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1

Entropy production due to conjugate natural convection in a nanofluid-filled enclosure with a stepped wall

Bouchoucha Abd el, Oztop Hakan F., Bessaih Rachid, Abu-Hamdeh Nidal

Engineering Transactions

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2023

|

Vol. 71, iss. 2

161-183

EN

The main aim of this paper is to improve the heat transfer in a square cavity with a body at the left wall filled with a Al2O3/water nanofluid for different geometries. Numerous simulation experiments are conducted. A relative temperature is maintained at the vertical and top horizontal walls while the bottom wall is warm. The finite volume approach is considered to resolve the equations governing the thermal transfer flow in the physical domain based on the SIMPLER algorithm. In this study, different values of the following parameters are considered: Rayleigh number (104 ≤ Ra ≤ 105) and solid volume fraction (0 ≤ φ ≤ 0.1) of nanoparticles (NPs). Parameters, such as the Rayleigh (Ra) and Bejan (Be) numbers, thermal conductivity, body’s dimensions, and NPs volume fraction, which directly affect the entropy generation and heat transfer rate, are studied in a particular way. The obtained results show that entropy generation goes ahead with the Ra increase and inverse to the solid volume fraction increase. One can notice that the heat transfer has a proportional relation with φ and Ra.

2

CuO–water mhd mixed convection analysis and entropy generation minimization in double-lid–driven u-shaped enclosure with discrete heating

Mliki Bouchmel, Miri Rached, Djebali Ridha, Abbassi Mohamed A.

Acta Mechanica et Automatica

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2023

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Vol. 17, no. 1

112--123

EN

The present study explores magnetic nanoliquid mixed convection in a double lid–driven U-shaped enclosure with discrete heat-ing using the lattice Boltzmann method (LBM) numerical method. The nanoliquid thermal conductivity and viscosity are calculated using the Maxwell and Brinkman models respectively. Nanoliquid magnetohydrodynamics (MHD) and mixed convection are analyzed and entropy generation minimisation has been studied. The presented results for isotherms, stream isolines and entropy generation describe the interaction between the various physical phenomena inherent to the problem including the buoyancy, magnetic and shear forces. The operating parameters’ ranges are: Reynolds number (Re: 1–100), Hartman number (Ha: 0–80), magnetic field inclination (γ: 0°–90°), nanoparticles volume fraction (ϕ: 0–0.04) and inclination angle (α: 0°–90°). It was found that the 𝑁𝑢𝑚 and the total entropy generation augment by increasing Re, ϕ: and γ. conversely, an opposite effect was obtained by increasing Ha and α. The optimum magnetic field and cavity inclination angles to maximum heat transfer are γ = 90° and α = 0.

3

Chemically reacting Jeffrey fluid flow over a deformable porous layer with entropy generation analysis

Das Utpal Jyoti

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 3

36--48

EN

Entropy generation of a steady Jeffrey fluid flow over a deformable vertical porous layer is analysed with consideration of a first-order chemical reaction and thermal diffusion. The porous material is modelled as a homogeneous binary mixture of fluid and solid phases where each point in the binary mixture is occupied concurrently by the fluid and solid. The combined phenomenon of solid deformation and fluid movement is taken into account. The impact of relevant parameters on the fluid velocity, solid displacement, temperature and concentration profiles is discussed. It is noticed that the Jeffrey fluid parameter enhances the entropy generation number, fluid velocity and solid displacement profiles, but a reverse effect is seen for the Bejan number. Further, entropy generation, fluid velocity and solid displacement reduce due to the higher estimates of the chemical reaction parameter, while the Bejan number enhances.

4

Numerical analysis of structure, stability and entropy generation in biogas coflow diffusion flames

Kumar R. Nivethana, Kumaran S. Muthu, Raghavan Vasudevan

Archive of Mechanical Engineering

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2022

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LXIX, nr 1

99--128

EN

Biogas is a gaseous biofuel predominantly composed of methane and carbon-dioxide. Stability of biogas flames strongly depend upon the amount of carbon-dioxide present in biogas, which varies with the source of biomass and reactor. In this paper, a comprehensive study on the stability and flame characteristics of coflow biogas diffusion flames is reported. Numerical simulations are carried out using reactive flow module in OpenFOAM, incorporated with variable thermophysical properties, Fick’s and Soret diffusion, and short chemical kinetics mechanism. Effects of carbon-dioxide content in the biogas, temperatures of the fuel or coflowing air streams (preheated reactant) and hydrogen addition to fuel or air streams are analyzed. Entropy generation in these flames is also predicted. Results show that the flame temperature increases with the degree of preheat of reactants and the flames show better stability with the preheated air stream. Preheating the air contributes to increased flame stability and also to a significant decrease in entropy generation. Hydrogen addition, contributing to the same power rating, is seen to be relatively more effective in increasing the flame stability when added to the fuel stream. Results in terms of flow, temperature, species and entropy fields, are used to describe the stability and flame characteristics.

5

Second law analysis of mhd forced convective nanoliquid flow through a two-dimensional channel

Miri Rached, Abbassi Mohamed A., Ferhi Mokhtar, Djebali Ridha

Acta Mechanica et Automatica

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2022

|

Vol. 16, no. 4

417--431

EN

The present study deals with fluid flow, heat transfer and entropy generation in a two-dimensional channel filled with Cu–water nanoliquid and containing a hot block. The nanoliquid flow is driven along the channel by a constant velocity and a cold temperature at the inlet, and the partially heated horizontal walls. The aim of this work is to study the influence of the most important parameters such as nanoparticle volume fraction (0%≤ϕ≤4%), nanoparticle diameter (5 nm≤dp≤55 nm), Reynolds number (50≤Re≤200), Hartmann number (0≤Ha≤90), magnetic field inclination angle (0≤γ≤π) and Brownian motion on the hydrodynamic and thermal characteristics and entropy generation. We used the lattice Boltzmann method (LBM: SRT-BGK model) to solve the continuity, momentum and energy equations. The obtained results show that the maximum value of the average Nusselt number is found for case (3) when the hot block is placed between the two hot walls. The minimum value is calculated for case (2) when the hot block is placed between the two insulated walls. The increase in Reynolds and Hartmann numbers enhances the heat transfer and the total entropy generation. In addition, the nanoparticle diameter increase reduces the heat transfer and the irreversibility, the impact of the magnetic field inclination angle on the heat transfer and the total entropy generation is investigated, and the Brownian motion enhances the heat transfer and the total entropy generation.

6

Second law optimization and parametric study of a solar air heater having artificially roughened absorber plate

Sahu Mukesh Kumar, Prasad Radha Krishna

Archives of Thermodynamics

|

2019

|

Vol. 40, no 2

107--135

EN

In present article a mathematical model of arc shape wire roughened solar air heater, on the basis of energy and exergy output rates, entropy generation rate and augmentation entropy generation number, has been developed. A parametric study leading to entropy generation minimization has also been performed. In the analysis the geometric and operating parameters which have been considered as variable are: inlet air temperature, duct depth, collector width to duct depth ratio, mass flow rate per unit collector area, and temperature rise parameter. Results have been presented to see the effects of these values on the energy and exergy output rates of the roughened solar air heater. Effect of different values of wire rib roughness parameters on entropy generation has also been presented. Finally, design curves and optimization for different rib roughness parameters on the basis of minimum entropy generation number with temperature rise parameter, have been presented and optimum values also have been found out 0.004 to 0.010 (Km2 )/W. The entropy generation rate obtained for the system, in the present work has been compared with those obtained for solar air heater with different roughness geometries on absorber plates available in the literature for common roughness parameters and operating parameters which validate the present results.

7

Entropy generation and squeezing flow past a Riga plate with Cattaneo-Christov heat flux

Atlas M., Hussain S., Sagheer M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2018

|

Vol. 66, nr 3

291--300

EN

In this article, we investigate the convective heat transfer of the two-dimensional unsteady squeezing flow past a Riga plate. To examine the heat transfer, Cattaneo-Christov heat flux model is used. Influence of entropy generation on heat transfer has been investigated numerically. With the help of suitable similarity transformation, the governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs). The obtained system of non-linear ordinary differential equations subject to the convective boundary conditions is solved by the shooting method using the computational software MATLAB. To strengthen the reliability of the results obtained by the shooting method, the MATLAB built-in function bvp4c has been used. The graphs show the effect of different physical parameters for velocity, temperature, concentration and tables are presented to observe the behaviour of skin friction and sherwood number under the influence of certain physical parameters. It is observed that for increasing values of thermal relaxation parameter, the temperature profile increases and an opposite behaviour is shown for the concentration profile. Moreover, with an increase in the Brinkman number, the entropy generation increases.

8

Thermal and hydraulic phenomena in boundary layer of minijets impingement on curved surfaces

Kura T., Fornalik-Wajs E., Wajs J.

Archives of Thermodynamics

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2018

|

Vol. 39, no 1

147--166

EN

Presented work considers flow and thermal phenomena occurring during the single minijet impingement on curved surfaces, heated with a constant heat flux, as well as the array of minijets. Numerical analyses, based on the mass, momentum and energy conservation laws, were conducted, regarding single phase and two-phase simulations. Focus was placed on the proper model construction, in which turbulence and boundary layer modeling was crucial. Calculations were done for various inlet parameters. Initial single minijet results served as the basis for the main calculations, which were conducted for two jet arrays, with flat and curved heated surfaces. Such complex geometries came from the cooling systems of electrical devices, and the geometry of cylindrical heat exchanger. The results, regarding Nusselt number, heated surface temperature, turbulence kinetic energy, production of entropy and vorticity, were presented and discussed. For assumed geometrical parameters similar results were obtained.

9

Entropy analysis of third-grade MHD convection flows from a horizontal cylinder with slip

Madhavi K., Prasad V. R., Gaffar S. A., Venkatadri K.

Archive of Mechanical Engineering

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2018

|

Vol. LXV, nr 3

417--440

EN

In thermos ﬂuid dynamics, free convection ﬂows external to diﬀerent geometries, such as cylinders, ellipses, spheres, curved walls, wavy plates, cones, etc., play major role in various industrial and process engineering systems. The thermal buoyancy force associated with natural convection ﬂows can play a critical role in determining skin friction and heat transfer rates at the boundary. In thermal engineering, natural convection ﬂows from cylindrical bodies has gained exceptional interest. In this article, we mathematically evaluate an entropy analysis of magnetohydrodynamic third-grade convection ﬂows from permeable cylinder considering velocity and thermal slip effects. The resulting non-linear coupled partial diﬀerential conservation equations with associated boundary conditions are solved with an eﬃcient unconditionally stable implicit ﬁnite diﬀerence Keller-Box technique. The impacts of momentum and heat transport coeﬃcients, entropy generation and Bejan number are computed for several values of non-dimensional parameters arising in the ﬂow equations. Streamlines are plotted to analyze the heat transport process in a two-dimensional domain. Furthermore, the deviations of the ﬂow variables are compared with those computed for a Newtonian ﬂuid and this has important implications in industrial thermal material processing operations, aviation technology, diﬀerent enterprises, energy systems and thermal enhancement of industrial ﬂow processes.

10

Entropy generation on mhd flow of Powell-Eyring fluid between radially stretching rotating disk with diffusion-thermo and thermo-diffusion effects

Khan N. A., Aziz S., Ullah S.

Acta Mechanica et Automatica

|

2017

|

Vol. 11, no. 1

20--32

EN

An investigation is performed for an alyzing the effect of entropy generation on the steady, laminar, axisymmetric flow of an incompressible Powell-Eyring fluid. The flow is considered in the presence of vertically applied magnetic field between radially stretching rotating disks. The Energy and concentration equation is taking into account to investigate the heat dissipation, Soret, Dufour and Joule heating effects. To describe the considered flow non-dimensionalized equations, an exact similarity function is used to reduce a set of the partial differential equation into a system of non-linear coupled ordinary differential equation with the associated boundary conditions. Using homotopy analysis method (HAM), an analytic solution for velocity, temperature and concentration profiles are obtained over the entire range of the imperative parameters. The velocity components, concentration and temperature field are used to determine the entropy generation. Plots illustrate important results on the effect of physical flow parameters. Results obtained by means of HAM are then compared with the results obtained by using optimized homotopy analysis method (OHAM). They are in very good agreement.

11

Statistical analysis of entropy generation in longitudinally finned tube heat exchanger with shell side nanofluid by a single phase approach

Konchada P. K., Pv V., Bhemuni V.

Archives of Thermodynamics

|

2016

|

Vol. 37, no. 2

3--22

EN

The presence of nanoparticles in heat exchangers ascertained increment in heat transfer. The present work focuses on heat transfer in a longitudinal finned tube heat exchanger. Experimentation is done on longitudinal finned tube heat exchanger with pure water as working fluid and the outcome is compared numerically using computational fluid dynamics (CFD) package based on finite volume method for different flow rates. Further 0.8% volume fraction of aluminum oxide (Al2O3) nanofluid is considered on shell side. The simulated nanofluid analysis has been carried out using single phase approach in CFD by updating the user-defined functions and expressions with thermophysical properties of the selected nanofluid. These results are thereafter compared against the results obtained for pure water as shell side fluid. Entropy generated due to heat transfer and fluid flow is calculated for the nanofluid. Analysis of entropy generation is carried out using the Taguchi technique. Analysis of variance (ANOVA) results show that the inlet temperature on shell side has more pronounced effect on entropy generation.

12

Weryfikacja średnicy rurek skraplacza na podstawie minimalizacji generacji entropii

Laskowski R., Rusowicz A., Smyk A.

Rynek Energii

|

2015

|

Nr 1

71--75

PL

Na podstawie minimalizacji generacji entropii wyznaczono optymalną wartość liczby Reynoldsa i średnicę rurki skraplacza bloku 200 MW. W modelu uwzględniono generację entropii w wyniku przepływu ciepła i oporów przepływu od strony wody chłodzącej. Na podstawie przeprowadzonej analizy otrzymano mniejszą średnicę wewnętrzną rurki średnio od 2 do 4 mm od aktualnej wartości równej 28 mm. Zmniejszanie średnicy rurki powoduje wzrost średniej prędkości wody chłodzącej, co skutkuje poprawą współczynników przejmowania i przenikania ciepła, zmniejszeniem powierzchni wymiany ciepła i wzrostem oporów przepływu.

EN

On the basis of entropy generation minimization determined the optimal value of the Reynolds number and tube diameter of power plant condenser 200 MW. The model includes the generation of entropy as a result of heat transfer and pressure drop from the cooling water. The analysis gave the smaller inside diameter of the tube of approximately average from 2 to 4 mm from the current value equal to 28 mm. Reducing the diameter of the tube increases the average speed of the cooling water, thereby improving the transfer coefficients and heat transfer reduction in the heat transfer surface area and increased flow resistance.

13

Zastosowanie metody minimalizacji generacji entropii do optymalizacji geometrycznej wymiennika typu rura w rurze

Laskowski R., Tomczak P., Jaworski M.

Chłodnictwo : organ Naczelnej Organizacji Technicznej

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2015

|

R. 50, nr 10-11

6--11

PL

W artykule dokonano analizy generacji entropii dla wymiennika typu rura w rurze, w którym czynnikami przekazującymi ciepło była woda. Rozważono cztery konfiguracje wymiennika z czynnikiem grzejnym w rurze wewnętrznej i zewnętrznej oraz przy przepływie współ i przeciwprądowym. Celem analiz było znalezienie średnicy wewnętrznej rury dla minimalnej generacji entropii. Uwzględniono generację entropii na skutek przepływu ciepła i wynikającą z oporów przepływu (spadków ciśnień) czynników przekazujących ciepło. Minimalną generację entropii w funkcji średnicy wewnętrznej rury uzyskano dla dwóch przypadków dla przepływu przeciwprądowego i współprądowego kiedy czynnik chłodniejszy przepływa przez wewnętrzną rurę a cieplejszy przepływa przez przestrzeń pomiędzy rurami. Dla dwóch pozostałych przypadków dla przepływu przeciwprądowego i współprądowego kiedy czynnik cieplejszy przepływa przez wewnętrzną rurę a chłodniejszy przepływa przez przestrzeń pomiędzy rurami generacja entropii maleje w przybliżeniu liniowo wraz ze wzrostem średnicy wewnętrznej rury i nie występuje ekstremum generacji entropii (minimum).

EN

The paper presents analysis of entropy generation for a double-tube heat exchanger with water as heat transferring fluids. Four heat exchanger configurations were considered: with the heating fluid in the inner and outer tubes, and with the parallel and counter flows. The aim of the analyses was to determine the tube inner [inner tube] diameter for which entropy generation is minimum. The entropy generation resulting from heat flow and from resistance to flow (pressure losses) of hest transferring fluids were taken into account. The minimum entropy generation as a function of the inner tube diameter was found for two cases: for the counter and parallel flows when the cold fluid flow through the inner tube and the hot fluid passed through the space between the tubes. For two other cases of the counter and parallel flows when the hot fluid flows through the inner tube and the cold fluid passes through the space between the tube, entropy generation is approximately linearly decreasing with the increase in the inner tube diameter, and there is no entropy generation extremum (minimum) in the range of dimensions analysed in the study.

14

Entropy generation in a condenser and related correlations

Laskowski R., Jaworski M., Smyk A.

Archives of Thermodynamics

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2015

|

Vol. 36, no. 2

27--48

EN

The paper presents an analysis of relations describing entropy generation in a condenser of a steam unit. Connections between entropy generation, condenser ratio, and heat exchanger effectiveness, as well as relations implied by them are shown. Theoretical considerations allowed to determine limits of individual parameters which describe the condenser operation. Various relations for average temperature of the cold fluid were compared. All the proposed relations were verified against data obtained using a simulator and actual measurement data from a 200 MW unit condenser. Based on data from a simulator it was examined how the sum of entropy rates, steam condenser effectiveness, terminal temperature difference and condenser ratio vary with the change in the inlet cooling water temperature, mass flow rate of steam and the cooling water mass flow rate.

15

Entropy generation minimization in steady-state and transient diffusional heat conduction processes Part I – Steady-state boundary value problem

Kolenda Z. S., Szmyd J. S., Huber J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2014

|

Vol. 62, nr 4

875--882

EN

An application of the Entropy Generation Minimization principle allows new formulation of the boundary and initial boundaryvalue problems. Applying Euler-Lagrange variational formalism new mathematical form of heat conduction equation describing steady-state processes have been derived. Mathematical method presented in the paper can also be used for any diffusion heat and mass transfer process. Linear and non-linear problems with internal heat sources have been analyzed.

16

Optimizing Natural Gas Fueling Station Reservoirs Pressure Based on Ideal Gas Model

Farzaneh-Gord M., Deymi-Dashtebayaz M.

Polish Journal of Chemical Technology

|

2013

|

Vol. 15, nr 1

88-96

EN

At CNG fuelling station, natural gas is usually stored in a cascade storage system to utilize the station more efficient. The cascade storage system is generally divided into three reservoirs, commonly termed low, medium and high-pressure reservoirs. The pressures within these three reservoirs have huge effects on the performance of a CNG fuelling station and a fast filling process of natural gas vehicle’s (NGV) cylinder. A theoretical analysis is developed to study the effects of the reservoirs pressures and temperatures on the performance of the CNG station. The analysis is based on the first and the second law of thermodynamics, conservation of mass and ideal gas assumptions. The results show that as the reservoir temperature decreases, the fill ratio increases and the pressure within the filling station reservoirs has no effects on the fill ratio. The non-dimensional entropy generation and filling time profiles have opposite trends and as entropy generation decreases, the filling time increases. The optimized non-dimensional low and medium pressure-reservoir pressures are found to be as 0.24 and 0.58 respectively in thermodynamic point of view.

17

Wpływ parametrów procesu na optymalne warunki pracy nośników katalizatorów stosowanych w procesach selektywnego utleniania i dopalania węglowodorów

Krajewski W., Kalinowski K., Najzarek Z.

Archiwum Gospodarki Odpadami i Ochrony Środowiska

|

2012

|

Vol. 14, nr 2

51-61

PL

Podano charakterystyki cieplno–przepływowe dla 11 nośników katalizatora. Dla tych nośników wyznaczono optymalne wartości liczb Bejana, przy których stosunek liczb Nusselta do bezwymiarowej szybkości generacji entropii osiąga wartość maksymalną. Te liczby wyznaczono zmieniając kolejno długość złoża, ciśnienie na wylocie ze złoża, temperaturę wlotowa powietrza na złoże i temperaturę ścianki. Podano korelacje na optymalne liczby Bejana w zależności od parametrów procesu. Przedstawiono również takie korelacje na optymalne liczby Reynoldsa oraz wartości maksymalne stosunku liczb Nusselta do bezwymiarowej szybkości generacji entropii.

EN

Heat-flow characteristics for the eleven catalyst carriers are presented. Within these carriers, optimal values of Bejan number were determined for which the maximal ratio of Nusselt number to the dimensionless entropy generation rate attained its maximum. These number values were determined under sequential changing of the bed length, the bed outlet pressure, the air temperature at the bed inlet, and the wall temperature. Correlations are given for the optimal Bejan number, depending on these process parameters. Such correlations are also presented for the optimal Reynolds number, as well as for the maximal ratio of Nusselt number to the dimensionless entropy generation rate.

18

Energia czy egzergia

Szargut J.

Rynek Energii

|

2010

|

nr 5

3-5

PL

W języku potocznym słowem "energia" określa się zwykle tylko energię podwyższonej jakości. Jakość tę określa egzergia, nie podlegająca prawu zachowania. Straty egzergii są proporcjonalne do entropii generowanej. Należy dążyć do ich zmniejszania w granicach opłacalności ekonomicznej i możliwości technologicznych. Znajomość analizy egzergetycznej jest niezbędna przy projektowaniu i udoskonalaniu procesów energetycznych.

EN

In a colloquial speech the word "energy" is used for the kinds of energy characterized with a higher quality. In a scientitic speech the quality of energy is expressed by means of exergy, exempt from the law of conservation. The losses of exergy are proportional to the generated entropy. For the reduction of these losses it should be striven in the limits of economic profitability and technological possibilities. The knowledge of the exergy analysis is indispensable in the design and improvement of energy processes.

19

Analiza procesu stacjonarnego przepływu ciepła na podstawie zasady minimalizacji generowania entropii

Hołda A.

Rudy i Metale Nieżelazne

|

2008

|

R. 53, nr 5

275-281

PL

W artykule porównano dwa przypadki przewodzenia ciepła w izolacji termicznej, problem klasyczny oraz minimalizujący generację entropii. Jako kryterium porównawcze wybrano wielkość ciepła odpadowego. Pokazano wpływ minimalizacji źródeł entropii przy przewodzeniu ciepła na bilans energetyczny procesu technologicznego. Rozważania poparto przykładami obniżającymi źródła entropii w izolacji.

EN

Comparison of the solution of two different boundary-value problems of heat conduction in solid isolation has been presented. The solution of the classical formulation of steady state problem and solution based on the entropy generation minimization principle are analyzed. Waste heat flow to surrounding has been chosen as the comparison criterion. Influence of the minimization of entropy generation an the energy balance and thermodynamic efficiency of the technological process has been shown. Theoretical considerations have been illustrated with numerical example.

20

Analysis of incompressible viscous flow through an inclined channel with isothermal walls using second law of thermodynamics

Banerjee M. K., Banerjee R.

International Journal of Applied Mechanics and Engineering

|

2007

|

Vol. 12, no 4

919-928

EN

In this paper, the second law analysis of alaminar flow of a viscous incompressible fluid through an inclined channel with isothermal walls is investigated. Based on some simplifying assumptions, analytical solutions for the fluid velocity and temperature are constructed. The expressions for the entropy generation rate and irreversibility ratio are obtained and the results are presented graphically and discussed quantitatively for several values of the group parameter [...].