Effect of oxygen fraction on local entropy generation in a hydrogen–air burner

This study considers numerical simulation of the combustion of hydrogen with air, including oxygen and nitrogen, in a burner and the numerical solution of local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber. The effects of equivalence ratio (ϕ) and oxygen percentage (γ) on the combustion and entropy generation rate are investigated for different ϕs (from 0.5 to 1.0) and γs (from 10 to 30%). The combustion is simulated for the fuel mass flow rate providing the same heat transfer rate to the combustion chamber in the each case. The numerical calculation of combustion is performed individually for all cases with the help of the Fluent CFD code. Furthermore, a computer program has been developed to calculate numerically the volumetric entropy generation rate distributions and the other thermodynamic parameters by using the results of the calculations performed with the FLUENT code. The calculations bring out that the increase of ϕ (or the decrease of λ) reduces significantly the reaction rate levels. The average temperatures in the combustion chamber increase about 70 and 23% with the increases of γ (from 10 to 30%) and ϕ (from 0.5 to 1.0), respectively. With the increase of γ from 10 to 30%, the volumetric local entropy generation rates decrease about 9 and 4% in the cases of ϕ=0.5 and 1.0, respectively, and while the total entropy generation rates decrease exponentially, the merit numbers increase. The useful energy transfer rate to irreversibility rate therefore improves as the oxygen percentage increases.     

Entropy generation in laminar jet: effect of velocity profiles at nozzle exit

Laminar free jet flow finds wide application in industry. Although considerable research studies were carried out in the past, but the irreversibility associated with the flow field due to heat transfer and viscous dissipation needs further investigation. In the present study, laminar free jet is considered and volumetric entropy generation in the flow field is computed. The normalized entropy ratio (entropy ratio generated in one-fourth of the jet length to total entropy generation), irreversibility, and the Merit number are determined for different velocity profiles leaving the nozzle. It is found that the uniform velocity profile results in less entropy generation due to viscous dissipation as compared to its counterpart corresponding to triangular velocity profile; however, the entropy generation due to heat transfer increases for the uniform profile.     

Effect of Richardson number on entropy generation over backward facing step

The flow over a backward facing step (BFS) has been taken as a useful prototype to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many practical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated by the lattice Boltzmann method. It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy generation number is a monotonic decreasing function of Richardson number, whereas the average Bejan number is a monotonic increasing function of Richardson number.     

Effects of temperature-dependent viscosity variation on entropy generation,heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Peclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].     

Entropy analysis for third grade fluid flow with Vogel model viscosity in annular pipe

The steady-state flow of a third grade fluid between concentric circular cylinders is considered and entropy generation due to fluid friction and heat transfer in the annular pipe is examined. Depending upon the fluid viscosity, entropy generation in the flow system varies. The third grade fluid is employed to account for the non-Newtonian effect while Vogel model is accommodated for temperature-dependent viscosity. The analysis is based on perturbation technique. The closed form solutions for velocity, temperature and entropy fields are presented. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that entropy generation number reduces with increasing viscosity parameter A, which is more pronounced in the region close to the annular pipe inner wall and opposite is true for increasing viscosity parameter B.     

Entropy generation in developing laminar fluid flow through a circular pipe with variable properties

Entropy generation in a circular pipe is analyzed numerically. A two-dimensional solution for the velocity ant temperature profiles is obtained considering temperature dependent thenmophysical properties. Uniform wall heat flux case is considered as the thermal boundary condition. The distribution of the entropy generation rate is investigated throughout the volume of the fluid as it flows through the pipe. Engine oil is selected as the working fluid. In addition, ethylene glycol and air are used in a parametric study. The total entropy generation rate is calculated by integration over the various cross-sections as well as over the entire volume. The results are compared with those obtained for the constant viscosity case. A considerable discrepancy is found between the two cases since the viscosity of these fluids is highly sensitive to the temperature variation.     

The thermodynamic design of heat and mass transfer processes and devices

This review article places in perspective the new work devoted both to the analysis of the thermodynamic irreversibility of heat and mass transfer components and systems and to the design of these devices on the basis of entropy generation minimization. The review focuses on the fundamental mechanisms responsible for the generation of entropy in heat and fluid flow and on the design tradeoff of balancing the heat transfer irreversibility against the fluid flow irreversibility. Applications are selected from the fields of heat exchanger design, thermal energy storage, and mass exchanger design. This article provides a comprehensive, up-to-date review of second-daw analyses published in the heat and mass transfer literature during the last decade.     

Analysis of Laminar Flow and Forced Convection Heat Transfer in a Porous Medium

The flow of an incompressible Newtonian fluid confined in a planar geometry with different wall temperatures filled with a homogenous and isotropic porous medium is analyzed in terms of determining the unsteady state and steady state velocities, the temperature and the entropy generation rate as function of the pressure drop, the Darcy number, and the Brinkman number. The one-dimensional approximate equation in the rectangular Cartesian coordinates governing the flow of a Newtonian fluid through porous medium is derived by accounting for the order of magnitude of terms as well as accompanying approximations to the full-blown three-dimensional equations by using scaling arguments. The one-dimensional approximate energy and the entropy equations with the viscous dissipation consisting of the velocity gradient and the square of velocity are derived by following the same procedure used in the derivation of velocity expressions. The one-dimensional approximate equations for the velocity, the temperature, and the entropy generation rate are analytically solved to determine the velocity, the temperature, and the entropy distributions in the saturated porous medium as functions of the effective process parameters. It is found that the pressure drop, the Darcy number, and the Brinkman number affect the temperature distribution in the similar way, and besides the above parameters, the irreversibility distribution ratio also affects the entropy generation rate in the similar way.     

Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition

The unsteady laminar magnetohydrodynamics(MHD) boundary layer flow and heat transfer of nanofluids over an accelerating convectively heated stretching sheet are numerically studied in the presence of a transverse magnetic field with heat source/sink. The unsteady governing equations are solved by a shooting method with the Runge-KuttaFehlberg scheme. Three different types of water based nanofluids, containing copper, aluminium oxide, and titanium dioxide, are taken into consideration. The effects of the pertinent parameters on the fluid velocity, the temperature, the entropy generation number, the Bejan number, the shear stress, and the heat transfer rate at the sheet surface are graphically and quantitatively discussed in detail. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. It is observed that the presence of the metallic nanoparticles creates more entropy in the nanofluid flow than in the regular fluid flow.     

Heat transfer in laminar pulsating flows of fluids with temperature dependent viscosities

The effect of time-dependent pressure pulsations on heat transfer in a pipe flow with constant temperature boundaries is analysed numerically when the viscosity of the pulsating fluid is an inverse linear function of the temperature. The coupled differential equations are solved using Crank-Nicholson semi-implicit finite difference formulation with some modifications.The results indicate local variations in heat transfer due to pulsations. They are useful in the design of heat exchangers working under pulsating flow conditions. The analytical results are presented for both heating and cooling. The conditions under which pulsating flows can augment the heat transfer are discussed. The results are applicable for heat exchangers with fluids of high Prandtl number.     

Entropy generation analysis of fully developed laminar forced convection in a helical tube with uniform wall temperature

In the present study, fully developed laminar flow and heat transfer in a helically coiled tube with uniform wall temperature have been investigated analytically. Expressions involving relevant variables for entropy generation rate contributed to heat transfer and friction loss, and total entropy generation rate have been derived. The effect of various flow and coil parameters like Reynolds number, curvature ratio, coil pitch, etc. on the entropy generation rate has been studied for two fluids- air and water. The results of the present study have been compared to the corresponding entropy generation values of straight pipe. Investigating the results, some optimum values for Reynolds number have been proposed and compared with the optimum Reynolds numbers of laminar flow inside a coiled tube subjected to constant heat flux boundary condition.     

Second law analysis of the 2D laminar flow of two-immiscible,incompressible viscous fluids in a channel

The laminar and fully developed flows of two immiscible fluids confined in a thin slit of constant wall heat fluxes are analyzed in terms of entropy generations due to irreversibility of forced convection heat transfer. The governing equations are analytically derived using expressions for velocity distributions. The derived equation for the dimensionless entropy generation number is used to interpret the relative importance of frictions to conduction by varying irreversibility distribution ratio ϕ. It is found that the minimum entropy generation takes place at the dimensionless half transverse distance (ξ) of 0.3 for values of ϕ higher than zero. The entropy generation near the plate increases more rapidly in fluid I than in fluid II as viscous dissipation effects becomes more important. The velocity profiles are found to be in agreement with the distributions of the dimensionless entropy generation number (N _S ) for two-immiscible incompressible flows in the slit.     

Heat transfer and entropy generation analysis of non-Newtonian fluid flow through vertical microchannel with convective boundary condition

The entropy generation and heat transfer characteristics of magnetohydrodynamic(MHD) third-grade fluid flow through a vertical porous microchannel with a convective boundary condition are analyzed. Entropy generation due to flow of MHD non-Newtonian third-grade fluid within a microchannel and temperature-dependent viscosity is studied using the entropy generation rate and Vogel's model. The equations describing flow and heat transport along with boundary conditions are first made dimensionless using proper non-dimensional transformations and then solved numerically via the finite element method(FEM). An appropriate comparison is made with the previously published results in the literature as a limiting case of the considered problem.The comparison confirms excellent agreement. The effects of the Grashof number, the Hartmann number, the Biot number, the exponential space-and thermal-dependent heat source(ESHS/THS) parameters, and the viscous dissipation parameter on the temperature and velocity are studied and presented graphically. The entropy generation and the Bejan number are also calculated. From the comprehensive parametric study, it is recognized that the production of entropy can be improved with convective heating and viscous dissipation aspects. It is also found that the ESHS aspect dominates the THS aspect.     

Numerical study on local entropy generation in a burner fueled with various fuels

This study considers numerical simulations of the combustions of hydrogen and various hydrocarbons with air, including 21% oxygen and 79% nitrogen, in a burner and the numerical solution of the local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber. The combustion is simulated for the fuel mass flow rates providing the same heat transfer rate to the combustion chamber in the each fuel case. The effects of (only in the case of H₂ fuel) and equivalence ratio () on the combustion and entropy generation rate are investigated for the different (from 5,000 to 10,000 W) and s (from 0.5 to 1.0). The numerical calculation of combustion is performed individually for all cases with the help of the Fluent CFD code. Furthermore, a computer program has been developed to numerically calculate the volumetric entropy generation rate distributions and the other thermodynamic parameters by using the results of the calculations performed with the FLUENT code. The calculations bring out that the maximum reaction rates decrease with the increase of (or the decrease of ). The large positive and negative temperature gradients occur in the axial direction, nonetheless, the increase of significantly reduces them. The calculations bring out also that with the increase of from 0.5 to 1.0, the volumetric local entropy generation rates decrease about 4% and that the merit numbers increase about 16%.     

Entropy generation in flow field subjected to a porous block in a vertical channel

Entropy generation in the flow field subjected to a porous block situated in a vertical channel is examined. The effects of channel inlet port height (vertical height between channel inlet port and the block center), porosity, and block aspect ratio on the entropy generation rate due to fluid friction and heat transfer in the fluid are examined. The governing equations of flow, heat transfer, and entropy are solved numerically using a control volume approach. Air is used as the flowing fluid in the channel. A uniform heat flux is considered in the block and natural convection is accommodated in the analysis. It is found that entropy generation rate due to fluid friction increases with increasing inlet port height, while this increase becomes gradual for entropy generation rate due to heat transfer for the inlet port height exceeding 0.03 m. The porosity lowers entropy generation rate due to fluid friction and heat transfer. The effect of block aspect ratio on entropy generation rate is notable; in which case, entropy generation rate increases for the block aspect ratio of 1:2.     

Entropy generation and natural convection in square cavities with wavy walls

The aim of the present work is to study the entropy generation in the natural convection process in square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the hot wall geometry affects notably the heat transfer rate in the cavity. It has been found in the present numerical study that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh numbers. The study is performed for Rayleigh numbers 10³ < Ra < 10⁵, irreversibility coefficients 10^?4 < φ < 10^?2, and Prandtl numbers Pr = 0.71. The total entropy generation is found to increase with increasing undulation number.     

Experimental evaluation of numerical simulation of cavitating flow around hydrofoil

Cavitation in hydraulic machines causes different problems that can be related to its unsteady nature. An experimental and numerical study of developed cavitating flow was performed. Until now simulations of cavitating flow were limited to the self developed “in house” CFD codes. The goal of the work was to experimentally evaluate the capabilities of a commercial CFD code (Fluent) for simulation of a developed cavitating flow. Two simple hydrofoils that feature some 3D effects of cavitation were used for the experiments. A relatively new technique where PIV method combined with LIF technique was used to experimentally determine the instantaneous and average velocity and void ratio fields (cavity shapes) around the hydrofoils. Distribution of static pressure on the hydrofoil surface was determined. For the numerical simulation of cavitating flow a bubble dynamics cavitation model was used to describe the generation and evaporation of vapour phase. An unsteady RANS 3D simulation was performed. Comparison between numerical and experimental results shows good correlation. The distribution and size of vapour structures and the velocity fields agree well. The distribution of pressure on the hydrofoil surface is correctly predicted. The numerically predicted shedding frequencies are in fair agreement with the experimental data.     

Second law analysis of water flow through smooth microtubes under adiabatic conditions

In the study, a second law analysis for a steady-laminar flow of water in adiabatic microtubes has been conducted. Smooth microtubes with the diameters between 50 and 150 μm made of fused silica were used in the experiments. Considerable temperature rises due to viscous dissipation and relatively high pressure losses of flow were observed in experiments. To identify irreversibility of flow, rate of entropy generation from the experiments have been determined in the laminar flow range of Re = 20-2200. The second law of thermodynamics was applied to predict the entropy generation. The results of model taken from the literature, proposed to predict the temperature rise caused by viscous heating, correspond well with the experimental data. The second law analysis results showed that the flow characteristics in the smooth microtubes distinguish substantially from the conventional theory for flow in the larger tubes with respect to viscous heating/dissipation (temperature rise of flow) total entropy generation rate and lost work.     

Groove geometry effects on turbulent heat transfer and fluid flow

The present work represents a two-dimensional numerical prediction of forced turbulent flow heat transfer through a grooved tube. Four geometric groove shapes (circular, rectangular, trapezoidal and triangular) were selected to perform the study, as well as two aspect ratios of groove-depth to tube diameter (e/D = 0.1 and 0.2). The study focuses on the influence of the geometrical shapes of grooves and groove-depth on heat transfer and fluid flow characteristics for Reynolds number ranging from 10,000 to 20,000. The characteristics of Nusselt number, friction factor and entropy generation are studied numerically by the aid of the computational fluid dynamics (CFD) commercial code of FLUENT. It is observed that the best performance occurs with the lower depth-groove ratio, whereas it is found that the grooved tube provides a considerable increase in heat transfer at about 64.4 % over the smooth tube and a maximum gain of 1.52 on thermal performance factor is obtained for the triangular groove with (e/D = 0.1).     

Numerical solutions of pulsating flow and heat transfer characteristics in a pipe

Numerical studies are made of flow and heat transfer characteristics of a pulsating flow in a pipe. Complete time-dependent laminar boundary-layer equations are solved numerically over broad ranges of the parameter spaces, i.e., the frequency parameter β and the amplitude of oscillation A. Recently developed numerical solution procedures for unsteady boundary-layer equations are utilized. The capabilities of the present numerical model are satisfactorily tested by comparing the instantaenous axial velocities with the existing data in various parameters. The time-mean axial velocity profiles are substantially unaffected by the changes in β and A. For high frequencies, the prominent effect of pulsations is felt principally in a thin layer near the solid wall. Skin friction is generally greateer than that of a steady flow. The influence of oscillation on skin friction is appreciable both in terms of magnitude and phase relation. Numerical results for temperature are analyzed to reveal significant heat transfer characteristics. In the downstream fully established region, the Nusselt number either increases or decreases over the steady-flow value, depending on the frequency parameter, although the deviations from the steady values are rather small in magnitude for the parameter ranges computed. The Nusselt number trend is amplified as A increases and when the Prandtl number is low below unity. These heat transfer characteristics are qualitatively consistent with previous theoretical predictions.