scholarly journals Analysis of entropy generation with heat generation in time dependent hydromagnetic flow of nanofluid in an oscillatory  semi- porous curved channel

2021 ◽  
Author(s):  
Muhammad Imran ◽  
Zaheer Abbas ◽  
Muhammad Naveed
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Brownian Motion ◽  
Entropy Generation ◽  
Heat Production ◽  
Time Dependent ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Radius Of Curvature ◽  
Curved Channel

The present study focusses on the investigation of thermodynamic optimization of hydromagnetic time dependent boundary layer nanofluid flow by employing entropy generation method (EMG) in semi- permeable oscillatory curved channel. We used Buongiorno model for nanofluid to address the impact of the parameters of Brownian motion and thermophoresis. The consequences of heat production are also taken into consideration in energy the equation. The mathematical form of boundary layer equations is accomplished by following the curvilinear coordinates scheme for the considered flow problem. The analytical convergent solution of the determined nonlinear PDEs is achieved through the process of homotopy analysis (HAM). A detailed analysis is conducted out to analyze the consequences of dissimilar variables concerned, such as non-dimensional radius of curvature, Lewis number, magnetic parameter, relation of wall oscillation frequency to its parameter of velocity, Reynolds number, Prandtl number, heat production and thermophoresis parameters, entropy generation rate, Brownian motion parameter and Brickman number, concentration and temperature difference parameters on temperature, velocity profile, concentration, pressure, drag surface force, Bejan number, entropy generation, rate of mass and heat transport are addressed in detail via tables and graphs. It is noted that, the magnitude of heat transmission rate (local Nusselt number) steadily decays for advanced values of radius of curvature variable and Reynolds number.

The Role of Fin Geometry in Heat Sink Performance

2006 ◽  
Vol 128 (4) ◽  
pp. 324-330 ◽  
Author(s):  
W. A. Khan ◽  
J. R. Culham ◽  
M. M. Yovanovich
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Entropy Generation ◽  
Heat Sink ◽  
Control Volume ◽  
Generation Rate ◽  
Heat Transfer Fluid ◽  
Entropy Generation Rate ◽  
Minimum Entropy ◽  
Axis Ratio

The following study will examine the effect on overall thermal/fluid performance associated with different fin geometries, including, rectangular plate fins as well as square, circular, and elliptical pin fins. The use of entropy generation minimization, EGM, allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by considering a control volume around the pin fin including base plate and applying the conservations equations for mass and energy with the entropy balance. The formulation for the dimensionless entropy generation rate is developed in terms of dimensionless variables, including the aspect ratio, Reynolds number, Nusselt number, and the drag coefficient. Selected fin geometries are examined for the heat transfer, fluid friction, and the minimum entropy generation rate corresponding to different parameters including axis ratio, aspect ratio, and Reynolds number. The results clearly indicate that the preferred fin profile is very dependent on these parameters.

A Prediction Method for the Local Entropy Generation Rate in a Transitional Boundary Layer With a Free Stream Pressure Gradient

2002 ◽  
Author(s):  
Ed Walsh ◽  
Roy Myose ◽  
Mark Davies
Keyword(s):  
Boundary Layer ◽  
Entropy Generation ◽  
Prediction Method ◽  
Accurate Method ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Suction Surface ◽  
Turbulent Region ◽  
Percentage Difference ◽  
Moderate Reynolds Number

To design an aerodynamically efficient blade the distribution of entropy generation on the blade surface should be known. Having only knowledge of the integrated loss, makes the task of improving the efficiency of a blade extremely difficult. A method to predict the entropy generation rate in steady, two-dimensional, incompressible, adiabatic boundary layer flows is presented, which gives both the distribution and magnitude of the entropy generation rate. This prediction method is based upon five correlations which are used to determine the: 1. entropy generated in the laminar region; 2. entropy generated in the turbulent region; 3. location of transition; 4. length of transition; 5. entropy generated in the transition region. These are then used to predict the entropy generation rate on the suction surface of a turbine rotor blade at a moderate Reynolds number; comparisons are then drawn with past measurements. The aim is to develop a quick, simple and relatively accurate method for the prediction of entropy in the boundary layers of turbomachines, although the method is not confined to this application. The only information required to implement this prediction method is the boundary layer edge velocity distribution and the turbulence intensity. A benefit of this method is that it does not rely upon dissipative CFD predictions, which are both slow to use in a design process and not yet sufficiently trustworthy. The dissipation coefficient and entropy generation rate predicted for this test case compare well to experimental measurements, with the percentage difference between the integrated entropy measured and predicted being approximately 13%. However, the difference in the turbulent region is found to be as high as 30%.

An Entropic Minimization Technique for Turbine Blade Profiles

2002 ◽  
Author(s):  
Ed Walsh ◽  
Mark Davies ◽  
Roy Myose
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Boundary Layers ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Incompressible Flows ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Minimization Technique ◽  
Boundary Layer Edge

The optimization of the boundary layer edge velocity distribution may hold the key to the minimization of entropy generation in the boundary layers of turbomachinery blades. A preliminary optimization analysis in the laminar region of a non film cooled turbine blade is presented, which demonstrates the concept of how the entropy generation rate may be reduced by varying the boundary layer edge velocity distribution along the suction surface, whilst holding the work done by the blade constant. In the laminar region the analytical technique developed by Pohlhausen and others to predict the boundary layer momentum thickness in the presence of pressure gradients has been adopted to predict the entropy generated as described in other papers by the same authors. The result gives an expression for the entropy generation rate in terms of the boundary layer edge velocity distribution for incompressible flows. The boundary layer edge velocity distribution may then be represented as a polynomial with undefined variables. This allows a minimization technique to be used to minimize the entropy generation rate on these variables. Constraints are included to keep the work output constant and the diffusion low to avoid separation. In this analysis it is only the laminar region that is considered for minimization, thus it is necessary to ensure that the modified boundary layer edge velocity distribution does not undergo transition earlier than the baseline boundary layer edge velocity distribution. This is accomplished by considering transition and separation criteria available in the literature. The result of this analysis indicates that the entropy generation rate may be reduced in the laminar boundary layers by using this technique.

Numerical Investigation of Local Entropy Generation for Laminar Flow in Rotating-Disk Systems

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Mohammad Shanbghazani ◽  
Vahid Heidarpoor ◽  
Marc A. Rosen ◽  
Iraj Mirzaee
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Local Entropy ◽  
Fluid Friction ◽  
Local Entropy Generation

The entropy generation is investigated numerically in axisymmetric, steady-state, and incompressible laminar flow in a rotating single free disk. The finite-volume method is used for solving the momentum and energy equations needed for the determination of the entropy generation due to heat transfer and fluid friction. The numerical model is validated by comparing it to previously reported analytical and experimental data for momentum and energy. Results are presented in terms of velocity distribution, temperature, local entropy generation rate, Bejan number, and irreversibility ratio distribution for various rotational Reynolds number and physical cases, using dimensionless parameters. It is demonstrated that increasing rotational Reynolds number increases the local entropy generation rate and irreversibility rate, and that the irreversibility is mainly due to heat transfer while the irreversibility associated with fluid friction is minor.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally-sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the non-dimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally-sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

Turbine Blade Entropy Generation Rate: Part II — The Measured Loss

2000 ◽  
Author(s):  
F. K. O’Donnell ◽  
M. R. D. Davies
Keyword(s):  
Boundary Layer ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Local Entropy ◽  
Suction Surface ◽  
Layer Velocity ◽  
Local Entropy Generation ◽  
Profile Loss

Using detailed boundary layer velocity measurements the profile loss, expressed in terms of local entropy generation rate, is evaluated at discrete locations along the suction surface of a turbine blade in a subsonic linear cascade at a chord Reynolds number of 1.8 × 103 under adiabatic test conditions. The distribution of loss through the entire boundary layer is thus established with particular attention given to the comparison of the relative contributions from the laminar, transitional and turbulent regions. It is found that 75% of the entropy generation occurs in the laminar region of the blade, with transition being one of the key features of the overall loss distribution. Traditional correlation methods are considered and shown to give accurate results when compared to the experimental measurements within both the laminar and turbulent regions, the application of such correlations is however dependant upon knowledge of the onset and extent of transition. Finally it is demonstrated that an existing method for the evaluation of local entropy generation rate from measurements of wall shear stress in laminar flow, may be adapted for use in turbulent flow and hence the possibility is presented for the measurement of loss from surface mounted sensors.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Vol 129 (3) ◽  
pp. 512-517 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time-averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the nondimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time-averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements, a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

scholarly journals Effect of Using Extra Fins on the Pin Fin Classic Geometry for Enhancement Heat Sink Performance using EGM Method

2018 ◽  
Vol 24 (4) ◽  
pp. 1 ◽  
Author(s):  
Kadhum Audaa Jehhef
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Cross Section ◽  
Entropy Generation ◽  
Heat Sink ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Minimum Entropy ◽  
Pin Fin ◽  
Pin Fins

In the present study, the effect of new cross-section fin geometries on overall thermal/fluid performance had been investigated. The cross-section included the base original geometry of (triangular, square, circular, and elliptical pin fins) by adding exterior extra fins along the sides of the origin fins. The present extra fins include rectangular extra fin of 2 mm (height) and 4 mm (width) and triangular extra fin of 2 mm (base) 4 mm (height). The use of entropy generation minimization method (EGM) allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by considering a control volume around the pin fin including a base plate and applying the conservations equations of mass and energy with the entropy balance. The dimensionless numbers used includes the aspect ratio (ε), Reynolds number (Re), Nusselt number (Nu), and the drag coefficients (CD). Fourteen different cross-section fin geometries are examined for the heat transfer, fluid friction, and the minimum entropy generation rate. The results showed that the Nusselt number increases with increasing the Reynolds number for all employed models. The ellipse models (ET and ER-models) give the highest value in the Nusselt number as compared with the classical pin fins. The fin of the square geometry with four rectangular extra fins (SR-models) gives an agreement in Nusselt number as compared with the previous study.  

Correlation of Mixing Efficiency and Entropy Generation Rate in a Square Cross Section Tee Junction Micromixer

2017 ◽  
Author(s):  
Aric M. Gillispie ◽  
Evan C. Lemley
Keyword(s):  
Reynolds Number ◽  
Entropy Generation ◽  
Molecular Diffusion ◽  
Chaotic Advection ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Analytical Relationship ◽  
Mixing Efficiency ◽  
Mixed Solution ◽  
Tee Junction

The potential applications of micromixers continues to expand in the bio-sciences area. In particular, passive micromixers that may be used as part of point-of-care (POC) diagnostic testing devices are becoming commonplace and have application in developed, developing, and relatively undeveloped locales. Characterizing and improving mixing efficiency in these devices is an ongoing research effort. Micromixers are used in some lab-on-chip (LOC) devices where it is often necessary to combine two or more fluids into a mixed solution for testing or delivery. The simplest micromixer incorporates a tee junction to combine two fluid species in anti-parallel branches, with the mixed fluid leaving in a branch perpendicular to the incoming branches. Micromixers rely on two modes of mixing: chaotic advection and molecular diffusion. In micro-mixers flow is typically laminar, making chaotic advection occur only via induced secondary flows. Hence, micromixers, unless carefully designed, rely almost exclusively on molecular diffusion of fluid species. A well designed micromixer should exhibit significant chaotic advection; which is also a sign of large strain rates and large entropy generation rates. This paper describes the development of an analytical relationship for the entropy generation rate and the mixing efficiency as function of the outgoing branch Reynolds number. Though there has been extensive research on tee junctions, entropy generation, and the mixing efficiencies of a wide variety of micromixers, a functional relationship for the mixing efficiency and the entropy generation rate has not been established. We hypothesize a positive correlation between the mixing index and the entropy generation rate. The worked described here establishes a method and provides the results for such a relationship. A basic tee junction with square cross sections has been analyzed using computational fluid dynamics to determine the entropy generation rate and outgoing mixing efficiencies for Reynolds numbers ranging from 25–75. The mixing efficiency is determined at a location in the outgoing branch where the effects of molecular diffusive mixing is minimized and chaotic advective mixing is the focus. The entropy generation rate has been determined for the indicated range of Reynolds number and decomposed into its viscous and diffusive entropy terms. The functional relationships that have been developed are applicable for micromixer design and serve as a reference for more complex passive micromixer designs.

The Effect of Reynolds Number, Compressibility and Free Stream Turbulence on Profile Entropy Generation Rate

2002 ◽  
Author(s):  
Philip C. Griffin ◽  
Mark R. D. Davies ◽  
Francis K. O’Donnell ◽  
Ed Walsh
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Laminar Boundary Layer ◽  
Entropy Generation ◽  
Free Stream ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Suction Surface ◽  
Free Stream Turbulence ◽  
Layer Velocity

Detailed aerodynamic data from the suction surface boundary layer on a turbine blade arranged in a linear subsonic cascade was acquired under high free stream turbulence conditions (∼ 5.2%) generated using a perforated plate placed upstream of the cascade. In addition, data was also obtained from a transonic turbine cascade utilizing the same blade profile but of much smaller chord at free stream turbulence levels of 3.5%. Velocity profiles from the laminar, transitional and turbulent boundary layers were measured at various locations along the airfoil suction surface for the incompressible regime at ReC of 76,000. For the compressible test cases, boundary layer velocity profiles were measured at two locations towards the aft section of the blade at ReC of 163,000 and MEx of 0.37 respectively. For both cases the boundary layer velocity profiles were acquired by traversing a single normal hot wire probe normal to the blade surface. In addition the extent of the transition region over the blade surface was determined for both compressible and incompressible regimes by the use of an array of heated thin film sensors over a range of Reynolds and exit Mach numbers. It was observed that an earlier transition ensued at high free stream turbulence conditions in comparison to a previous investigation at comparable ReC and lower turbulence level (0.8% Tu). In addition comparisons were made to existing incompressible data at ReC = 185,000 and 0.8% free stream turbulence intensity. One of the primary observations resulting from an earlier transition was a thicker turbulent boundary layer, but in addition it was also noted that shear strain rates in the laminar boundary layer were significantly higher than those obtained at the 0.8% turbulence intensity. Further analyses also elucidated the presence of fluctuating components of velocity in the laminar boundary layer and were attributed to the effects of the free stream turbulence. This leads to the notion of a hybrid boundary layer, possessing both laminar and turbulent characteristics. These findings have implications regarding the profile loss of the blade, that is the loss generated in blade boundary layers and wakes normally associated with phenomena such as viscous shear, Reynolds stress production, shock wave formation and heat transfer across temperature differences and can be quantified in terms of the amount of entropy generated. For the purposes of this study entropy creation is solely restricted to that arising due to fluid dynamic phenomena, thereby assuming an adiabatic and quasi-isothermal flow. The entropy generation rate per unit volume is obtained directly from the boundary layer velocity profile; further integration gives rise to the entropy generation rate over the boundary layer at a point or over the entire suction surface length. Even though the number of quantitative measurement points on the transonic cascade was limited due to the very thin boundary layer present, no effects attributable to compressibility were observed on the entropy generation rate at the Mach number in question. Increased free stream turbulence had a greater effect on the generated entropy due to increased viscous shear in the laminar boundary layer and increased Reynolds stress production. In contrast, free stream turbulence did not have any significant effect on the turbulent boundary layer in the context of this study, as it was observed that the amount of entropy generated in the turbulent boundary layer was approximately equivalent for both turbulence levels at comparable Reynolds number.

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