Natural Convection Heat Transfer and Entropy Generation in a Porous Trapezoidal Enclosure Saturated with Power-Law Non-Newtonian Fluids

Abstract

In the present study, natural convection heat transfer and its associated entropy generation in a porous trapezoidal enclosure saturated with a power-law non-Newtonian fluid has been numerically investigated. Horizontal walls of the enclosure are assumed to be adiabatic while the side walls are considered to be kept at a constant temperature. A continuum-based approach is adapted here to model the fluid flow through porous media and the Darcy’s law is modified to account for non-Newtonian rheological behavior of the fluid. The obtained governing equations are discretized using the finite volume method and a detailed parametric study is undertaken to account for the effects of various relevant parameters of the problem on the heat transfer and entropy generation rates. It was shown that the impact of the power-law index on both entropy generation and heat transfer significantly intensifies in a convection-dominated flow regime inside the enclosure, especially for a shear thinning liquid. Moreover, heat transfer rate and entropy generation increase as the sidewall angle is elevated.     

Energetic and Exergetic Performances of Plate Heat Exchanger Using Brine-Based Hybrid Nanofluid for Milk Chilling Application

Abstract

Theoretical study on the energetic and exergetic performances of a counter-flow corrugated plate heat exchanger using hybrid nanofluids for the milk chilling application has been done in the present investigation. Magnesia-silver and Alumina-silver nanoparticles have been dispersed in the ethylene glycol–water mixture and propylene glycol–water mixture (20:80 brine solutions) with different particle volume concentration separately. Effect of particle volume concentration and flow rate of the hybrid nanofluid on the heat transfer rate, convective, and overall heat transfer coefficients, mass flow rate of milk, pressure drop, pumping power, entropy generation rate, second law efficiency, irreversibility, irreversibility distribution ratio, non-dimensional exergy (NDE) destruction, and performance index have been studied. It has been observed that heat transfer rate, convective and overall heat transfer coefficients, pressure drop, pumping power, irreversibility, entropy generation rate, second law efficiency, and milk flow rate increase; while NDE destruction, performance index, and irreversibility distribution ratio decrease with the hybrid nanofluid flow rate and the volume concentration of the nanofluid. Within studied ranges, the hybrid nanofluid yields the maximum improvement of heat transfer rate and convective heat transfer coefficient of about 1.6% and 9.4%, respectively, compared to base fluid. It has also been found that silver?+?alumina shows slightly better performance improvement and hence hybrid nanofluid is recommended as a suitable alternative for the milk chilling units.     

Teaching elementary thermodynamics and energy conversion: Opinions

This presentation deals with innovation in teaching and understanding of thermodynamic principles. Key features of the approach being advocated are: (a) postulation of the existence of entropy, (b) explicitly associating energy transfers with other transports, (c) stating the 2nd Law in terms of Gibbs' available-energy, (d) systematic use of software such as EES. The paper outlines and elaborates upon an introductory course. Major headings in the course are: basic concepts: properties, additive properties and balances, primitive properties, energy, 1st Law. entropy, elementary academic applications of balances, available-energy, second law, exergy, thermostatic property relations, EES. Applications to processes, fluid flow, Heat transfer, thermochemical. Applications to devices, single-process, compound-process, systems (consisting of devices and processes functioning together).     

Performance improvement of a butane/octane absorption chiller

To improve the coefficient of performance (COP) of an absorption chiller working with the n-butane as refrigerant and the n-octane as absorbent, a thermodynamic analysis based on the first and the second law of thermodynamic is required. A simulation model is established to calculate the different thermodynamic properties of each point of the cycle such as compositions, flow rates, and temperatures. Heat transfer rates and some performance parameters are calculated using the first law analysis. Compared to an ideal machine, the performances are degraded because of the irreversibilities occurring in the different components of the machine. The second law analysis provides the entropy generation in each element and its contribution at the degradation of the COP as well as the total entropy generation of the system. We have proposed a modification of the initial configuration of the machine to reduce the energy losses occurring in the components of high entropy generation and to improve the performance. This recuperation increases the COP from 0.36 to 0.59 and the efficiency from 0.24 to 0.39.     

Effects of rarefaction,viscous dissipation and rotation mode on the first and second law analyses of rarefied gaseous slip flows confined between a rotating shaft and its concentric housing

A parametric analytical study is carried out to scrutinize the mechanism of fluid flow, heat transfer and entropy generation in a low-speed rarefied gaseous flow confined between a shaft and its concentric housing, i.e., the cylindrical Couette flow. In the first law analysis, closed form solutions for the radial temperature profiles are obtained by incorporating the calculated velocity distribution into the energy equation. The derivations for three thermal cases, which are founded on imposing different thermal conditions, namely, the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT) boundary conditions, are presented. In the second law analysis, the contributions of thermal diffusion and fluid friction irreversibility to the total entropy generation in the micro domain are illustrated, and the relevant expressions for the Bejan number and the entropy generation number as well as the average entropy generation rate are derived. Finally, the variations of major variables with influential parameters such as the Knudsen number, the Brinkman number and rotation mode are investigated to elucidate the associated effects of rarefaction phenomenon, viscous dissipation and geometric condition on the characteristics of the flow.     

Entropy generation analysis in a uniformly heated microchannel heat sink

Present investigation analyzes the issue of entropy generation in a uniformly heated microchannel heat sink (MCHS). Analytical approach used to solve forced convection problem across MCHS, is a porous medium model based on extended Darcy equation for fluid flow and two-equation model for heat transfer. Simultaneously, closed form velocity solution in a rectangular channel is employed to capture z-directional viscous effect diffusion and its pronounced effect on entropy generation through fluid flow. Subsequently, governing equations are cast into dimensionless form and solved analytically. Second law analysis of problem is then conducted on the basis of obtained velocity and temperature fields and expressions for local and average entropy generation rate are derived in dimensionless form. Average entropy generation rate is then utilized as a criterion for assessing the system performance. Finally, the effect of influential parameters such as, channel aspect ratio (α_S), group parameter (Br/Ω), thermal conductivity ratio (C) and porosity (ε) on thermal and total entropy generation is investigated. In order to examine the accuracy of the analysis, the results of thermal evaluation are compared to one of the previous investigations conducted for thermal optimization of MCHS.     

Variational setting for reversible and irreversible fluids with heat flow

This paper derives and discusses variational formulations for heat flows subject to physical constraints that involve the (generally) non-conserved balance of internal energy and the entropy representation kinetics in the form of the Cattaneo equation of heat. Another approach is also outlined which uses the (generally) non-conserved balance of the entropy and the energy-representation counterpart of the Cattaneo equation called Kaliski’s equation. Results of nonequilibrium statistical mechanics (Grad’s theory) lead to nonequilibrium corrections to entropy and energy of the fluid in terms of the nonequilibrium density distribution function, f. These results also yield coefficients of the wave model of heat such as: relaxation time, propagation speed and thermal inertia. With these data a quadratic Lagrangian and a variational principle of Hamilton’s type follows for a fluid with heat flux in the field representation of fluid motion. For an irreversible heat transfer we show that despite of generally non-canonical form of the matter tensor the coefficients in source terms of the variational conservation laws can be suitably adjusted, so that physical (source-less and canonical) conservation laws are obtained for the energy and momentum. We discuss canonical and generalized conservation laws and show the satisfaction of the second law under the constraint of canonical conservation laws.     

Entropy Generation Due to the Flow of a Non-Newtonian Fluid with Variable Viscosity in a Circular Pipe

The non-Newtonian fluid can be considered as a third-grade fluid with variable viscosity. In this case, the rate of fluid strain can be formulated using the third-grade fluid analogy. In the present study, entropy generation due to non-Newtonian fluid flow in a pipe is investigated. A third-grade fluid with variable viscosity is accommodated in the analysis. Analytical solutions for velocity and temperature distributions are presented, and an entropy generation number is computed for different non-Newtonian parameters, viscosity parameters, and Brinkman numbers. It is found that increasing the non-Newtonian parameter lowers the entropy generation number. This is more pronounced in the region close to the pipe wall. Increasing the viscosity parameter and Brinkman number enhances the entropy generation number, particularly in the vicinity of the pipe wall.     

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.     

Second law optimization of convective heat transfer through a duct with constant heat flux

A second law analysis is carried out on convective heat transfer from a fluid flowing in a duct with constant heat flux. The entropy generated is expressed as a function of the initial temperature difference and the frictional pressure drop. Since the loss in available energy is directly proportional to the entropy generated, an optimum value of the initial temperature difference is found where the entropy generated is the minimum. A similar optimum is found for the ratio of heat transfer to pumping power. An optimum fluid velocity which corresponds to the minimum loss of available power is recommended.     

Entropy analyses for hyperbolic heat conduction based on the thermomass model

This paper is divided into three major sections with the first one introducing the concept of generalized entropy in extended irreversible thermodynamics briefly, that is, the entropy of a non-equilibrium system depend not only on the classical variables but also on the dissipative fluxes, which makes the hyperbolic equation of heat conduction based on the Cattaneo–Vernotte model compatible with the second law of thermodynamics. The second section deals with the hyperbolic heat conduction based on the thermomass model. According to the Einstein’s mass-energy relation, the phonon gas in dielectrics can be viewed as a kind of weighty compressible fluid, and the momentum equation of the phonon (thermomass) gas in the dielectrics, which consists of the driving force, inertia and resistance of phonon (thermomass) gas, is just the damped thermal wave equation. In the third section our analyses show that the contribution of the kinetic energy of the phonon gas in the expression of extended entropy based on the thermomass model is identical with that of the heat flux in the expression of generalized entropy in extended irreversible thermodynamics. It implies that the hyperbolic heat conduction based on the thermomass model is compatible with the second law of thermodynamics.     

The Second Law of Thermodynamics for a Two-Temperature Model of Heat Transport in Metal Films

ABSTRACT

The second law of thermodynamics asserts that heat will always flow “downhill”, i.e., from an object having a higher temperature to one having a lower temperature. For a parabolic rigid heat conductor with a single temperature T and a single heat-flux q this amounts to the statement that the inner product of q and ?T must be non-positive for every point x of the conductor and for every non-negative time t. For a homogeneous and isotropic body in which classical Fourier law with a heat conductivity coefficient k is postulated, the second law is satisfied if k is a positive parameter. For ultra-fast pulse-laser heating on metal films, a parabolic two-temperature model coupling an electron temperature T_e with a metal lattice temperature T_l has been proposed by several authors. For such a model, at a given point of space x and a given time t there are two different temperatures T_e and T_l as well as two different heat-fluxes q _e and q _l related to the gradients of T_e and T_l, respectively, through classical Fourier law. As a result, for a homogeneous and isotropic model the positive definiteness of the heat conductivity coefficients k_e and k_l corresponding to T_e and T_l, respectively, implies that the second law of thermodynamics is satisfied for each of the pairs (T_e, q _e) and (T_l, q _l), separately. Also, the positive definiteness of k_e and k_l, and of the corresponding heat capacities c_e and c_l as well as of a coupling factor G imply that a temperature initial-boundary value problem for the two-temperature model has unique solution. In the present paper, an alternative form of the second law of thermodynamics for the two-temperature model with k_l = 0 and q _l =  0 is obtained from which it follows that in a one-dimensional case the electron heat-flux q_e(x, t) has direction that is opposite not only to that of ?T_e(x, t)/?x but also to that of ?T_l(x, t + τ_T)/?x, where τ_T is an intrinsic small time of the model. Also, for a general two-temperature rigid heat conductor in which k_e, k_l, c_e, c_l, and G are positive, an inequality of the second law of thermodynamics type involving a pair (T_e ? T_l, q _e ?  q _l) is postulated to prove that a two-heat-flux initial-boundary value problem of the two-temperature model has a unique solution. For a one-dimensional case, the semi-infinite sectors of the plane ( q _l, q _e) over which uniqueness does not hold true are also revealed.     

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.     

Performance and flow-induced vibration characteristics for conical-ring turbulators

In the present study, the performance characteristics of the conical-ring turbulators are determined by means of the entropy-generation minimization method based on the second law and enhancement efficiency based on the first law of thermodynamics. The relations between these performance and flow-induced vibration characteristics have been examined. The maximum entropy generation, at the same Reynolds number, occurs in sequence by the conical rings with 10, 20 and 30 mm pitches, respectively. The conical rings are thermodynamically advantageous (N_s,a<1) up to 8000 Reynolds number with respect to entropy generation. The enhancement efficiency increases as the pitch decreases and varies between 0.86 and 1.16. The turbulators with 20 and 30 mm pitch, especially, produce vortices having low amplitudes up to a Reynolds number of 12,000.     

Second law analysis of a waste heat recovery steam generator

In recent years a great deal of attention is focussed on the efficient utilization of energy resources with minimum heat loss. There is a growing interest on second law analysis to minimize the entropy generation in various thermal units and thereby to improve and optimize the design and performance. In the present work, a waste heat recovery steam generator is considered, which consists of an economizer, an evaporator and a super heater. The unit produces superheated steam by absorbing heat from the hot flue gases. A general equation for the entropy generation has been proposed, which incorporates all the irreversibilities associated with the process. By using suitable non-dimensional operating parameters, an equation for entropy generation number is derived. The effect of various non-dimensional operating parameters, on the entropy generation number are investigated. The role of gas specific heat, non-dimensional inlet gas temperature difference ratio (τ), heat exchanger unit sizes (NTUB, NTUS, NTUE) on entropy generation number are also reported. The results will help to understand the influence of different non-dimensional operating parameters on entropy generation number, which in turn will be useful to optimize the performance of the unit.     

Thermodynamic stability of elementary chemical reactions proceeding at finite rates revisited using Lyapunov function analysis

The thermodynamic stability of a few representative elementary chemical reactions proceeding at finite rates has been investigated using the recently proposed thermodynamic Lyapunov function and following the steps of Lyapunov’s second method (also termed as the direct method) of stability of motion. The thermodynamic Lyapunov function; L_s, used herein is the excess rate of entropy production in the thermodynamic perturbation space, which thereby inherits the dictates of the second law of thermodynamics. This Lyapunov function is not the same as the excess entropy rate that one encounters in thermodynamic (irreversible) literature. The model chemical conversions studied in this presentation are A+B→v_xX and A+B⇌ν_xX. For the sake of simplicity, the thermal effects of chemical reactions have been considered as not adding to the perturbation as our main aim was to demonstrate how one should use systematically the proposed thermodynamic Lyapunov function following the steps of Lyapunov’s second method of stability of motion. The domains of thermodynamic stability under the constantly acting small disturbances, thermodynamic asymptotic stability and thermodynamic instability in these model systems get established.     

Entropic analysis of adsorption open cycles for air conditioning. Part 2: interpretation of experimental data

The full second‐law analysis, developed in Part 1 (M. Pons and A. Kodama, Int. J. Energy Res. 2000; 24 : 251–262) is applied to experimental results. That approach takes into account the irreversibilities due to the open character of the cycle. Measurements are performed on a solid desiccant cooling unit operated in the ventilation mode. Experimental data permit us to establish the entropy balance of the unit. The results show that the sum of all the considered entropy productions completely explain the difference between the Carnot COP and the actual COP of the unit. The effects of three experimental parameters are investigated: the rotation speed of the dehumidifier (desiccant wheel), the air velocity and the regeneration temperature. Experimental results show that there exists an optimal rotation speed which results from a combination between the different entropy productions in the cycle. When the air velocity is increased, together with an accordingly optimized rotation speed, the cooling capacity increases while the COP decreases due to increases in the entropy productions in the dehumidifier and sensible heat exchanger. Moreover, it appears that the most significant entropy productions take place in the dehumidifier and heating system. In the investigated experimental unit, these two entropy productions have similar magnitudes. However, when the regeneration temperature is increased, the irreversibilities due to mass exchanges with outside air become comparable to these and surely should not be forgotten in a global optimization of the process. The present analysis is a solid basis for reducing the largest entropy productions thus optimizing the process. Copyright © 2000 John Wiley & Sons, Ltd.     

CFD-based analysis of entropy generation due to mean and fluctuating fields during turbulent natural convection in a square enclosure

The current study aims to numerically investigate the entropy generation during the natural convection flow of air in a square cavity. The governing equations for the conservation of mass, momentum, energy, and turbulence are solved using a control volume-based technique employing the commercial code Fluent. Runs have been performed for both laminar and turbulent flow regimes by varying the Rayleigh number (Ra) from 10³ to 10¹⁰. On the other hand, various viscous distribution coefficients (ϕ = 10⁻⁴, 10⁻³, and 10⁻²) and constant Prandtl number (Pr = 0.71) were considered. Given the conflicting perspectives in the literature regarding the entropy generation under turbulent regimes, more research is needed to better understand the impact that the fluctuating flow has on entropy production. The four terms of entropy generation inherent to turbulent natural convection (entropy generation due to dissipation in the mean and the fluctuating velocity fields in addition to the heat flux due to the mean and the fluctuating temperature) are computed in the present work and compared to calculations based on only mean values of temperature and velocity gradients. It was found that taking into account the fluctuating terms of temperatures and velocities augment the total entropy generation by 10.10%, 14.43%, and, 17.70%, up to 32.60%, respectively, for Ra = 5 × 10⁸, Ra = 10⁹, Ra = 1.58 × 10⁹, and Ra = 10¹⁰. The gain shows the tendency to increase with the Rayleigh number. Thus, the fluctuating terms cannot be neglected particularly for high Rayleigh numbers. Furthermore, unlike entropy production due to the mean flow field, numerical outcomes reveal that the generated irreversibilities due to fluctuating flow are located around the upper hot and the lower cold corners of the heated walls. In addition, a numerical relationship between the first and the second laws of thermodynamics has been derived. A promising result that emerged from this study has shown that the Nusselt number and therefore the first law of thermodynamics is sufficient to estimate the heat part of entropy generation without the necessity of using the second law.     

Analysis of entropy generation using nanofluid flow through the circular microchannel and minichannel heat sink

In this paper, different types of entropy generations in the circular shaped microchannel and minichannel are discussed analytically using different types of nanoparticles and base fluids. In this analysis, Copper (Cu), alumina (Al₂O₃) as the nanoparticle and H₂O, ethylene glycol (EG) as the base fluids were used. The volume fractions of the nanoparticles were varied from 2% to 6%. In this paper, the irreversibility or entropy generation analysis as the function of entropy generation ratio, thermal entropy generation rate and fluid friction entropy generation rate for these types of nanofluids in turbulent flow condition have been analyzed using available correlations. Cu–H₂O nanofluid showed the highest decreasing entropy generation rate ratio (36%) compared to these nanofluids flow through the microchannel at 6 vol.%. The higher thermal conductivity of H₂O causes to generate much lower thermal entropy generation rate compared to the EG base fluid. The fluid friction entropy generation rate decreases fruitfully by the increasing of volume fraction of the nanoparticles. Cu–H₂O and Cu–EG nanofluid gave the maximum decreasing rates of the fluid friction entropy generation rate are 38% and 35% respectively at 6% volume fraction of the nanoparticles. Smaller diameter showed less entropy generation in case of all nanofluids.     

Entropy optimized flow of Darcy-Forchheimer viscous fluid with cubic autocatalysis chemical reactions

Background and objectiveThe dynamic of entropy generation phenomenon is important in industrial and engineering process and thermal polymer processing. In order to improve the thermal efficiency of industrial and systems, the main concern of scientists is to reduce the entropy generation. The optimized frame for the Darcy-Forchheimer flow accounted by curved surface has been worked out this continuation. The applications of the chemically reactive material are focused via heterogeneous and homogeneous chemical utilizations. The thermal and velocity slip constraints are imposed for investigating the flow phenomenon. Additionally, the determination of heating phenomenon is investigated by incorporating the heat source features. The importance of entropy generation and Bejan number is also signified.MethodologyNonlinear partial systems are reduced to dimensionless differential system through suitable variables. The problem consists of highly nonlinear equations are numerically worked out with appliances of ND-solve procedure.ResultsInfluence of fluid flow, thermal field, entropy rate, concentration and Bejan number via influential variables are examined. A slower velocity change due to implementation of slip is noticed. The applications of Brinkman number offer resistance to fluid particles while an enhancement in the Bejan number is claimed.ConclusionsFor an augmentation in curvature variable, the concentration and velocity show reverse effect. There is an increase in temperature distribution against heat generation parameter. Velocity field is reduced against higher porosity and slip parameters. Temperature has revers trends against radiation and thermal slip parameters. Larger Schmidt number decreases concentration distribution. Entropy rate is augmented versus larger radiation parameters. An augmentation in Brinkman number leads to improve the velocity filed whereas it reduces the Bejan number. Brinkman number influence on Bejan number is similar to that of homogenous reaction parameter on concentration. The comparative simulations against the reported results are performed.