Total Entropy Generation Number Research Articles

Thermodynamic optimisation of rectangular and elliptical microchannels with nanofluids

The thermodynamic optimisation of laminar flow in rectangular and elliptical microchannels subjected to low or high heat flux is analytically studied. Two mathematical models are developed, by incorporating the aspect ratio term, to evaluate entropy generation numbers. Two relations for calculating the conductivity and the viscosity of CuO-water nanofluids, based on experimental data from literature, are proposed. An entropy generation analysis is proposed to optimise the geometry of the microchannel and the working fluid for each heat flux condition. It has been revealed that at low heat flux, using water in microchannels with aspect ratio e = 1 is more efficient. However, at high heat flux, it is more advisable to use microchannels with the smallest possible aspect ratio containing CuO-water nanofluids with higher conductivity and higher nanoparticles concentration. For the two cases, the rectangular microchannel reaches the minimum value of total entropy generation number compared to the elliptical microchannel.

Magnetorheological rotational flow with viscous dissipation

Effects of a magnetic field and fluid nonlinearity are investigated for the rotational flow of the Carreau-type fluid while viscous dissipation is taken into account. The governing motion and energy balance equations are coupled, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow-gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, and the Deborah number on the stability of the flow were investigated. The introduction of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slow down the fluid motion. It, however, increases the fluid temperature. Moreover, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and increases with increasing Brinkman number.

Entropy Generation Analysis and Performance Evaluation of Turbulent Forced Convective Heat Transfer to Nanofluids

The entropy generation analysis of fully turbulent convective heat transfer to nanofluids in a circular tube is investigated numerically using the Reynolds Averaged Navier–Stokes (RANS) model. The nanofluids with particle concentration of 0%, 1%, 2%, 4% and 6% are treated as single phases of effective properties. The uniform heat flux is enforced at the tube wall. To confirm the validity of the numerical approach, the results have been compared with empirical correlations and analytical formula. The self-similarity profiles of local entropy generation are also studied, in which the peak values of entropy generation by direct dissipation, turbulent dissipation, mean temperature gradients and fluctuating temperature gradients for different Reynolds number as well as different particle concentration are observed. In addition, the effects of Reynolds number, volume fraction of nanoparticles and heat flux on total entropy generation and Bejan number are discussed. In the results, the intersection points of total entropy generation for water and four nanofluids are observed, when the entropy generation decrease before the intersection and increase after the intersection as the particle concentration increases. Finally, by definition of Ep, which combines the first law and second law of thermodynamics and attributed to evaluate the real performance of heat transfer processes, the optimal Reynolds number Reop corresponding to the best performance and the advisable Reynolds number Read providing the appropriate Reynolds number range for nanofluids in convective heat transfer can be determined.

Effect of Magnetic Field on Natural Convection and Entropy Generation in Al2O3/Water Nanofluid-Filled Enclosure With Twin Protruding Heat Sources

In this paper, the effect of magnetic field on natural convection of Al2O3/water nanofluid in an enclosure containing twin protruding heat sources placed on top and bottom walls arranged in-line and staggered manner is presented. For this purpose, coupled equations governing fluid flow and heat transfer are solved in Cartesian framework using streamline upwind/Petrov–Galerkin (SUPG) finite element method. Numerical computations are performed to predict the fluid flow, heat transfer, and entropy generation for a wide range of Hartmann number (0.0 ≤ Ha ≤ 100.0), Rayleigh number (103≤Ra≤106), and nanoparticle volume fraction (0.0≤ϕ≤0.1). The simulated results indicate that, for both in-line and staggered arrangement, the entropy generation due to heat transfer is significant along isothermal surfaces, whereas entropy generation due to fluid friction is higher at no-slip walls and along the regions of contact between adjacent recirculation cells. For both in-line and staggered arrangement, increase in global total entropy generation and average Nusselt number along top and bottom heat sources is obtained with decreasing Ha and increasing Ra. Furthermore, for both in-line and staggered arrangement, variation in global total entropy generation and average Nusselt number along top and bottom heat sources with increasing nanoparticle volume fraction, depend on both Ha and Ra.

Three dimensional simulation of natural convection and entropy generation in an air and MWCNT/water nanofluid filled cuboid as two immiscible fluids with emphasis on the nanofluid height ratio's effects

Abstract This paper reports a numerical study of the natural convection and entropy generation for a layered fluid system in a cuboid enclosure which is differentially heated from sides and filled by two immiscible gas/liquid fluids (air and MWCNTs-water nanofluid). This study emphasize on the effects of the liquid interface aspect ratio, solid volume fraction of nanofluid, and Rayleigh number on the fluid flow, heat transfer and entropy generation. The fluid flow streamlines, contours of local fluid friction irreversibility, temperature, and local heat transfer irreversibility in the 3D enclosure are obtained. The local and averaged Nusselt number and volumetric entropy generation are also discussed. The results show that the nanofluid interface aspect ratio has significant influences on the fluid flow, heat transfer performance and entropy generation. Moreover, it is shown that the total entropy generation and mean Nusselt number are reduced by increasing of nanofluid interface aspect ratio and are enhanced by increasing of Rayleigh number.

Entropy generation for mixed convection in a square cavity containing a rotating circular cylinder using a local radial basis function method

The entropy generation for steady mixed convection due to a concentric isothermal rotating circular cylinder within a square enclosure is numerically investigated using a local radial basis function interpolation method. The top and bottom walls of the enclosure are adiabatic while the left and right walls have lower constant temperature, and the rotating concentric circular cylinder with high constant temperature hence induces the mixed convection. Air is considered as the working fluid and Prandtl number is fixed at 0.71. With the restriction of Taylor instability for viscous fluid flow, the Reynolds number should be below 60 and ranges from 1 to 50 for present work. Numerical results are obtained for various irreversibility distribution ratios (10−3⩽Φ⩽10−1) and Richardson numbers (0.1⩽Ri⩽20). The variation of total entropy generation and average Bejan number with different parameters are discussed and analyzed in detail. The numerical results indicate that the total entropy generation increases with the irreversibility distribution ratio, Reynolds number and Richardson number generally. The average Bejan number decreases with the irreversibility distribution ratio and Richardson number generally while it almost keeps constant for Ri⩽1 and it decreases with Reynolds number remarkably for Ri⩾10 since the sufficient increase of entropy generation due to fluid friction corresponding to the obvious change of flow patterns. The maximum value of local entropy generation due to heat transfer and fluid friction is found around the wall of the rotating cylinder.

Second Law Analysis of Magnetorheological Rotational Flow With Viscous Dissipation

In this study, the influences of the applied magnetic field and fluid elasticity were investigated for a nonlinear viscoelastic fluid obeying the Carreau equation between concentric annulus where the inner cylinder rotates at a constant angular velocity and the outer cylinder is stationary. The governing motion and energy balance equations are coupled while viscous dissipation is taken into account, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, the Deborah number, and the fluid elasticity on the stability of the flow were investigated. The application of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slowdown the fluid motion and thus increases the fluid temperature. However, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and it increases with increasing Brinkman number.

Entropy generation of mixed convection in a vertical parallel plate microchannel with asymmetric wall heat flux

In this study, the results of a parametric analysis of the entropy generation of mixed convection in a vertical parallel plate microchannel with asymmetric wall heat flux are presented. The fluid flow was assumed as Newtonian and fully developed. Analytical equations were derived to estimate the entropy generation and a specific MATLAB code was created to solve the governing equations. The effects of the modified mixed convection parameter (Grq/Re), the Brinkman number (Br), the Knudsen number (Kn), and the ratio of wall heat flux (rq) on the entropy generation are presented and discussed. The results revealed that, while increment of Kn reduces the entropy generation, conversely, increment of Br/τ enhances it. For each condition analysed, the entropy generation number related to heat transfer (NR) is smaller than the entropy generation number related to fluid friction (NF), indicating that NF is dominant on the total entropy generation number (NS).

Entropy generation analysis for laminar thermal augmentation with conical strip inserts in horizontal circular tubes

Our previous investigations demonstrated that conical strip inserts have good thermo-hydraulic performances based on evaluation criteria of the First Law of Thermodynamics. The present work is dedicated to further analyze the performances of these inserts from a viewpoint of entropy generation. Effects of alignment method and geometrical parameters on entropy generations of laminar heat transfer in the tubular flow are investigated. Local entropy generations are presented for discussion. Results show that entropy generation rates caused by non-staggered strips are about 81.1% that of staggered alignment, while the heat transfer rates and PECs of the former are about 33.8% and 13.5% larger than the latter counterparts, respectively. Moreover, the entropy generation rate (and thus irreversible loss) caused by heat transfer process overwhelms the counterpart by viscous flow. The total entropy generation number of enhanced tube, ranging between 0.0657 and 0.0975, is most sensitive to geometry angle with a maximum averaged relative variation of 32.2%. Its variation trend with Re is concave with a pit at Re = ∼600. In brief, non-staggered inserts with a larger geometry angle and smaller strip-wall gap and pitch, facilitate a better thermo-hydraulic performance at Re = ∼600 from the viewpoint of exergy loss reduction.

Heat transfer and entropy generation of natural convection in nanofluid-filled square cavity with partially-heated wavy surface

A numerical investigation is performed into the heat transfer performance and entropy generation of natural convection in a partially-heated wavy-wall square cavity filled with Al2O3–water nanofluid. The simulations focus specifically on the effects of the nanoparticle volume fraction, the Rayleigh number and the wavy-surface geometry parameters on the mean Nusselt number, total entropy generation and Bejan number. The results show that the mean Nusselt number increases and the total entropy generation decreases as the volume fraction of Al2O3 nanoparticles increases. By contrast, the mean Nusselt number reduces and the total entropy generation increases as the amplitude and wavelength of the wavy-surface increase. Moreover, the Bejan number increases with an increasing amplitude and increasing wavelength of the wavy-surface. Finally, for all values of the Rayleigh number, the Nusselt number increases and the entropy generation reduces as the peak in the wavy surface approaches the horizontal center-plane of the cavity. Overall, the results presented in this study provide a useful source of reference for enhancing the natural convection heat transfer performance in partially-heated wavy-wall cavities while simultaneously reducing the entropy generation.

An analysis on free convection flow, heat transfer and entropy generation in an odd-shaped cavity filled with nanofluid

A study of natural convective flow, heat transfer and entropy generation in an odd-shaped geometry is presented here. The geometry considered is a combination of the horizontal and vertical enclosure shapes. The cavity is filled with Cu–water nanofluid. The numerical study focuses specifically on the effect of natural convection parameter and solid volume fraction of nanoparticle on the average Nusselt number, total entropy generation and Bejan number. Also isotherms, stream function and entropy generation due to heat transfer are presented for various Rayleigh number and solid volume fraction. The governing equations are solved by using penalty finite element method with Galerkins weighted residual technique. The results reveal that increasing Rayleigh number causes increase of the average Nusselt number as well as the heat transfer term of entropy generation and decrease of the viscous term. The proper choice of Rayleigh number could be able to maximize heat transfer rate simultaneously minimizing entropy generation.

Forced convection in micro-channels filled with porous media in local thermal non-equilibrium conditions

An analytic solution on fully developed forced convection, in parallel plates porous micro-channels is accomplished in Local Thermal Non-Equilibrium (LTNE) condition. The analysis is realized in steady state regime for rarefied gaseous slip flows between two parallel plates with assigned heat flux. The Darcy–Brinkman model is considered in the momentum equation and two energy equations are used to evaluate solid and fluid temperatures. The entropy generation analysis is performed and the total entropy generation number is evaluated as a function of the different dimensionless parameters. The effect of tangential momentum and thermal accommodation coefficients are examined. Results are reported in terms of average Nusselt numbers, dimensionless temperature profiles and total entropy generation number as a function of Biot number (Bi), effective thermal conductive ratio (κ), Darcy number (Da), accommodation coefficients (tangential momentum and thermal) and Knudsen number. Results show that heat transfer increases as Bi increases and reaches asymptotic values. Different trends are observed with respect to tangential momentum accommodation coefficient for assigned thermal accommodation. Total entropy generation number as a function of Da−0.5 presents minimum values with respect to Bi, accommodation coefficients and Brinkman number.

Heat transfer in flow of nonlinear fluids with viscous dissipation

The rotational flow of viscoplastic fluids between concentric cylinders is examined while dissipation due to viscous effects through the energy balance. The viscosity of fluid is simultaneously dependent on shear rate and temperature. Exponential dependence of viscosity on temperature is modeled through Nahme law, and the shear dependency is modeled according to the Carreau equation. Hydrodynamically, stick boundary conditions are applied, and thermally, both constant temperature and constant heat flux on the exterior of cylinders are considered. The governing motion and energy balance equations are coupled adding complexity to the already highly correlated set of differential equations. Introduction of Nahme number has resulted in a nonlinear base flow between the cylinders. As well, the condition of constant heat flux has moved the point of maximum temperature toward the inner cylinder. Taking viscous heating into account, the effects of parameters such as Nahme and Brinkman numbers, material time and pseudoplasticity constant on the stability of the flow are investigated. Moreover, the study shows that the total entropy generation number decreases as the fluid elasticity increases. It, however, increases with increasing Nahme and Brinkman numbers.

Analysis of heatlines and entropy generation during free convection within trapezoidal cavities

In this article natural convection flows have been studied within trapezoidal cavities where left wall of the cavity is hot and right wall is maintained at constant cold temperature while the top and bottom walls are adiabatic. The results are presented in terms of streamlines, heatlines, isotherms, entropy generation due to fluid friction, entropy generation due to heat transfer, average Bejan number, total entropy generation and average Nusselt number. It may be concluded that, the trapezoidal cavity with φ=60° is the optimal shape for thermal processing at Pr=0.015 whereas square cavity (φ=90°) is the optimal design for the thermal processing at Pr=7.2 based on lower Stotal and higher Nul¯.

Numerical Simulations for the Analysis of Entropy Generation During Natural Convection in Porous Rhombic Enclosures

Entropy generation analysis has been introduced to investigate the effectiveness in heat transfer during natural convection within porous rhombic enclosures of various inclination angles ϕ for differential (case 1) and Rayleigh Benard (case 2), heating situations. The results are presented in terms of streamlines (ψ), isotherms (θ), and entropy generation maps (S θ and S ψ ). Entropy production on the basis of various heating patterns and geometrical orientations have been reported based on the relation between total entropy generation (Stotal) and average Nusselt number via Bejan Number, which relates the available thermal energy to irreversibilities.

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.

Entropy generation of forced convection film condensation on a horizontal elliptical tube

The aim of this study is to analyze the entropy generation number in forced convection film condensation on a horizontal isothermal elliptical tube. A numerical approach has been used to investigate how parameters, including ellipticity of ellipse, Reynolds and Brinkman numbers affect the irreversibility. The results show that the minimization of total entropy generation number (NS) can be achieved by reducing the values of Reynolds and Brinkman numbers. Also, it was concluded that the effect of ellipticity on total entropy generation number is significant for e>0.7 and increasing ellipticity, increases the amount of NS.

The effect of temperature-dependent viscosity on entropy generation in curved square microchannel

The effect of temperature-dependent viscosity on the thermodynamic performance of the curved square microchannel in laminar flow is numerically investigated in terms of entropy generation. The classical Navier–Stokes equations and constant wall temperature boundary conditions are adopted; aniline and ethylene glycol are selected as the working fluids. The results show that the Nusselt number, heat transfer entropy generation number and frictional entropy generation number are less for the temperature-dependent viscosity than for the constant viscosity when aniline is heated. However, the opposite conclusions can be drawn when aniline is cooled. The total entropy generation number extrema exist for the cases of aniline heated and cooled. The differences between the results obtained with and without considering temperature-dependent viscosity is more obvious when aniline is cooled than when aniline is heated. The difference between the Brinkman numbers obtained with and without considering temperature-dependent viscosity grows as the mass flow rate increases when ethylene glycol is heated. The temperature-dependent effect on entropy generation is more pronounced for ethylene glycol than for aniline, since the former has larger viscosity than the latter.

Viscous dissipation effect on entropy generation in curved square microchannels

The viscous dissipation effect on the thermodynamic performance of the curved square microchannels in laminar flow is numerically investigated. The classical Navier–Stokes equations are adopted; aniline and ethylene glycol are selected as the working fluids. The results show that the heat transfer entropy generation number and frictional entropy generation number augment relatively under viscous dissipation effect for the case of fluid heated, and the opposite results can be found for the case of fluid cooled. The heat transfer entropy generation number increases with Reynolds number at large Reynolds number region under viscous dissipation effect when ethylene glycol is heated. The total entropy generation number extremum exists for aniline, and the extremum happens earlier when aniline is heated than when aniline is cooled. The smaller the curvature radius is, the earlier the extremum appears. The extremum does not occur for ethylene glycol due to the predomination of frictional entropy generation in the total entropy generation.

Effects of Thermal Boundary Conditions on Entropy Generation during Natural Convection

A comprehensive numerical study on entropy generation during natural convection is studied in a square cavity subjected to a wide variety of thermal boundary conditions. Entropy generation terms involving thermal and velocity gradients are evaluated accurately based on the elemental basis set via the Galerkin finite element method. The thermal and fluid irreversibilities during the conduction and convection dominant regimes are analyzed in detail for various fluids (Pr = 0.026,988.24) within Ra = 103–105. Further, the effect of Ra on the total entropy generation and average Bejan number is discussed. It is observed that thermal boundary conditions significantly affect the thermal mixing, temperature uniformity, and the entropy generation in the cavity. A case where the bottom wall is hot isothermal with linearly cooled side walls and adiabatic top wall is found to result in high thermal mixing and a higher degree of temperature uniformity with minimum total entropy generation.