Friction Irreversibility Research Articles

Entropy production due to free convection in partially heated isosceles triangular enclosures

A numerical analysis of the entropy production has been performed due to natural convection heat transfer and fluid flow in isosceles triangular enclosures with partially heated from below and symmetrically cooled from sloping walls. Governing equations are solved by finite difference method. Governing parameters on flow and temperature fields are Rayleigh number (10 3 ⩽ Ra ⩽ 8.8 × 10 5), dimensionless length of heater (0.25 ⩽ (ℓ′ = ℓ/ L) ⩽ 1.0), dimensionless location of heater (0.25 ⩽ ( c′ = c/ L) ⩽ 0.75) and inclination angle of slopping walls (30° ⩽ β ⩽ 60°). Heat transfer results are presented in terms of local and mean Nusselt numbers ( Nu) while entropy production results are shown with entropy production number ( N s) and Bejan number ( Be). Isotherms, streamlines, contours of entropy production due to heat transfer and fluid friction irreversibility are plotted. It is observed that entropy production number increases but Bejan number decreases with increasing of Rayleigh number. However, both entropy production due to heat transfer and fluid friction irreversibility are affected by higher inclination angle of triangle and length of heater.

Generalized irreversible heat-engine experiencing a complex heat-transfer law

The fundamental optimal relation between optimal power-output and efficiency of a generalized irreversible Carnot heat-engine is derived based on a generalized heat-transfer law, including a generalized convective heat-transfer law and a generalized radiative heat-transfer law, q ∝ (Δ T n ) m . The generalized irreversible Carnot-engine model incorporates several internal and external irreversibilities, such as heat resistance, bypass heat-leak, friction, turbulence and other undesirable irreversibility factors. The added irreversibilities, besides heat resistance, are characterized by a constant parameter and a constant coefficient. The effects of heat-transfer laws and various loss terms are analyzed. The results obtained corroborate those in the literature.

Numerical investigation on developing laminar forced convection and entropy generation in a wavy channel

The present paper investigates the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The effects of aspect ratio (W/H) and Reynolds number (Re) on entropy generation are the major concerns. The studied cases cover W/H=1, 2 and 4, and Re range from 100 to 400. The flow features, including secondary flow motion and temperature distribution as well as the detailed distributions of local entropy generation due to frictional and heat transfer irreversibilities are reported. Through the evaluations of entropy generation in the whole flow field, the case of W/H=1 is found to have the minimal entropy generation among all of the analyzed cases. Besides, the higher Re is found to be beneficial for obtaining the lower values of the total resultant entropy generation in the flow field. Accordingly, the case with W/H=1 and higher Re is suggested to be used under the current flow conditions, so that the irreversibility resulted from the developing laminar forced convection in the wavy channel could be least and the best exergy utilization could be achieved.

On the importance of thermal boundary conditions in heat transfer and entropy generation for natural convection inside a porous enclosure

The aim of the present paper is to analyze the importance of thermal boundary conditions of the heated/cooled walls in heat transfer and entropy generation characteristics inside a porous enclosure, heated from below. Both the heating and the cooling are carried out uniformly and non-uniformly and the results are compared. The laminar, steady, natural convection heat transfer is calculated by solving numerically the mass, momentum, and energy conservation equations whilst viscous dissipation and the work of pressure forces are included in the energy equation. Moreover, the generation of entropy is calculated taking into account both heat transfer irreversibility and fluid friction irreversibility. As the thermal boundary conditions, sinusoidal temperature distributions are invoked for the non-uniformly heated/cooled walls. Comparison between the results of the present numerical model with the previously published works provides excellent agreement. Results are presented in terms of streamlines, isothermal lines, iso-entropy generation lines, and iso-Bejan lines. Additionally, variations of average Nusselt number, global entropy generation rate, and global Bejan number are analyzed over a wide range of Darcy-modified Rayleigh number ( 10 < Ra < 1000 ). Inspection of the results indicates that thermal boundary conditions are of profound influences on the induced flow as well as heat transfer characteristics and possess prominent consequences on entropy generation rates. It is demonstrated that, the optimum case with respect to heat transfer as well as entropy generation could be achieved by non-uniform heating.

Effects of corrugation angle on developing laminar forced convection and entropy generation in a wavy channel

This paper investigates the effects of corrugation angle (β) on the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The studied cases cover β = 10-, 15-, 20-, 25-, 30- and 35°, whilst Reynolds number (Re) is varied as 100, 200 and 400. The analyzed flow characteristics include recirculating flows, secondary vortices, temperature distributions, and friction factor as well as Nusselt number. In particular, the effects of corrugation angle on the distributions and magnitudes of local entropy generation resulted from frictional irreversibility (S ′′′ ) and heat transfer irreversibility (S ′′′ ) are separately discussed in detail in the present paper. Based on the minimal entropy generation principle, the optimal corrugation angle and favorable Re are reported.

Convective exergy losses of developing slip flow in microchannels

A numerical formulation of convective exergy losses in microchannels is developed. Using a new convection model (called Non-Inverted Skew Upwind Scheme (NISUS)), the predicted velocity field is post-processed to determine frictional irreversibilities within the microchannel. Boundary conditions are established from a first-order slip velocity, based on streamwise temperature gradients and transverse velocity gradients at the wall. Parametric studies are conducted for varying flow rates, channel aspect ratios, slip coefficients and pressure ratios across the microchannel. The predicted exergy destruction results provide useful new data, from which design modifications can be made to reduce power input when transporting fluid through a microchannel.

Entropy generation minimization of free convection film condensation on an elliptical cylinder

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This analysis provides us how the geometric parameter-ellipticity affects entropy generation during film-wise condensation heat transfer process. The results observe that local condensate film thickness decreases with an increase in ellipticity of a cylinder. From the first law point of view, the local heat transfer coefficient enhances as ellipticity increases. Meanwhile, from the second law point of view, entropy generation increases with increasing the value of ellipticity. We derive an expression for entropy generation, which accounts for the combined action of the specified irreversibilities. The result demonstrates that thermal irreversibility dominates over film flow friction irreversibility. Finally, an expression of minimizing entropy generation in laminar film condensation heat transfer is obtained.

Thermodynamic analysis of free convection film condensation on an elliptical cylinder

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This is the first approach to investigate how the geometric parameter‐ellipticity and surface tension affect local entropy‐generation rate during film‐wise condensation heat transfer process. The results observe that entropy generation decreases with decreasing ellipticity. It indicates that the entropy generation number is nearly unaffected by surface tension forces at small ellipticity like e ≤ 0.7, but somewhat influenced at large ellipticity for the whole perimeter. From the second law point of view, local entropy generation increases with ellipticity as local heat transfer coefficient does. Furthermore, the entropy‐generation rate due to gravity‐driven film flow friction is proportional to Brinkman group parameter. The irreversibility ratio indicates that film flow friction irreversibility starts to dominate over heat transfer irreversibility in the lower half of streamwise length for higher values of Brinkman group parameter (Br/T = 1).

06/01351 Augmentation of heat transfer coefficient by using 90† broken transverse ribs on absorber plate of solar air heater: Sahu, M. M. and Bhagoria, J. L. Renewable Energy, 2005, 30, (13), 2057–2073

Three-dimensional laminar forced convective flow and entropy generation in a 180-deg curved rectangular duct with longitudinal ribs equipped on the heated wall are investigated by numerical methods. The development of secondary vortices, temperature and local entropy generation distributions as well as the overall entropy generation in whole flow fields, including the entrance and fully developed region, are analyzed. The effects of rib size are particularly highlighted in the present paper. Calculations of cases with various rib sizes under different Dean numbers and external heat fluxes are carried out to examine the influence of rib on the flow field and entropy generation. The entropy generated from frictional irreversibility and heat transfer irreversibility is investigated separately in detail. The results reveal that the addition of rib can effectively reduce the entropy generation from heat transfer irreversibility since the secondary vortices are augmented by the rib, through which the heat transfer performance is enhanced, in turn making the temperature gradient become smoother. Nevertheless, the entropy generation due to frictional irreversibility is raised at the same time because larger fluid friction is resulted from the wider solid walls and the complex flows disturbed by ribs. Due to the opposite influences of rib on the entropy generations from irreversibilities, the analysis of the optimal trade-off is carried out based on the minimal entropy generation principle. The optimal rib size which induces the minimal entropy generation in the flow fields is found to be dependent on the external heat flux and Dean number. Even under some flow conditions, the resultant entropy generation could not be reduced but becomes worse when ribs are added. These results provide worthwhile information for considerations of adding ribs on a curved duct and the determinations of rib sizes from view point of thermodynamic second law.

A numerical study on entropy generation and optimization for laminar forced convection in a rectangular curved duct with longitudinal ribs

The effects of longitudinal ribs on laminar forced convection and entropy generation in a curved rectangular duct are investigated in the present paper by numerical methods. The major concern is to explore the optimal rib number and arrangement of the mounted rib based on the minimal entropy generation principle. The detailed information of local distributions of entropy generation due to frictional and heat transfer irreversibility as well as the overall entropy generation in the whole flow field are analyzed separately. The results show that the flow features in the curved duct, including the secondary flow motion, and the distributions of velocity and temperature, are considerably influenced by the number and arrangement of mounted ribs. Through the comparison of the cases with none to four ribs mounted on duct walls with various arrangements, it is found that a single rib on the heated duct wall is the most effective way to reduce entropy generation, whereas additional ribs can not give further reduction in entropy generation. The rib arrangement is suggested to be used in practical applications so that the irreversibility due to the laminar forced convection in the curved duct would be minimal and the best exergy utilization could be achieved.

Upper entropy bounds for transient forced convection

This article develops upper bounds for total entropy associated with convective heat transfer and transient fluid motion in an enclosure. Entropy production includes both friction and thermal irreversibilities due to fluid mixing in the enclosure. An integral formulation of entropy transport is developed in terms of the temperature excess (difference between the point-wise and spatially averaged temperature). The thermal irreversibility of entropy production is written in terms of the squared temperature excess. In this way, an upper entropy bound can be derived with respect to geometrical parameters and initial temperatures. Furthermore, this entropy bound is minimized by re-formulating the minimization problem in terms of a standard form of eigenvalue problem. Several example problems are considered and a spectral method is used to solve the governing energy equation. Theoretical predictions are compared successfully against numerical simulations for cases involving both Neumann and Dirichlet boundary conditions.

Fuel channel friction and thermal irreversibilities in a proton exchange membrane fuel cell

In this article, entropy production of gas friction and thermal irreversibilities in a rectangular channel of a proton exchange membrane fuel cell (PEMFC) is studied. A 2-D formulation of gas motion, heat transfer and entropy production is developed. Effects of varying channel height collapse onto a single curve with the same optimum, when entropy production is re-formulated in terms of an irreversibility distribution ratio. Predicted results are compared successfully against past data involving channel flow profiles.

Numerical analysis of entropy generation and optimal Reynolds number for developing laminar forced convection in double-sine ducts with various aspect ratios

In the present paper, the entropy generation in a double-sine duct, which is frequently used in plate heat exchangers, is investigated by numerical methods. The Reynolds number ( Re) at inlet covers ranges from 86 to 2000, and wall heat flux ( q″) varies as 160, 320 and 640 W/m 2. Three aspect ratio ( Λ/ a) cases, including Λ/ a = 2, 4 and 8, are investigated. The results indicate that the entropy generation, S gen ∗ , in cases with larger Re and smaller q″ is dominated by the entropy generation due to frictional irreversibility ( S P ∗ ); whereas the entropy generation is dominated by the entropy generation due to heat transfer irreversibility ( S T ∗ ) in cases with smaller Re and larger q″. There is no monotonic relationship between Λ/ a and S P ∗ or S T ∗ . For all cases with different Re and q″, S P ∗ is found to be minimal in Λ/ a = 2 case, whereas S T ∗ is minimal in Λ/ a = 4 case. The optimal aspect ratio, ( Λ/ a) opt, with which the minimal S gen ∗ can be obtained, is found to be dependent on Re and q″. In q″ = 160 W/m 2 case, ( Λ/ a) opt = 2 when Re > 540; ( Λ/ a) opt = 4 when Re < 540. In q″ = 320 W/m 2 case, ( Λ/ a) opt = 2 when Re > 662; ( Λ/ a) opt = 4 when Re < 662. In q″ = 640 W/m 2 case, ( Λ/ a) opt = 2 when Re > 1008; ( Λ/ a) opt = 4 when Re < 1008. An optimal Re, which is found to increase with q″, exists for every case with specific Λ/ a and q″ to induce the minimal S gen ∗ . These results provide important information for the heat exchanger design since the thermal system could have the least irreversibility and best exergy utilization if the optimal Re and optimal aspect ratio is used according to the practical design conditions.

Entropy Based Design of Fuel Cells

AbstractThis article aims to develop an entropy based method of systematically improving efficiency of fuel cells. Entropy production of both electrochemical and thermofluid irreversibilities is formulated based on the Second Law. Ohmic, concentration, and activation irreversibilities occur within the electrodes, while thermal and friction irreversibilities occur within the fuel channel. These irreversibilities reduce the overall cell efficiency by generating voltage losses. Unlike past studies, this article considers fuel channel irreversibilities within the total entropy production, for both solid oxide fuel cells (SOFCs) and proton exchange membrane fuel cells (PEMFCs). Predicted results of entropy production are shown at varying operating temperatures, surface resistances, and channel configurations. Numerical predictions are compared successfully against past measured data of voltage profiles, thereby providing useful validation of the entropy based formulation. The Second Law stipulates the maximum theoretical capability of energy conversion within the fuel cell. Unlike past methods characterizing voltage losses through overpotential or polarization curves, the entropy based method provides a useful alternative and systematic procedure for reducing voltage losses.

Numerical investigation on laminar forced convection and entropy generation in a curved rectangular duct with longitudinal ribs mounted on heated wall

Three-dimensional laminar forced convective flow and entropy generation in a 180-deg curved rectangular duct with longitudinal ribs equipped on the heated wall are investigated by numerical methods. The development of secondary vortices, temperature and local entropy generation distributions as well as the overall entropy generation in whole flow fields, including the entrance and fully developed region, are analyzed. The effects of rib size are particularly highlighted in the present paper. Calculations of cases with various rib sizes under different Dean numbers and external heat fluxes are carried out to examine the influence of rib on the flow field and entropy generation. The entropy generated from frictional irreversibility and heat transfer irreversibility is investigated separately in detail. The results reveal that the addition of rib can effectively reduce the entropy generation from heat transfer irreversibility since the secondary vortices are augmented by the rib, through which the heat transfer performance is enhanced, in turn making the temperature gradient become smoother. Nevertheless, the entropy generation due to frictional irreversibility is raised at the same time because larger fluid friction is resulted from the wider solid walls and the complex flows disturbed by ribs. Due to the opposite influences of rib on the entropy generations from irreversibilities, the analysis of the optimal trade-off is carried out based on the minimal entropy generation principle. The optimal rib size which induces the minimal entropy generation in the flow fields is found to be dependent on the external heat flux and Dean number. Even under some flow conditions, the resultant entropy generation could not be reduced but becomes worse when ribs are added. These results provide worthwhile information for considerations of adding ribs on a curved duct and the determinations of rib sizes from view point of thermodynamic second law.

Microfluidic exergy loss in a non-polarized thermomagnetic field

In this article, exergy losses of fluid motion in a microchannel are investigated. Thermal, friction and electromagnetic irreversibilities contribute to the total rate of exergy destruction. Additional input power from the externally applied electric field is needed to overcome these irreversibilities and deliver specified rates of mass and heat flow through the microchannel. Different cases of steady-state heat transfer in a non-polarized electromagnetic field are considered. Predicted results of fluid velocity, exergy destruction and optimal Reynolds number are presented and compared successfully against past data and measurements involving exergy destruction. It is shown that exergy destruction increases with stronger magnetic fields and wider microchannels. Furthermore, the optimal Reynolds number (minimizing the rate of exergy destruction) increases at lower microchannel aspect ratios.

Entropy generation and optimal analysis for laminar forced convection in curved rectangular ducts: A numerical study

The present paper analyzes entropy generation induced by forced convection in a curved rectangular duct with external heating by numerical methods. The problem is assumed as steady, three-dimensional and laminar. The local entropy generation distributions as well as the overall entropy generation in the whole flow fields, including the entrance region and fully developed region, are analyzed. The effects of three important factors, including Dean number, external wall heat flux and cross-sectional aspect ratio, on entropy generated from frictional irreversibility and heat transfer irreversibility are investigated separately in detail. The results show that the major source of entropy generation in the flow fields with larger Dean number and smaller wall heat flux comes from frictional irreversibility; whereas for the flow fields with smaller Dean number and larger wall heat flux the entropy generation is dominated by heat transfer irreversibility. The competition between the entropy generation from the irreversibility caused by fluid friction and heat transfer is complicatedly related with the three factors, making the relationship between the resultant entropy generation and the three factors non-monotonous. Based on the minimal entropy generation principal, the optimal condition can induce the minimal entropy generation in the flow fields. Through the optimal analysis, the optimal aspect ratio is found to be dependent on heat flux and Dean number. For each case with specific aspect ratio and wall heat flux, there exists an optimal Dean number, and the optimal Dean number is found to increase with wall heat flux. The detailed optimal analysis is provided in the present paper, which is worthwhile for heat exchanger design from the second law of thermodynamics since the thermal system could have the least irreversibility and best exergy utilization if the optimal Dean number and aspect ratio can be selected according to the practical design conditions.

Particle Image Velocimetry Based Measurement of Entropy Production With Free Convection Heat Transfer

Local entropy production rates are determined from a numerical and experimental study of natural convection in an enclosure. Numerical predictions are obtained from a control-volume-based finite element formulation of the conservation equations and the Second Law. The experimental procedure combines methods of particle image velocimetry and planar laser induced fluorescence for measured velocity and temperature fields in the enclosure. An entropy based conversion algorithm in the measurement procedure is developed and compared with numerical predictions of free convection in the cavity. The predicted and measured results show close agreement. A measurement uncertainty analysis suggests that the algorithm postprocesses velocities (accurate within ±0.5%) to give entropy production data, which is accurate within ±8.77% near the wall. Results are reported for free convection of air and water in a square cavity at various Rayleigh numbers. The results provide measured data for tracking spatial variations of friction irreversibility and local exergy losses.

Second Law Analysis of Laminar Flow In A Channel Filled With Saturated Porous Media

The entropy generation rate in a laminar flow through a channel filled with saturated porous media is investigated. The upper surface of the channel is adiabatic and the lower wall is assumed to have a constant heat flux. The Brinkman model is employed. Velocity and temperature profiles are obtained for large Darcy number (Da) and used to obtain the entropy generation number and the irreversibility ratio. Generally, our result shows that heat transfer irreversibility dominates over fluid friction irreversibility (i.e. 0 &lt; ø &lt; 1), and viscous dissipation has no effect on the entropy generation rate at the centerline of the channel.

An analytical solution and computer simulation for a multi-plate thermoacoustic system

In this paper, an analytical model for a multi-plate thermoacoustic system is developed. The governing momentum and energy equations are simplified to quasi-one-dimensional forms using reasonable approximations. The expressions for the fluctuating velocity (u1), fluctuating temperature (T1), Nusselt number (Nu), fluid friction irreversibility (NsFF), heat transfer irreversibility (NsHT), energy flux density (Ė) and transverse velocity (v1) are derived using a first order perturbation expansion of the governing momentum and energy equations. Finally, a wave equation is modelled for the present problem by using the continuity, momentum and energy equations.