Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford, is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case.

Heat transfer and entropy generation optimization of forced convection in a porous-saturated duct of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy-Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation. (c) 2006 Elsevier Ltd. All rights reserved.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Equivalence between the application of entransy and entropy generation

Recently, a group of researchers proposed the concept of entransy by analogy with the electrical energy stored in a capacitor, the entransy being a measure of the ability of a body or a system to transfer heat. In comparative terms, the entransy dissipation rate is related with the loss of heat transfer ability just like the exergy destruction rate is proportional to the loss of work ability, being these losses caused by the irreversibilities related to the thermodynamic processes. Some authors have questioned the need for the concept of entransy, claiming that this concept is only an extension of a well established theory of heat transfer. The objective of this work is show the equivalence between the application of the concepts of entransy and entropy generation rate, which can be verified using various application examples. The application examples used here are the thermodynamic modeling of three physical models of solar energy collectors and a physical model of a sensible heat storage system. Analytical results are shown and compared. The results showed that the application of the concept of entransy provided identical expressions obtained by the concept of entropy generation, indicating a duplication of concepts. (C) 2014 Elsevier Ltd. All rights reserved.

Entropy generation for microscale forced convection: effects of different thermal boundary conditions, velocity slip, temperature jump, viscous dissipation, and duct geometry

This work presents closed form solutions for fully developed temperature distribution and entropy generation due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001

Thermal characterization of a cross-flow heat exchanger with a new flow arrangement

The objective of the present paper is to thermally characterize a cross-flow heat exchanger featuring a new cross-flow arrangement, which may find application in contemporary refrigeration and automobile industries. The new flow arrangement is peculiar in the sense that it possesses two fluid circuits extending in the form of two tube rows, each with two tube lines. To assess the heat exchanger performance, it is compared against that for the standard two-pass counter-cross-flow arrangement. The two-part comparison is based on the thermal effectiveness and the heat exchanger efficiency for several combinations of the heat capacity rate ratio, C*, and the number of transfer units, NTU. In addition, a third comparison is made in terms of the so-called ""heat exchanger reversibility norm"" (HERN) through the influence of various parameters such as the inlet temperature ratio, T, and the heat capacity rate ratio, C*, for several fixed NTU values. The proposed new flow arrangement delivers higher thermal effectiveness and higher heat exchanger efficiency, resulting in lesser entropy generation over a wide range of C* and NTU values. These metrics are quantified with respect to the arrangement widely used in refrigeration industry due to its high effectiveness, namely, the standard two-pass counter-cross-flow heat exchanger. The new flow arrangement seems to be a promising avenue in situations where cross-flow heat exchangers for single-phase fluid have to be used in refrigeration units. (c) 2009 Elsevier Masson SAS. All rights reserved.

Numerical investigations of flow and energy fields near a thermoacoustic couple

The flow field and the energy transport near thermoacoustic couples are simulated using a 2D full Navier-Stokes solver. The thermoacoustic couple plate is maintained at a constant temperature; plate lengths, which are short and long compared with the particle displacement lengths of the acoustic standing waves, are tested. Also investigated are the effects of plate spacing and the amplitude of the standing wave. Results are examined in the form of energy vectors, particle paths, and overall entropy generation rates. These show that a net heat-pumping effect appears only near the edges of thermoacoustic couple plates, within about a particle displacement distance from the ends. A heat-pumping effect can be seen even on the shortest plates tested when the plate spacing exceeds the thermal penetration depth. It is observed that energy dissipation near the plate increases quadratically as the plate spacing is reduced. The results also indicate that there may be a larger scale vortical motion outside the plates which disappears as the plate spacing is reduced. (C) 2002 Acoustical Society of America.

Extension of Murray's law using a non-Newtonian model of blood flow.

BACKGROUND: So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. RESULTS: We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. CONCLUSION: It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Otimização ecológica dos ciclos ar-padrão Otto e Diesel

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Ecological optimization of an irreversible Brayton cycle with regeneration, inter-cooling and reheating

A mathematical model is developed for an irreversible Brayton cycle with regeneration, inter-cooling and reheating. The irreversibility are from the thermal resistance in the heat exchangers, the pressure drops in pipes, the non-isentropic behavior in the adiabatic expansions and compressions and the heat leakage to the cold source. The cycle is optimized by maximizing the ecological function, which is achieved by the search for optimal values for the temperatures of the cycle and for the pressure ratios of the first stage compression and the first stage expansion. The advantages of using the regenerator, intercooler and reheater are presented by comparison with cycles that do not incorporate one or more of these processes. Optimization results are compared with those obtained by maximizing the power output and it is concluded that the point of maximum ecological function has major advantages with respect to the entropy generation rate and the thermal efficiency, at the cost of a small loss in power.

Modeling the exergy behavior of human body

Exergy analysis is applied to assess the energy conversion processes that take place in the human body, aiming at developing indicators of health and performance based on the concepts of exergy destroyed rate and exergy efficiency. The thermal behavior of the human body is simulated by a model composed of 15 cylinders with elliptical cross section representing: head, neck, trunk, arms, forearms, hands, thighs, legs, and feet. For each, a combination of tissues is considered. The energy equation is solved for each cylinder, being possible to obtain transitory response from the body due to a variation in environmental conditions. With this model, it is possible to obtain heat and mass flow rates to the environment due to radiation, convection, evaporation and respiration. The exergy balances provide the exergy variation due to heat and mass exchange over the body, and the exergy variation over time for each compartments tissue and blood, the sum of which leads to the total variation of the body. Results indicate that exergy destroyed and exergy efficiency decrease over lifespan and the human body is more efficient and destroys less exergy in lower relative humidities and higher temperatures. (C) 2012 Elsevier Ltd. All rights reserved.

Analysis of a new cross flow heat exchanger flow arrangement - Extension to several rows

The present paper presents a theoretical analysis of a cross flow heat exchanger with a new flow arrangement comprehending several tube rows. The thermal performance of the proposed flow arrangement is compared with the thermal performance of a typical counter cross flow arrangement that is used in chemical, refrigeration, automotive and air conditioning industries. The thermal performance comparison has been performed in terms of the following parameters: heat exchanger effectiveness and efficiency, dimensionless entropy generation, entransy dissipation number, and dimensionless local temperature differences. It is also shown that the uniformity of the temperature difference field leads to a higher thermal performance of the heat exchanger. In the present case this is accomplished thorough a different organization of the in-tube fluid circuits in the heat exchanger. The relation between the recently introduced "entransy dissipation number" and the conventional thermal effectiveness has been obtained in terms of the "number of transfer units". A case study has been solved to quantitatively to obtain the temperature difference distribution over two rows units involving the proposed arrangement and the counter cross flow one. It has been shown that the proposed arrangement presents better thermal performance regardless the comparison parameter. (C) 2012 Elsevier Masson SAS. All rights reserved.

Human thermal comfort: an irreversibility-based approach emulating empirical clothed-body correlations and the conceptual energy balance equation

Exergetic analysis can provide useful information as it enables the identification of irreversible phenomena bringing about entropy generation and, therefore, exergy losses (also referred to as irreversibilities). As far as human thermal comfort is concerned, irreversibilities can be evaluated based on parameters related to both the occupant and his surroundings. As an attempt to suggest more insights for the exergetic analysis of thermal comfort, this paper calculates irreversibility rates for a sitting person wearing fairly light clothes and subjected to combinations of ambient air and mean radiant temperatures. The thermodynamic model framework relies on the so-called conceptual energy balance equation together with empirical correlations for invoked thermoregulatory heat transfer rates adapted for a clothed body. Results suggested that a minimum irreversibility rate may exist for particular combinations of the aforesaid surrounding temperatures. By separately considering the contribution of each thermoregulatory mechanism, the total irreversibility rate rendered itself more responsive to either convective or radiative clothing-influenced heat transfers, with exergy losses becoming lower if the body is able to transfer more heat (to the ambient) via convection.