Entropy generation in turbulent natural convection due to internal heat generation

In this study numerical predictions of entropy generation in turbulent natural convection due to internal heat generation in a square cavity are reported for the first time. Results of entropy generation analysis are obtained by solving the entropy generation equation. The values of velocity and temperature, which are the inputs of the entropy generation equation, are obtained by an improved thermal lattice-BGK model proposed in this paper. The analyzed range is wide, varying from the steady laminar symmetric state to the fully turbulent state. Distributions of entropy generation numbers, for various Rayleigh numbers, Prandtl numbers, and Eckert numbers, are given.     

Entropy generation in combined heat and mass transfer

Irreversible entropy generation for combined forced convection heat and mass transfer in a twodimensional channel is investigated. The heat and mass transfer rates are assumed to be constant on both channel walls. For the case of laminar flow, the entropy generation is obtained as a function of velocity, temperature, concentration gradients and the physical properties of the fluid. The analogy between heat and mass transfer is used to obtain the concentration profile for the diffusing species. The optimum plate spacing is determined, considering that either the mass flow rate or the channel length are fixed. For the turbulent flow regime, a control volume approach that uses heat and mass transfer correlations is developed to obtain the entropy generation and optimum plate spacing.     

Entropy flow and generation in radiative transfer between surfaces

Entropy of radiation has been used to derive the laws of blackbody radiation and determine the maximum efficiency of solar energy conversion. Along with the advancement in thermophotovoltaic technologies and nanoscale heat radiation, there is an urgent need to determine the entropy flow and generation in radiative transfer between nonideal surfaces when multiple reflections are significant. This paper investigates entropy flow and generation when incoherent multiple reflections are included, without considering the effects of interference and photon tunneling. The concept of partial equilibrium is applied to interpret the monochromatic radiation temperature of thermal radiation, T_λ(λ, Ω), which is dependent on both wavelength λ and direction Ω. The entropy flux and generation can thus be evaluated for nonideal surfaces. It is shown that several approximate expressions found in the literature can result in significant errors in entropy analysis even for diffuse-gray surfaces. The present study advances the thermodynamics of nonequilibrium thermal radiation and will have a significant impact on the future development of thermophotovoltaic and other radiative energy conversion devices.     

Entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes

The entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes was numerically performed by using a Reynolds stress model. The simulations were conducted for a smooth tube and five cases of corrugated tubes with Reynolds number (Re) ranging from 10,020 to 40,060 at a constant wall temperature condition. The effects of corrugation pitch and height on the flow patterns as well as local thermal and frictional entropy generation are detailed in the near wall region. The results indicate that the local heat transfer entropy generation is significantly evident at the sub-layer region and the detached vortex region, and the local thermal entropy is improved with increases in the secondary flow. Local friction entropy generation is mainly located at the windward of the corrugation and the severely turbulent fluctuation region and is mainly induced by the velocity gradient. The average friction entropy generation exhibits an exponential growth, while the average heat transfer and the total entropy generation display a linear growth trend with increased Re. The average Bejan number (Be) exhibits an exponential decline, and the minimum value can reach 0.69. From a comprehensive viewpoint, it is optimal for the Re to be lower than 30,050. When Re <20,030, higher and dense corrugations are beneficial. When 20,030?Hl/D?=?0.08 is not recommended.     

Entropy generation analysis of nanofluids flow in various shapes of cross section ducts

The selection of flow passage's cross section shape is important in thermal system design such as compact heat exchanger. A variety of duct's shapes can be used to enhance the thermal performance. However, it must be noted that different thermal and friction characteristics can be initiated due to this approach. Therefore this paper investigates the entropy generation characteristics of three types of duct's cross section subjected to constant heat flux. The considered shapes are circular, square and triangle (equilateral). Al₂O₃ and MWCNT based nanofluids are used as working fluids in the analysis. The study found that the total entropy generation of Al₂O₃ based nanofluids decreases with the increase of particle volume fractions. However, this parameter increases when working fluid's mass flow rate and heat flux applied to the duct increase. On the aspect of cross section's shape, circular duct exhibits lowest total entropy generation compared to other considered shapes. Moreover, it was also found that MWCNT based water nanofluids exhibit lower total entropy generation compared to Al₂O₃ based nanofluids due to its high thermal conductivity value.     

Experimental investigation of oxide nanofluids laminar flow convective heat transfer

In the present investigation nanofluids containing CuO and Al₂O₃ oxide nanoparticles in water as base fluid in different concentrations produced and the laminar flow convective heat transfer through circular tube with constant wall temperature boundary condition were examined. The experimental results emphasize that the single phase correlation with nanofluids properties (Homogeneous Model) is not able to predict heat transfer coefficient enhancement of nanofluids. The comparison between experimental results obtained for CuO / water and Al₂O₃ / water nanofluids indicates that heat transfer coefficient ratios for nanofluid to homogeneous model in low concentration are close to each other but by increasing the volume fraction, higher heat transfer enhancement for Al₂O₃ / water can be observed.     

Characteristics of flow and heat transfer of nanofluids under laminar states

The current article used four different models (single-phase, Mixture, Eulerian, and discrete phase model) to investigate the flow and heat transfer characteristics of nanofluids under a laminar state. We explored the Al₂O₃-water nanofluid inside a microscale trapezoidal channel and the CuO-oil inside a circular channel with a regular size. The velocity and temperature fields of nanofluids were discussed by comparing the differences among each model. It is revealed that the change of flow characteristics of nanofluid plays a more decisive role in its heat transfer enhancement besides the improvement of its physical properties.     

Entropy generation minimization of combined heat and mass transfer devices

This paper details a simple procedure by which the entropy generation in simultaneous heat and mass exchange devices can be minimized. Effectiveness for these devices is defined and a new parameter, ‘modified heat capacity rate ratio’ is introduced. It is found that the entropy generation of a combined heat and mass exchange device is minimized (at constant value of effectiveness) when the modified heat capacity rate ratio is equal to one irrespective of the value of other independent parameters. Several typical examples of the cooling towers have been studied to illustrate this concept. A practical application of the concept is also illustrated using a humidification–dehumidification desalination system.     

Entropy generation due to flow across the abrupt contraction of pipe joints

The flow experiencing the abrupt contraction suffers from the viscous dissipation due to vast change in flow field across the plane of contraction. In the present study, simulation of flow field and entropy generation rate due to viscous dissipation are carried out for different upstream Reynolds numbers. The flow situation is considered to be isothermal to avoid the influence of heat transfer on the entropy generation rate. A control volume approach is introduced when discretizing the governing equations of flow. In order to secure the grid independent solution the grid independent tests are conducted. It is found that overshooting of axial velocity occurs along the symmetry axis across the plane of contraction. Entropy generation rate enhances with increasing Reynolds numbers. The location of maximum entropy generation rate becomes almost identical for all Reynolds numbers considered in the present study.     

Heat transfer enhancement of nanofluids flow in microtube with constant heat flux

In this paper, laminar convective heat transfer in a two-dimensional microtube (MT) with 50 μm diameter and 250 μm length with constant heat flux is numerically investigated. The governing (continuity, momentum and energy) equations were solved using the finite volume method (FVM) with the aid of SIMPLE algorithm. Different types of nanofluids Al₂O₃, CuO, SiO₂ and ZnO, with different nanoparticle size 25, 45, 65 and 80 nm, and different volume fractions ranged from 1% to 4% using ethylene glycol as a base fluid were used. This investigation covers Reynolds number in the range of 10 to 1500. The results have shown that SiO₂–EG nanofluid has the highest Nusselt number, followed by ZnO–EG, CuO–EG, Al₂O₃–EG, and lastly pure EG. The Nusselt number for all cases increases with the volume fraction but it decreases with the rise in the diameter of nanoparticles. In all configurations, the Nusselt number increases with Reynolds number.     

Numerical analysis of laminar flow heat transfer of nanofluids in a flattened tube

In this work, a three-dimensional analysis is used to study the heat transfer performance of nanofluid flows through a flattened tube in a laminar flow regime and constant heat flux boundary condition. CuO nanoparticles dispersed in ethylene glycol with particle volume concentrations ranging between 0 and 4 vol.% were used as working fluids for simulating the heat transfer of nanofluids. Effects of some important parameters such as nanoparticle volume concentration, particles Brownian motions, and Reynolds number on heat transfer coefficient have been determined and discussed in details. Results have shown that the heat transfer coefficient increases with increase in the volume concentration level of the nanoparticle, Brownian motion and the Reynolds number. Numerical results have been validated by comparison of simulations with those available in the literature.     

H形树网通道中湍流对流换热熵产分析

在管壁恒热流密度条件下,以H形树网通道中湍流对流换热过程为研究对象,推导出了熵产率解析式和每一级通道无量纲数Be的解析式,分析了通道级数对熵产率和无量纲数Be的影响。结果表明:对于树网中任意一级通道,传热熵产率随着通道级数的增大而呈指数增长,粘性耗散熵产率随着通道级数的增大而减小;对于树网中的n级通道,总传热熵产率和总粘性耗散熵产率均随通道级数的增大而增大,但总传热熵产率的增大速率大于总粘性耗散熵产率的增大速率,并且总粘性耗散熵产率随通道级数的增大而趋近于一确定值。任意一级通道的Be数随第一级通道的Be数增大而增大,随通道级数的增大而趋近于1。     

Entropy generation of convection heat transfer in an asymmetrically heated packed duct

An expression for the volumetric rate of entropy generation has been derived and displayed graphically to analyze the convection heat transfer for a fully established flow in a rectangular packed duct with L/H=16 and H/W=0.125. The top and bottom walls of the duct are heated by constant, asymmetric heat fluxes, while the other walls are insulated that is the L2 thermal boundary conditions. Entropy generation maps reveal the regions where excessive entropy generation occurs due to physical and geometric parameters for a specified task within the system.     

Numerical study of turbulent flow and heat transfer characteristics of nanofluids considering variable properties

Turbulent flow and heat transfer of three different nanofluids (CuO, Al₂O₃ and SiO₂) in an ethylene glycol and water mixture flowing through a circular tube under constant heat flux condition have been numerically analyzed. New correlations for viscosity up to 10% volume concentration for these nanofluids as a function of volume concentration and temperature are developed from the experiments and are summarized in the present paper. In our numerical study, all the thermophysical properties of nanofluids are temperature dependent. Computed results are validated with existing well established correlations. Nusselt number prediction for nanofluids agrees well with Gnielinski correlation. It is found that nanofluids containing smaller diameter nanoparticles have higher viscosity and Nusselt number. Comparison of convective heat transfer coefficient of CuO, Al₂O₃ and SiO₂ nanofluids have been presented. At a constant Reynolds number, Nusselt number increases by 35% for 6% CuO nanofluids over the base fluid.     

Alterations to coherent flow structures and heat transfer due to pulsations in an impinging air-jet

An investigation was carried out to study the effect of flow pulsation on the characteristics of a planar air jet impinging normally on a heated surface. Such information was further utilized to determine the influence of flow characteristics in the plane of impingement on Nusselt number distribution. Time-resolved system properties were investigated with modern instrumentation that allowed instantaneous heat transfer and flow velocity measurements to be performed simultaneously. Based on good coherence function estimates between the signals, heat transfer measurements were used in return to infer flow dynamics near the impingement surface. Experiments were performed for steady and pulsating jets at jet Reynolds numbers of 1 000, 5 500, and 11 000, pulse frequencies up to 82 Hz (corresponding to Strouhal numbers below 0.13), and pulse amplitude at the nozzle exit up to 50 % of the mean flow velocity. Special techniques commonly used for periodically disturbed flow fields elucidated the dynamics of the pulse and associated coherent flow structures. Results indicated the parametric conditions for which alterations are expected in time-averaged heat transfer from the surface. Engineering applications include cooling of electronic packages and heat transfer to gas turbine blades.     

Forced convective heat transfer of nanofluids in microchannels

Convective heat transfer coefficient and friction factor of nanofluids in rectangular microchannels were measured. An integrated microsystem consisting of a single microchannel on one side, and two localized heaters and five polysilicon temperature sensors along the channel on the other side were fabricated. Aluminum dioxide (Al₂O₃) with diameter of 170 nm nanofluids with various particle volume fractions were used in experiments to investigate the effect of the volume fraction of the nanoparticles to the convective heat transfer and fluid flow in microchannels. The convective heat transfer coefficient of the Al₂O₃ nanofluid in laminar flow regime was measured to be increased up to 32% compared to the distilled water at a volume fraction of 1.8 volume percent without major friction loss. The Nusselt number measured increases with increasing the Reynolds number in laminar flow regime. The measured Nusselt number which turned out to be less than 0.5 was successfully correlated with Reynolds number and Prandtl number based on the thermal conductivity of nanofluids.     

Pool boiling heat transfer of non-Newtonian nanofluids

This paper reports on the investigation of pool boiling heat transfer of γ-Al₂O₃/CMC non-Newtonian nanofluids. To prepare nanofluids, γ-Al₂O₃ nanoparticles were dispersed in CMC solution (carboxy methyl cellulose in water) using ultrasonic mixing and mechanical mixer. Different concentrations of CMC non-Newtonian fluids and γ-Al₂O₃/CMC non-Newtonian nanofluids were tested under nucleate pool boiling heat transfer conditions. Experiments were carried out at atmospheric pressure. Results show that the pool boiling heat transfer coefficient of CMC solutions is lower than water. The decrease in boiling heat transfer is more pronounced at higher CMC concentrations and, as a result, higher solution viscosity. Adding nanoparticles to CMC non-Newtonian solutions results in an improved boiling heat transfer performance. The enhancement in the boiling heat transfer coefficient increases with the nanoparticle concentration; at a concentration of 1.4 wt.%, the boiling heat transfer coefficient increases by about 25% when compared to the base fluid.     

Analytical solution for slip flow and heat transfer due to a stretching sheet

An analysis has been carried out to investigate the analytical solution to the flow and heat transfer characteristics of a viscous flow over a stretching sheet in the presence of second‐order slip in flow. The governing partial differential equations of flow and heat transfer are converted into non‐linear ordinary differential equations by using suitable similarity transformations. The exact solution of momentum equation is assumed in exponential form and analytical solutions of heat transfer for both PST and PHF cases are obtained by the power series method in terms of Kummer's hypergeometric function. The temperature profiles are drawn for different governing parameters. The numerical values of wall temperature gradient and wall temperature are compared with earlier numerical results which have a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21044     

The rate of heat flow through a flat vertical wall due to conjugate heat transfer

Free convection along both sides of a vertical flat plate is studied within the framework of the laminar boundary-layer theory and for the case where only the temperature of the fluid far away from the wall is prescribed. Corrections to the Pohlhausen solution for the temperature at the plate surface are calculated. It is found that for good thermal conductors, the corrections are small (within a few percent), while for poor thermal conductors the corrections may be substantial (～30% for a wall with conductivity similar to brick). In addition, expressions for the heat transfer coefficient h as well as for the Nusselt number are derived and the corresponding convective heat transfer rate is determined.