Frictional Entropy Generation Research Articles

Entropy generation and exergy efficiency analysis of ethylene glycol-water based nanodiamond + Fe3O4 hybrid nanofluids in a circular tube

The entropy generation and exergy efficiency of nanodiamond+Fe3O4 hybrid nanofluids in a circular tube are inspected experimentally. The hybrid nanofluids were prepared in a 60% ethylene glycol and 40% water by weight base fluid and their thermophysical properties were evaluated at different particle loadings and temperatures. The pumping power, friction factor, and heat transfer were evaluated at various particle loading (0.05% to 0.2%) and Reynolds number (2000 to 8000) as well. The results indicated that the thermal conductivity and viscosity are augmented by 14.65% and 79%, respectively at 0.2% particle loading and 60 °C compared to the base fluid. At a particle loading of 0.2% nanofluid and a Reynolds number of 7218, the following results are obtained compared to the base fluid data: the Nusselt number, frictional entropy generation, exergy efficiency, friction factor, and thermal performance factor are increased by 19.67%, 210.6%, 17.54%, 15.11%, and 14.19%, respectively; while the thermal entropy generation is decreased by 22.93%. New regression equations are modeled to evaluate the Nusselt number, friction factor, and thermophysical properties.

RETRACTED: Free convection of non‐Newtonian nanofluid flow inside an eccentric annulus from the point of view of first‐law and second‐law of thermodynamics

AbstractThe current work aims to perform the hydrothermal and entropy generation (EG) characteristics in a naturally cooled eccentric horizontal annulus filled with non‐Newtonian water‐magnetite/CNT nanofluid (NF). The wall temperature of both cylinders is constant and the temperature of the outer cylinder is lower than that of the inner cylinder. The impacts of vertical eccentricity, nanoadditive concentration (φ) and Rayleigh number () on the first and second‐laws performance features of the annulus are investigated numerically. It was found the average Nusselt number (), the global thermal EG (TEG) and the global frictional EG (FEG) augment with boosting both the and φ. In addition, it was depicted that the negative eccentricity is desirable and undesirable from the perspective of the first and second‐laws of thermodynamics. Moreover, the outcomes revealed that the first‐law/second‐law performance of the aqueous magnetite/CNT NF is better/weaker than that of the aqueous magnetite NF. Furthermore, for all the examined cases, the TEG rates are much higher than the FEG rates, and as a result, the pattern of total EG changes follows the TEG. Among all the studied cases, the minimum total EG was 4 W/K, which belonged to the case of = 0.9%, = 0%, = 103 and = 0.001.

Entropy and thermal performance analysis of PCM melting and solidification mechanisms in a wavy channel triplex-tube heat exchanger

This paper aims to perform the entropy analysis and thermal performance evaluation of a wavy-channels triplex-tube latent heat storage heat exchanger (LHSHE) during melting and solidification mechanisms. The system with different wave amplitudes was examined for different temperatures and Reynolds numbers of the heat transfer fluid (HTF). Water is passed in the inner and outer tubes in opposite directions and the PCM is placed in the middle tube. The heat exchanger was analyzed based on the temperature, liquid fraction and velocity of the PCM as well as thermal (ST‴) and frictional (Sf‴) entropy generation rates. The results show that for a higher wave amplitude, shorter melting and solidification times are achieved. Both frictional and thermal entropy generation rates increase to the maximum values and then decrease during the melting and solidification. The frictional entropy generation rate reaches almost zero quickly during the solidification. For both melting and solidification, the magnitude of ST‴ is significantly higher than Sf‴ in the phase change problem. The maximum values of ST‴ are 0.05 and 0.13 W/Km3 for the melting and solidification mechanisms, respectively, for the dimensionless wave amplitude of 0.3. The results show the crucial role of entropy generation on the performance of the LHSHE.

The entropy generation analysis of forward and backward laminar water flow in a plate-pin-fin heatsink considering three different splitters

The application of splitters has been proven to be useful to control the separated wake downstream of the pin-fins. This paper aims to evaluate the thermal (Ṡth) and frictional (Ṡf) irreversibility rates in the fluid flow inside the plate-pin-fin heatsinks (PPFHSs). To this end, the numerical analysis of forward and backward water flow inside the PPFHS with three different attached splitters was performed considering Re of between 50 and 250. The main objective was to determine the locations with intense thermal and frictional entropy generation rates inside the fluid flow geometry. Based on the results, the frictional entropy generation rate is significantly lower than that the thermal term. Also, the pin-fin with arched splitter has the minimum thermal irreversibilities as compared to straight and wavy splitters. Furthermore, the major irreversibilities are associated with the locations near the pin-fin lateral and frontal surfaces as well as the plate fin walls and heatsink upper case and lower base. Moreover, it was shown that for all considered cases and two flow directions, the increasing of the Re results in decreasing and increasing the thermal and frictional entropy generation rates, respectively.

Hydrothermal and entropy generation specifications of a hybrid ferronanofluid in microchannel heat sink embedded in CPUs

The objective of this numerical work is to evaluate the first law and second law performances of a hybrid nanofluid flowing through a liquid-cooled microchannel heatsink. The water-based hybrid nanofluid includes the Fe3O4 and carbon nanotubes (CNTs) nanoparticles. The heatsink includes a microchannel configuration for the flow field to gain heat from a processor placed on the bottom of the heatsink. The effects of Fe3O4 concentration (φFe3O4), CNT concentration (φCNT) and Reynolds number (Re) on the convective heat transfer coefficient, CPU surface temperature, thermal resistance, pumping power, as well as the rate of entropy generation due to the heat transfer and fluid friction is examined. The results indicated higher values of convective heat transfer coefficient, pumping power, and frictional entropy generation rate for higher values of Re, φFe3O4 and φCNT. By increasing Re, φFe3O4and φCNT, the CPU surface temperature and the thermal resistance decrease, and the temperature distribution at the CPU surface became more uniform. To achieve the maximum performance of the studied heatsink, applying the hybrid nanofluid with low φFe3O4and φCNT was suggested, while the minimum entropy generation was achieved with the application of nanofluid with high φFe3O4and φCNT.

Second law analysis of recharging microchannel using entropy generation minimization method

This work deals with numerical study of entropy generation in recharging and simple microchannel to explore effect of geometrical modification on thermodynamic irreversibility in a system. This work also investigates effects of geometrical and thermo-physical parameters on entropy generation in recharging microchannel system, by varying number of small channels, substrate thickness, channel wall width, channel aspect ratio, substrate material, and applied heat flux. Numerical simulations are carried out by considering water as working fluid with Reynolds number 100-500. Results reveal that recharging microchannel shows maximum 47% reduction in total entropy generation compared to simple microchannel, which indicates that thermodynamic irreversibility is lower in recharging microchannel compared to simple microchannel. Thermal entropy generation in recharging microchannel decreases with increasing number of small channels, channel aspect ratio, and substrate material thermal conductivity, whereas it increases with increasing substrate thickness, channel wall width, and applied heat flux. Moreover, frictional entropy generation in recharging microchannel is invariant with substrate thickness, channel wall width, substrate material, and applied heat flux. These parametric investigations indicate that consideration of entropy generation in microchannel solid substrate during entropy generation analysis is quite important, as it strongly influence entropy generation in a system.

Heat transfer of nanofluid through helical minichannels with secondary branches

Heat transfer, fluid flow characteristics and entropy generation of water-Al2O3 nanofluid for cylindrical heat sinks with helical minichannels that have secondary branches are investigated experimentally. The minichannels helix angles are 45, 60 and 90 degrees; the volume fraction of nanoparticles variation is 0.05% – 0.1%; the Reynolds number range is between 113 to 478. The effects of the helix angle of minichannels, Reynolds number and nanoparticle volume fraction are studied. The heat transfer enhances with increasing Reynolds number, decreasing helix angle and increasing volume fraction of nanoparticles. However, with increasing Reynolds number, increasing helix angle and decreasing nanoparticles volume fraction, the friction factor decreases. The experimental results show that the secondary branches decreased the friction factor and Nusselt number. The maximum enhancement of Nusselt number in helix angle 60 and 45 for pure water are 31.1% and 51.3% greater in comparing with the straight minichannel, respectively; moreover, maximum enhancement of the Nusselt number of nanofluid compared with the pure water was about 14.3% for 0.1% vol. The thermal entropy generation rate decreases and, the frictional entropy generation rate increases with increasing the nanoparticles volume fraction and decreasing the helix angle. Furthermore, two new correlations are obtained for the Nusselt number and friction factor.

Research on the Thermal Hydraulic Performance and Entropy Generation Characteristics of Finned Tube Heat Exchanger with Streamline Tube

Thermal hydraulic performance of the fin-and-tube heat exchanger is presented in this paper. The purpose of this investigation was to investigate the heat transfer mechanism and flow characteristics in the finned tube heat exchanger with streamline tube. The streamline tube in this paper had the streamline cross section which was composed of a semicircle and a half diamond. Three-dimensional numerical simulation was presented and validated by the experiment and the other numerical simulation from public articles. The present simulation had good agreement with the experimental results. The difference of the j factor and f factor between the experimental results and present simulation results by k-ε-enhance model was less than 7.6%. The geometrical parameters were considered as every single variable to investigate the thermal hydraulic performance. The results showed that smaller transversal and larger tube pitch provided greater compactness and better thermal performance. Moreover, a larger angle was not only beneficial to enhance the thermal performance, but also helpful to improve the overall performance. Secondly, the effects of angle on the heat transfer performance and fluid flow characteristics were investigated as the perimeter kept constant. It was shown that the overall performance of the streamline tube was better than the circular tube. Lastly, the entropy generation including frictional entropy generation and the thermal entropy generation were analyzed. It can be concluded that by using the streamline tube, the wake region can be obviously reduced, and thermal performance can be improved.

A two-phase closed thermosyphon operated with nanofluids for solar energy collectors: Thermodynamic modeling and entropy generation analysis

Two-Phase Closed Thermosyphons (TPCTs) is a high-efficiency heat transfer technology being widely utilized in the fields of built and solar energy exploitations. In present work, a 2-D steady-state model is innovatively proposed to investigate thermal performance and flow dynamics of a single TPCT containing nanofluids. Conservation equations for mass, momentum, and energy were fully solved by the dichotomy algorithm. The effects of input powers, nanoparticles materials (Al2O3, Fe2O3 and Cu), and concentration levels (φ = 0–12 wt%) on the thermodynamics and entropy generation of the thermosyphon were numerically investigated and the results were evaluated through those from the pure water. A substantial change in the liquid film thickness, flow velocity profile, interfacial shear force, local heat transfer coefficient, temperature distribution, entropy generation rate and thermal resistance were subsequently obtained when using a nanofluid. Our numerical results revealed that nanofluids in thermosyphon could effectively enhance thermal performance by decreasing the evaporator temperature, thereby reducing overall entropy generation by about 41%, 32% and 29% for Cu, Fe2O3 and Al2O3 in comparison with pure water, respectively. Additionally, entropy generation significantly decays when nanoparticle concentration levels promote. Numerical results further indicate that the flow resistance of working fluid increases, maximum friction entropy generation increases by approximately 36.37%, 15.15%, and 9.09% for Cu, Fe2O3, Al2O3 of φ = 9 wt%, respectively. Moreover, the existence of an optimum concentration level for nanoparticles in maximizing the heat transfer limit was theoretically achieved for all nanofluids. Current results agreed well with experimental data within average deviation being no more than 10%. In conclusions, results suggest that TPCT-solar collect using nanofluid has a low simple payback period to absorb solar radiation to convert thermal energy compared to the conventional one charged with pure water.

Investigation of Forced Convection Enhancement and Entropy Generation of Nanofluid Flow through a Corrugated Minichannel Filled with a Porous Media.

Corrugating channel wall is considered to be an efficient procedure for achieving improved heat transfer. Further enhancement can be obtained through the utilization of nanofluids and porous media with high thermal conductivity. This paper presents the effect of geometrical parameters for the determination of an appropriate configuration. Furthermore, the optimization of forced convective heat transfer and fluid/nanofluid flow through a sinusoidal wavy-channel inside a porous medium is performed through the optimization of entropy generation. The fluid flow in porous media is considered to be laminar and Darcy–Brinkman–Forchheimer model has been utilized. The obtained results were compared with the corresponding numerical data in order to ensure the accuracy and reliability of the numerical procedure. As a result, increasing the Darcy number leads to the increased portion of thermal entropy generation as well as the decreased portion of frictional entropy generation in all configurations. Moreover, configuration with wavelength of 10 mm, amplitude of 0.5 mm and phase shift of 60° was selected as an optimum geometry for further investigations on the addition of nanoparticles. Additionally, increasing trend of average Nusselt number and friction factor, besides the decreasing trend of performance evaluation criteria (PEC) index, were inferred by increasing the volume fraction of the nanofluid (Al2O3 and CuO).

Effects of the porous medium and water-silver biological nanofluid on the performance of a newly designed heat sink by using first and second laws of thermodynamics

Abstract The aim of this numerical investigation is to evaluate the laminar forced convection of biologically synthesized water-silver nanofluid through a heat sink (HS) filled with porous foam (PHS) using first and second laws of thermodynamics. The impacts of inlet velocity (V = 0.5–3 m·s−1) and volume fraction of nanofluid (φ = 0–1%) on the performance metrics of HS are assessed and the outcomes are compared with those of the non-porous HS (NHS). The outcomes revealed that for both the PHS and NHS, the increase of V causes an intensification in convection coefficient, pumping power, and entropy generation due to fluid friction, while the maximum CPU temperature, thermal resistance, and entropy generation due to the heat transfer reduces by boosting V. Also, it was found that the augmentation of V results in intensification in convection coefficient, pumping power, overall hydrothermal performance, and frictional entropy generation, while the opposite is true for maximum CPU temperature, thermal resistance, and thermal entropy generation. Furthermore, it was reported that, except for φ = 0.5%, the overall hydrothermal performance of NHS is better than that of PHS, while PHS has better second-law performance than NHS in all the studied cases. Also, it can be concluded that the best hydrothermal performance for PHS belongs to φ = 1% and V = 0.5 m·s−1, while for NHS, these values are 1% and 2 m·s−1.

Circular Microchannel Heat Sink Optimization Using Entropy Generation Minimization Method

Abstract The performance of the microchannel heat sink (MCHS) in electronic applications needs to be optimized corresponding to the number of channels (N). In this study optimization of the number of channels corresponding to the diameter of the microchannel ( D N {D_{N}} ) using an entropy generation minimization approach is achieved for the MCHS used in electronic applications. The numerical study is performed for constant total heat flow rate ( q ˙ t o t ) ({\dot{q}_{tot}}) and total mass flow rate ( m ˙ t o t ) ({\dot{m}_{tot}}) . The results indicate that the dominance of frictional entropy generation ( S g e n , F r {S_{gen,Fr}} ) increases with the reduction in diameter. However, the entropy generation due to heat transfer ( S g e n , H T {S_{gen,HT}} ) decreases with the reduction in diameter. Therefore, the optimum diameter ( D ∗ {D^{\ast }} ) is calculated corresponding to the minimum total entropy generation ( S g e n , t o t a l {S_{gen,total}} ) for the optimum number of channels ( N ∗ {N^{\ast }} ). Furthermore, the entropy generation number ( N S {N_{S}} ) and Bejan number ( B e Be ) are also calculated.

Entropy Study on the Enhanced Heat Transfer Mechanism of the Coupling of Detached and Spiral Vortex Fields in Spirally Corrugated Tubes

The present work numerically studied the enhanced heat transfer mechanism of the coupled fields of detached and spiral vortices in symmetrical and asymmetrical spirally corrugated tubes. The heat transfer and viscous dissipation were analyzed by evaluating the entropy combined with the flow patterns, and the global entropy generation rate was analyzed by considering the local Nusselt number and friction factor. The results indicated that, both the leeside and windward corrugation angles had obvious effects on the strength of detached vortex and spiral flow, and also the location of the vortex. The maximum values of the heat transfer entropy were located at the boundary layers, and the heat transfer entropy of the secondary flow region was more distinguished than in other parts of the main flow region. The maximum values of friction entropy generation were located at both the boundary layers and the core of detached vortex. The performance evaluation criterion (PEC) presents nearly the same values for the four cases, when the Reynolds number (Re) is less than 6,300. In addition, the PEC of symmetrical spirally corrugated tube with corrugation angle equal to 25° showed the best performance, when Re is greater than 6,300. To keep the PEC above 1, Re should not exceed 33,000.

Entropy generation of turbulent Cu–water nanofluid flows inside thermal systems equipped with transverse-cut twisted turbulators

In the present study, numerical simulations have been carried out on thermal characteristics and second-law analysis of turbulent Cu–H2O nanofluid flow with the nanoparticle volume fraction of $$0 < \phi < 1.5\%$$ inside heat exchangers fitted by transverse-cut twisted tapes (TCTTs) with alternate axis. The transverse-cut ratios are in the range of 0.7 < b/c < 0.9 and 2 < s/c < 2.5, and the Reynolds number is varied between 5000 and 15,000. The impacts of the design variables on the turbulent kinetic energy, temperature distribution, thermal and frictional entropy generations and Bejan number have been evaluated. The simulations show that the TCTTs with b/c = 0.7 generate higher turbulent kinetic energy compared to the b/c = 0.9 due to higher swirl generation and flow disturbance. The additional recirculating flow produced near the alternate edges is another main physical factor for heat transfer augmentation. It is found that raising the nanoparticles volume concentration reduces the thermal entropy generation which is attributed to the thermal conductivity enhancement of nanofluids. Besides, raising the nanoparticles volume concentration from 0 to 1.5% reduces the $${{N}_{\text{g,thermal}}}$$ by 23%.

Second law analysis of hybrid nanofluid flow in a microchannel heat sink integrated with ribs and secondary channels for utilization in miniature thermal devices

A second law assessment is conducted to study irreversibility values for the stream of a hybrid water-based nanofluid within a microchannel heat sink fitted with secondary channels and rectangular ribs. The hybrid nanofluid has been synthesized from the graphene nanoplatelets on which the silver nanoparticles have been decorated. In the fluid part, entropy generations caused by heat transfer and friction are intense in the interfaces of solid-fluid, whereas lower thermal entropy generation occurs in the dead zones. In the solid part, thermal entropy generation in corners of the solid-fluid interface is higher than other regions. The lowest thermal entropy generation happens at the front of ribs, whereas the frictional entropy generation demonstrates lowest values at the heat sink central part. With the elevation of either Reynolds number (Re) or weight fraction, the entropy produced by heat exchange reduces. A 7 % decline in the total entropy generation happens by adding the nanoparticles with concentration of 0.1 % at Re = 300, while a 17 % reduction in this parameter happens with elevating the Re from 100 to 500 at concentration of 0.06 %. Furthermore, with the growth of concentration and decrement of Re, the contribution of solid to thermal entropy generation intensifies compared with the fluid.

Influence of thermohydraulic irreversibilities on the efficiency of high temperature superconducting (HTS) cables

High Temperature Superconducting (HTS) cables are emerging as the alternate to the conventional cables for power transmission and distribution due to their higher efficiency with fewer losses and robustness in handling large current densities with lower cross sectional area of the conductor. However, these cables encounter the AC losses due to Joules heating while carrying the transport current. In addition, these cables receive the heat loads from the ambient through the cable shield as heat intrusions. Hence, these cables are internally cooled with forced flow of LN2 to maintain the temperature of the superconductor below to its critical temperature. Due to the forced circulation of LN2 and heat loads, thermal and velocity gradients are developed in the HTS cables which accounts to entropy generation rate. The heat loads, frictional losses due to turbulent flow of LN2 in the corrugated former and entropy generation rate rises the temperature of LN2 above to its saturation temperature and boiling takes place. Hence, the current carrying capability of HTS tapes and the ability of electrical insulation of insulating layers in HTS cable will be reduced. To operate such cable efficiently for long length requires larger pump work for circulating LN2 between the terminations. Further, the losses in the pump work due to frictional entropy generation and losses in the heat transfer rate due to thermal entropy generation leads to quenching of HTS tapes and higher energy consumption thereby reduction in the efficiency of the HTS cable which is not advisable. Motivated by the challenges in reducing the pump work with higher cooling capacity, in this present work a novel method is proposed to estimate the loss contribution in thermohydraulic characteristics in HTS cables during the forced convective cooling at different heat loads.A computational domain is modeled, meshed and analyzed using commercial software ANSYS®. The analysis is carried out with time averaged Reynolds averaged Navier-Stokes (RANS) equations which are solved using Finite Volume Method (FVM) of discretization with κ−εturbulent scheme. In the present analysis, temperature dependent thermophysical properties of LN2 are considered at an operating temperature of 77 K and pressure of 2.7 bar. Further, the flow rates ranging from 11–20 L/min and the heat loads ranging from 1–3 W/m are considered to estimate the entropy generation rate and exergy destruction due to losses. The results obtained from the computational investigation are validated with the experimental results that are available in the literature. From the analysis, it is identified that higher the heat loads higher will be the entropy generation and exergy destruction. Further, the minimum exergy destruction is identified due to contributions of thermal and frictional losses. Furthermore, the exergy efficiency and irreversibility distribution ratio are estimated to identify the influence of thermal losses at different heat loads. It is observed that increase in the heat loads increases the thermal losses thereby contributing to lower efficiency of HTS cable.

Thermo-hydraulic and entropy generation analysis of recharging microchannel using water-based graphene–silver hybrid nanofluid

This work numerically investigates thermo-hydraulic and entropy generation characteristics of water-based graphene–silver (Gr–Ag) hybrid nanofluid with temperature-dependent properties in recharging microchannel (RMC). The thermal, hydraulic, and entropy generation characteristics in recharging microchannel are examined for different nanofluid volume concentrations and inlet velocity. The outcome of this study reveals that the utilization of Gr–Ag hybrid nanofluid in recharging microchannel enhances heat transfer performance. With an increase in both nanofluid volume concentration and fluid inlet velocity, substrate maximum temperature and thermal resistance decrease, whereas the uniformity in temperature distribution and average heat transfer coefficient enhanced. Moreover, the use of hybrid nanofluid in recharging microchannel shows higher pressure drop and requires more pumping power. Recharging microchannel (RMC) exhibits better overall performance compared to simple microchannel (SMC) with maximum performance factor value of 1.72. Further, frictional entropy generation increases, and thermal entropy generation decreases with increasing nanofluid volume concentration and inlet velocity. Both total entropy generation and Bejan number decrease with nanofluid volume concentration. Overall, the use of recharging microchannel (RMC) can be beneficial for high heat flux removal applications from both first and second law of thermodynamics perspective. Second, the utilization of water-based Gr–Ag hybrid nanofluid is beneficial when pumping power is not a constraint.

Second law assessment of nanofluid flow in a channel fitted with conical ribs for utilization in solar thermal applications: Effect of nanoparticle shape

This research tries to assess the second law characteristics of the water–boehmite alumina nanofluids in a rectangular channel enhanced with the conical ribs. The effects of different arrangements of the ribs and various shapes of the nanoparticles are evaluated. Shear Stress Transport (SST) k-ω model is implemented to perform the simulations. Based on the observations, the highest and lowest temperature gradients occur at the dead zones and the reattachment regions, respectively. For all the nanoparticle shapes, by the increase in the rib height and the reduction in the rib pitch, the entropy generated by the heat transfer diminishes while the entropy generated by the friction intensifies. Because of the dominance of the thermal entropy generation compared to the fractional one, the total irreversibility decreases by rising the rib height and reducing the rib pitch. The Oblate spheroid (Os)-shaped nanoparticles cause the highest thermal entropy generation followed by the brick-, blade-, cylinder-, and platelet-shaped nanoparticles, respectively. Moreover, the maximum frictional entropy generation belongs to the nanofluid having the platelet-shaped nanoparticles followed by respectively the cylinder-, blade-, brick-, and Os-shaped nanoparticles. The results also reveal that using the platelet-shaped nanoparticles besides greater rib heights and lower rib pitches are optimal based on the second law of thermodynamics causing the smaller total irreversibility. Furthermore, the Bejan number demonstrates the great values in all the cases under study.

Irreversibility characteristics of a modified microchannel heat sink operated with nanofluid considering different shapes of nanoparticles

In the current paper, the influences of the water–boehmite alumina nanofluid with various nanoparticle shapes on the second law attributes in the microchannel heat sink are analyzed. This assessment is carried out for five nanoparticle shapes (i.e., platelet, cylinder, blade, brick, and oblate spheroid) at four Reynolds numbers (i.e., Re = 300, Re = 800, Re = 1300, and Re=1800). Furthermore, the concentration is considered constant equal to 1% for all the modes. For all the nanoparticle shapes, the thermal entropy generation is diminished and frictional entropy generation is augmented by rising the Re. The oblate spheroid nanoparticles result in the highest entropy generation followed by the brick, blade, cylinder, and platelet nanoparticle shapes, respectively. By the changes of the Re, the variations of the thermal entropy generation are low, but the frictional entropy generation has significant changes. The greater Re numbers and the nanofluid with the platelet-shaped nanoparticles are optimal because result in the lowest irreversibility. In the nanofluid having the platelet-shaped nanoparticles, the total entropy generation decreases 17.4% by rising the Re from 300 to 1800. Besides, the Bejan number declines by the increase of the Re, and has its smallest value for the platelet nanoparticles-based nanofluid. Besides, the difference among the Bejan numbers of the various nanoparticle shapes is more noticeable at larger Re numbers.

Numerical investigations on entropy generation in cross-wavy channels

The numerical study to research the influence of ratio of channel amplitude to pitch of cross-wavy on entropy generation is conducted in this paper. In Reynolds number range of 200-1200, five types of cross-wavy channel are analyzed. The simulation results show the thermal entropy generation rising rate is fast when Reynolds number less than 700 and then flat. In addition, it is smaller with increasing channel amplitude to pitch value. The frictional entropy generation increases almost linearly with Reynolds number. However, it is much less than thermal entropy generation under the same conditions. In brief, the channels which have larger ratio of amplitude to pitch can reduce the total irreversibility to the least under the same flow conditions.