Viscous dissipation effect on entropy generation for non-Newtonian fluids in microchannels

An analytical study on the viscous dissipation effect on entropy generation in fully developed forced convection for single phase non-Newtonian fluid flow in circular microchannels is reported. In the first-law analysis, closed form solutions of the temperature distributions in the radial direction for the models with and without viscous dissipation term in the energy equation are obtained. In the second-law analysis, the two models are compared by analyzing their relative deviations in dimensionless entropy generation and Bejan number for different Brinkman number and power-law index. The findings show that under certain conditions the viscous dissipation effect on entropy generation in microchannels is significant and should not be neglected.     

A numerical investigation of entropy generation in the entrance region of curved pipes at constant wall temperature

In this study, developing incompressible viscous flow and heat transfer in the curved pipes are studied numerically to analyze the entropy generation and thermodynamic optimization in the entrance region at a constant wall temperature. The governing equations including continuity, momentum and energy equations are solved using a second order finite difference method based on the projection algorithm. Entropy generation and optimal Reynolds number calculation based on the entropy generation minimization are carried out for two cases considering the two groups of non-dimensional parameters both numerically and analytically. The comparison of the numerical results in the entrance region with the analytical ones in the fully developed region indicates that both solutions predict nearly the same optimal Reynolds numbers, specially, for the first group of the non-dimensional parameters.     

Optimum wall thickness ratio based on the minimization of entropy generation in a viscous flow between parallel plates

The influence of the geometrical and physical parameters on entropy generation for a viscous flow between infinite parallel walls of finite thickness is studied by solving the momentum and energy conservation equations. The conjugate heat transfer problem in the fluid and solid walls is solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid–wall interfaces. Analytic solutions for the velocity and temperature fields in the fluid and walls are used to calculate the local and global entropy generation rate. Conditions under which this quantity is minimized are determined for certain suitable combination of geometrical and physical parameters of the system. Special attention has been given to the effect of the wall thickness on the entropy generation rate. It is found that the global entropy generation reaches a minimum for specific values of the wall thickness ratio, when the other parameters are fixed.     

Salient features of Dufour and Soret effect in radiative MHD flow of viscous fluid by a rotating cone with entropy generation

BackgroundHere physical characteristics of convective magnetohydrodynamic flow of viscous liquid subject to a rotating cone are discussed. Dissipation, Joule heating, thermal flux and heat generation/absorption are scrutinized in energy expression. Physical aspects of diffusion-thermo and thermo diffusion effect are deliberated. Thermo-diffusion is the mechanisms of transportation in which particles are transferred in a multi-factor mixture determined by temperature gradient. Furthermore irreversibility analysis is considered.MethodNonlinear partial differential system are reduced to ordinary one with the help of similarity variables. Here we implemented ND solve technique to get numerical results for given nonlinear system.ResultsCharacteristics of influential variables for entropy optimization, velocity, concentration, Bejan number and temperature are scrutinized. Numerical outcomes of gradient of velocity and Nusselt and Sherwood numbers are examined through tabulated form. Velocity components are declined against higher velocity slip parameters. For larger estimation of heat generation and radiation parameters the temperature is upsurges. Entropy generation and Bejan number are boost up via rising values of diffusion and radiation parameters. For larger estimation of Brinkman number both Bejan number and entropy rate have opposite effect. Comparative studies of the current and previous results are discussed in tabularized form and have a good agreement.     

Modelling of roughness effects on heat transfer in thermally fully-developed laminar flows through microchannels

In this paper, roughness was modelled as a pattern of parallelepipedic elements of height k periodically distributed on the plane walls of a microchannel of height H and of infinite span. Two different approaches were used to predict the influence of roughness on heat transfer in laminar flows through this microchannel. Three-dimensional numerical simulations were conducted in a computational domain based on the wavelength λ. A one-dimensional model (RLM model) was also developed on the basis of a discrete-element approach and the volume averaging technique. The numerical simulations and the rough-layer model agree to show that the Poiseuille number Po and the Nusselt number Nu increase with the relative roughness. The RLM model shows that the roughness effect may be interpreted by using effective roughness heights k_eff and k_effθ for predicting Po and Nu respectively. k_eff and k_effθ depend on two dimensionless local parameters: the porosity of the rough-layer and the roughness height normalized with the distance between the rough elements. The present results show that roughness increases the friction factor more than the heat transfer coefficient (performance evaluation criteria < 1), for a relative roughness height expected in the fabrication of microchannels (k/(H/2) < 0.46) or k/D_h < 0.11).     

A numerical study on entropy generation induced by turbulent forced convection in curved rectangular ducts with various aspect ratios

The present paper analyzes the entropy generation induced by turbulent forced convection in a curved rectangular duct with external heating by numerical methods. The problem is assumed as steady, three-dimensional and turbulent. The flow features, including the secondary flow motions, the distribution of local entropy generation as well as the overall entropy generation in the whole flow fields, are analyzed. For a baseline case with Re = 20,000, external heat flux q? = 0.112 and aspect ratio γ = 1, the results show the entropy generation induced by the frictional irreversibility concentrates within the regions adjacent to the duct walls, whereas the entropy generation resulted from the heat transfer irreversibility only significantly occurs near the outer wall of the duct where the external heat flux imposed. Except the baseline case, two additional cases with aspect ratio equal to 0.25 and 4 are calculated. Through the comparison of the three aspect-ratio cases, it is seen that the resultant entropy generations in the flow fields for the three cases are all dominated by the frictional irreversibilities. Among the three aspect-ratio cases, the resultant entropy generation is minimal in the γ = 1 case. Accordingly, the case with γ = 1 is concluded to be the optimal aspect ratio under the current flow condition based on the minimal entropy generation principle.     

Temperature and entropy generation behavior in rectangular ducts with 3-D heat transfer coupling (conduction and convection)

Temperature and entropy generation fields are evaluated for 3-D heat transfer coupling (conduction and convection) using a mathematical and computational model. Results are obtained from numerical simulation and analyzed for conditions of fully developed laminar flow inside rectangular ducts. Thermal boundary conditions, at the walls cross section and axial direction, are non-uniform and not imposed. A numerical method of modified TDMA algorithm combined with an iterative solution for the system of algebraic equations obtained was developed. Equations were discretised by finite differences. Convergence is guaranteed by applying the first law of thermodynamics. Considering the thinness of the walls, conduction effectiveness is well represented as 1-D. The methodology applied considers air, water and oil as working fluids at 300 K and carbon-steel as wall material. Results for these cases are presented with the intention of finding, the best fluid heating conditions as a first approach to the design of heat exchangers systems.     

MHD-conjugate heat transfer analysis for a vertical flat plate in presence of viscous dissipation and heat generation

In this paper, the effects of magnetic field, viscous dissipation and heat generation on natural convection flow of an incompressible, viscous and electrically conducting fluid along a vertical flat plate in the presence of conduction are investigated. Numerical solutions for the governing momentum and energy equations are given. A discussion is provided for the effects of magnetic parameter, viscous dissipation parameter and heat generation parameter on two-dimensional flow. Detailed analysis of the velocity profile, temperature distribution, skin friction, rate of heat transfer and the surface temperature distribution are shown graphically.     

An analysis of entropy generation through a circular duct with different shaped longitudinal fins for laminar flow

The present study focuses on the entropy generation analysis in a circular duct with internal longitudinal fins of different shape for laminar flow. Three different fin shapes are chosen for the analysis: Thin, triangular and V-shaped fins. Calculations are performed for various dimensionless lengths and number of fins, dimensionless temperature difference and fin angle for triangular and V-shaped fins. It is found that the number of fins and dimensionless length of the fins for both thin fins and triangular fins, and the fin angle for triangular and V-shaped fins have significant effect on both entropy generation and pumping power. Further, both entropy generation and pumping power also are influenced by dimensionless temperature difference.     

Assessment of errors on the kinetic data by entropy generation analysis

Metal hydride systems are utilized in many practical applications such as hydrogen storage, heat pumps, etc. The establishment of a metal hydride system requires the expression of reaction rate for the first step design, from an engineering standpoint. However, improper experimental determination of intrinsic kinetics usually leads to significant errors in the kinetic data. This paper presents a novel methodology of estimating these errors based on the entropy generation analysis. For this purpose, numerical simulation is performed taking into account the experimental conditions for a real case. The results showed that if the operating conditions (i.e. hydrogen pressure, heat transfer coefficient) and the size of the experimental setup are not chosen properly, the kinetic data obtained from the experiments will be largely misled. Therefore it should be carefully taken into account in order to minimize the relative errors induced on the kinetic data.     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

Analysis of entropy generation distribution in micro-combustors with baffles

This study presents the analysis of entropy generation distribution in H₂/air premixed flame in micro-combustors with baffles. The numerical simulation of combustion is performed with the help of Ansys Fluent code. The entropy generation rates are derived from entropy transport equation and calculated based on the numerical results. The entropy generation caused by various irreversible processes such as chemical reaction, thermal conduction and mass diffusion are studied in micro-combustors with baffles. The effects of the height of the baffles, H₂/air mass flow rate and equivalence ratio are investigated. It is found that a higher baffle will lead to more entropy generation and relatively larger destruction of available energy. The exergy efficiency decreases significantly when the H₂/air mass flow rate is increased. The lean and rich H₂/air mixture shows an obvious lower entropy generation rate and higher exergy efficiency than the stoichiometric mixture.     

Viscous dissipation effects on the asymptotic behaviour of laminar forced convection for Bingham plastics in circular ducts

The present study concentrates on the effects of viscous dissipation and the yield shear stress on the asymptotic behaviour of the laminar forced convection in a circular duct for a Bingham fluid. It is supposed that the physical properties are constant and the axial conduction is negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial distributions of wall heat flux which yield a thermally developed region. It is shown that if the asymptotic value of wall heat flux distribution is vanishes, the asymptotic value of the Nusselt number is zero. The case of the asymptotic wall heat flux distribution non-vanishing giving a value of the Nusselt number dependent on the Brinkman number and on the dimensionless radius of the plug flow region was also analysed. For an infinite asymptotic value of wall heat flux distributions, the asymptotic value of the Nusselt number depends on the dimensionless radius of the plug flow region and on the dimensionless parameter which depends on the asymptotic behaviour of the wall heat flux. The condition of uniform wall temperature and convection with an external isothermal fluid were also considered. The comparison with other existing solutions in the literature in the Newtonian case is analysed.     

Entropy generation for compressible natural convection with high gradient temperature in a square cavity

Entropy generation due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subjected to different side wall temperatures for compressible and incompressible natural convection flows. Based on the obtained velocity and temperature values, the distributions of local entropy generation, average entropy generation and average Bejan number are determined and compared for compressible and incompressible regimes. It is found that the entropy generated for compressible flow always is more than incompressible flow. The study is performed for Ra = 10⁴–10⁸, ε = 0.01(incompressible regime) and 0.6 (compressible regime), Ge = 10⁻⁵ and Pr = 0.7.     

Viscous dissipation effects on parallel plates with constant heat flux boundary conditions

This paper investigates basic analytical expressions for Nusselt number with the effect of viscous dissipation on the heat transfer between infinite fixed parallel plates, where the focus is on hydro-dynamically and thermally fully developed flow of a Newtonian fluid with constant properties, neglecting the axial heat conduction. Thermal boundary conditions considered are: both the plates kept at different constant heat fluxes, both the plates kept at equal constant heat fluxes, and one plate insulated. From the analysis, new expressions for Nusselt numbers have been found, as a function of various definitions of the Brinkman number.     

某双级跨音速燃气透平全三元粘性流场的数值分析

求解了某双级跨音速燃气透平的全三元粘性湍流流场,计算结果表明用基于有限体积法的数值模拟方法求解多级跨音速透平粘性含激波流场结果合理,数值计算具有较高的效率。在分析了各排叶片叶型的主要气动特性基础上,认为该透平总体承载能力比较合理。     

Numerical investigation on developing laminar forced convection and entropy generation in a wavy channel

The present paper investigates the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The effects of aspect ratio (W/H) and Reynolds number (Re) on entropy generation are the major concerns. The studied cases cover W/H = 1, 2 and 4, and Re range from 100 to 400. The flow features, including secondary flow motion and temperature distribution as well as the detailed distributions of local entropy generation due to frictional and heat transfer irreversibilities are reported. Through the evaluations of entropy generation in the whole flow field, the case of W/H = 1 is found to have the minimal entropy generation among all of the analyzed cases. Besides, the higher Re is found to be beneficial for obtaining the lower values of the total resultant entropy generation in the flow field. Accordingly, the case with W/H = 1 and higher Re is suggested to be used under the current flow conditions, so that the irreversibility resulted from the developing laminar forced convection in the wavy channel could be least and the best exergy utilization could be achieved.     

A numerical study of laminar convective heat transfer in microchannel with non-circular cross-section

Three-dimensional numerical simulations of the laminar flow and heat transfer of water in silicon microchannels with non-circular cross-sections (trapezoidal and triangular) were performed. The finite volume method was used to discretize the governing equations. Numerical results were compared with experimental data available in the literature, and good agreements were achieved. The effects of the geometric parameters of the microchannels were investigated, and the variations of Nusselt number with Reynolds number were discussed from the field synergy principle. The simulation results indicate that when the Reynolds numbers are less than 100, the synergy between velocity and temperature gradient is much better than the case with Reynolds number larger than 100. There is an abrupt change in the intersection angle between velocity and temperature gradient around Re=100. In the low Reynolds number region the Nusselt number is almost proportional to the Reynolds number, while in the high Reynolds number region, the increasing trend of Nusselt number with Reynolds number is much more mildly, which showed the applicability of the field synergy principle. In addition, for the cases studied the fully developed Nusselt number for the microchannels simulated increases with the increasing Reynolds number, rather than a constant.     

Analysis of entropy generation due to natural convection in square enclosures with multiple discrete heat sources

Entropy generation due to natural convection in an enclosure heated locally from below with two isoflux sources was investigated. The flow and temperature fields were determined by numerical simulation of two-dimensional laminar conservation equations for mass, momentum and energy. For heaters of equal length and strength, the effects of Rayleigh number and heater position on flow and temperature fields and local entropy generation were examined. For heaters of unequal heater length and heater strength, the effects of heater length and strength ratios were investigated. Minimum entropy generation rate was achieved for the same condition at which the minimum peak heater temperature was obtained.     

Numerical study of heat transfer in a laminar mist flow over a isothermal flat plate

A model for predicting heat and mass transfer in a laminar two-phase gas-vapor-drop mist flow over a flat isothermal flat is developed. Using this model, a numerical study is performed to examine the influence of thermal and flow parameters, i.e., Reynolds number, flow velocity, temperature ratio, concentration of the liquid phase, and drop size, on the profiles of velocity, temperature, composition of the two-phase mixture, and heat-transfer intensification ratio. It is shown that, as the concentration of the liquid phase in the free flow increases, the rate of heat transfer between the plate surface and the vapor-gas mixture increases dramatically, whereas the wall friction increases only insignificantly.