has better thermal characteristics compared with the regular nanofluid. The findings show that a decrease in the nanoparticle volume fraction and Eckert number minimizes entropy generation in the system.     

Entropy analysis of MHD flow of Jeffrey fluid in an inclined channel

This study is aimed at investigating the influence of entropy analysis of magnetohydrodynamic flow of Jeffrey fluid in an inclined micro-channel in the presence of thermal radiation and field suction/injection. We have improved the mathematical model of the physical problem under consideration. The designed equations have been solved by applying the shooting-based fourth-order, Runge–Kutta method with the boundary conditions, which describe velocity slip and temperature jump conditions at the fluid–wall inter-face. Numerical efforts are described graphically and mentioned quantitatively concerning different parameters such as Jeffery parameter, Bejan number, and entropy generation embedded in the problem. The numerical results for the expression of the irreversibility ratio are obtained. It is observed that the wall inclination strengthens the entropy production rate in the micro-channel, and the thermal buoyancy layer induces an increase in fluid velocity as suction.     

Entropy and radiation on a pipe MHD flow with variable viscosity

The present work, the entropy generation due to radiation and variable viscosity magnetohydrodynamic effects with a porous medium in a circular pipe, has been obtained and studied numerically. The governing continuity, momentum, and energy equations in cylindrical coordination are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically by a Runge-Kutta method and shooting technique. Numerical results are presented for velocity, temperature profiles, pressure profile, entropy generation rates, and Bejan number for different physical parameters of the problem. Also, the effects of the pertinent parameters on the skin friction and the rate of heat transfer are obtained and discussed numerically and illustrated graphically.     

Entropy generation through hexagonal cross‐sectional duct for constant wall temperature in laminar flow

Second law analysis of heat transfer in laminar flow for hexagonal cross‐section duct was analysed analytically. Geometrical effect of hexagonal duct was considered. The variation of total entropy generation was studied along the duct length. As a working fluid water and unused engine oil were used to compare the effect of fluid in the duct. Results were compared with circular cross‐section duct. It is found that the non‐dimensional entropy generation in a hexagonal cross‐section duct can be as high as a factor of four than that for a circular duct. Further, the unused engine oil gives up to about ten times lower non‐dimensional entropy generation values than that of water but needs about ten times more pumping power to heat transfer ratio. Copyright © 2004 John Wiley & Sons, Ltd.     

Entropy generation on unsteady stagnation-point Casson nanofluid flow past a stretching sheet in a porous medium under the influence of an inclined magnetic field with homogeneous and heterogeneous reactions

This study explores the entropy generation analysis on unsteady nonlinear radiative ethylene glycol-based Casson nanofluid flow near stagnation point towards a stretching sheet through a porous medium. Analysis has been accomplished in the presence of an inclined magnetic field, heat generation, homogeneous–heterogeneous reactions, and viscous dissipation with velocity slip and convective boundary conditions. The nondimensional governing equations are solved by the shooting technique with the help of the RK45 method. We have experimented with copper and silver nanoparticles and a comparative analysis has been highlighted for both copper and silver nanofluids. Numerical outcomes are executed by the MATLAB built-in bvp4c function. The consequences of the experiment for various pertinent flow parameters are portrayed by graphs and tables for both the Ag- and Cu-Casson nanofluids. Results reveal that the enhancement of nanoparticles volume fraction accelerates temperature but it slows down concentration and velocity distributions. Higher values of the Eckert number boost velocity and temperature but reduce skin friction coefficient and Nusselt number. Enhancement of the Brinkman number boosts up entropy generation but it slows down Bejan's number. The results of the model can be applied in the movement of biological fluids, separation of biomolecules, glass manufacturing, paper production, food processing, crude oil purification, polymer drag reduction, and cooling atomic reactors.     

Entropy generation analysis on forced and free convection flow in a vertical porous channel with aligned magnetic field and Navier slip

The entropy generation rate in a vertical porous channel with injection and suction walls and a uniform magnetic field provided at an angle $\xi$ to the flow direction is studied using an analytical perturbation technique in the presence of Navier slip and buoyancy force. The momentum and energy equations were solved for exemplary values of fluid convection's physical characteristics. Important parameters' impacts on adequate numbers are graphically portrayed and conveyed.     

Hydromagnetic stability of dissipative couette flow: Wide-gap problem

A numerical solution to the eigenvalue problem of MHD stability of Couette flow between concentric rotating cylinders with nonconducting walls, is presented here. The numerical values of the critical Taylor number, Ta_c, and the critical wave number, a_c are listed in a table for different values of η (ratio of the two radii), μ (ratio of the angular velocities of the two cylinders) and Q, the magnetic field parameter. It is observed that, owing to an increase in the gap-width, Ta_c decreases or the flow becomes destabilized. a_c increases with increasing Q and μ < 0, but decreases when μ > 0 and by increasing the width between two cylinders.     

Entropy Analysis of a Coupled‐Convection Flow through a Vertical Channel Partially Filled by a Porous Medium with Injection/Suction and Slip Boundary Conditions

Flow fields, thermal fields, and entropy generation have been investigated for fully developed mixed convection flow between two vertical porous plates. The vertical channel is partially filled by a porous medium, and channel walls are subjected to a constant injection velocity at the left wall and constant suction velocity at the right wall. The viscous dissipation effects and velocity slip for the longitudinal component of the velocity at the channel walls are also taken into account. The momentum and energy equations for the mixed convection problem in the vertical channel are solved by means of the perturbation series method, by taking perturbation parameter proportional to the Brinkman number. For the present problem, numerical solution is also obtained and compared with the analytical solution. The effects of various pertinent parameters on the velocity distribution, temperature distribution, entropy generation rate, and Bejan number are investigated and discussed graphically.     

Improved velocity and temperature profiles for integral solution in the laminar boundary layer flow on a semi‐infinite flat plate

One of the most important problems in Mechanical Engineering is the determination of laminar boundary layer thickness over a flat plate. Integral solution and similarity solutions are two well‐known methods for calculation of boundary layer thickness. However, integral solution method is a computational cost‐effective method rather than the similarity solution method. Velocity and temperature profiles must be determined for the integral solution method. Velocity boundary layer thickness can be determined by the velocity profile whereas for determination of thermal boundary layer thickness both velocity and temperature profiles must be used. Available velocity profiles do not give an exact value for velocity boundary layer thickness, while the Nusselt number is affected by these profiles. In this study, a new velocity profile is proposed which gives an exact value for laminar boundary layer thickness on a flat plate. In addition, two temperature profiles are proposed that give the exact values of the Nusselt number over a flat plate for uniform temperature and uniform heat flux boundary conditions. The calculated constants in the velocity boundary layer thickness equation and the Nusselt relations are validated with the results of the similarity solution method. Excellent agreement between the results of the two methods is observed.     

A UNIFIED ENGINEERING MODEL FOR STEADY AND QUASI-STEADY SHEAR-DRIVEN GAS MICROFLOWS

We analyze one-dimensional plane Couette flows in the entire Knudsen regime with the objective of modeling shear-driven rarefied gas flows encountered in various microelectromechanical system (MEMS) components. Using the linearized Boltzmann solutions available in the literature and hard sphere direct simulation Monte Carlo (DSMC) results, we develop a unified empirical model that includes analytical expressions for the velocity distribution and shear stress for steady plane Couette flows. We also present extension of this model to time-periodic oscillatory Couette flows. Comparisons between the extended model and ensemble averaged unsteady DSMC computations show good agreements in the quasi-steady flow limit, where the Stokes number (β) based on the plate separation distance and oscillation frequency is ≤ 0.25. Overall, the new model accurately predicts the velocity distribution and shear stress for steady and quasi-steady (β ≤ 0.25) flows in a wide Knudsen number range (K_n ≤ 12), and it is strictly valid for low subsonic flows with Mach number ≤ 0.3.     

The effect of radial temperature gradient and axial magnetic field on the stability of couette flow: The narrow gap problem

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under the following conditions: (i) the inner cylinder rotating with the outer cylinder stationary, (ii) corotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, (v) conducting and nonconducting walls, and (vi) the presence of a radial temperature gradient. Results for the critical wave number a_c, and the critical Taylor number T_c, are presented. The variation of T_c is shown on graphs for both the conducting and nonconducting walls and for different values of ±μ (= Ω₂/Ω₁, where Ω₂ is the angular velocity of the outer cylinder, and Ω₁ is the angular velocity of the inner cylinder), the magnetic field parameter Q, which is the square of the Hartmann number and ± N (= Ra/Ta, where Ra is the Rayleigh number). The effects of ±μ, N and Q on the stability of flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, this being more so in the presence of conducting walls and a negative temperature gradient.     

Measurement and analysis of tip clearance unsteady flow spectrum in axial-flow fan rotor

The dynamic pressure measurement device and test technology are described in this study. The tip clearance unsteady flow development from the inlet to the outlet of an axial-flow rotor was revealed by analyzing pressure frequency spectrum acquired from measuring the unsteady pressure field of the tip endwall. The experiment provides test basis for thoroughly understanding the tip clearance unsteady flow and building interaction models of tip clearance flow and main flow. __________ Translated from Compressor, Blower & Fan Technology, 2007, (5): 12–15 [译自: 风机技术]