Second law analysis of fully developed laminar flow for rectangular ducts with semicircular ends

Second law analysis is performed analytically for rectangular ducts with semicircular ends in laminar flow. Two different situations are considered for the analysis. In the first case, boundaries of duct are considered in constant wall temperature. In the second case, constant wall heat flux boundary conditions applied. Entropy generation is obtained for various cross sectional areas, various wall heat flux and Reynolds numbers. It is found that with the increasing aspect ratio (β) values for both constant wall temperature (CWT) and constant heat flux (CHF) total entropy generation increases, however, required pumping power also increases.     

An analysis of entropy generation through a circular duct with different shaped longitudinal fins for laminar flow

The present study focuses on the entropy generation analysis in a circular duct with internal longitudinal fins of different shape for laminar flow. Three different fin shapes are chosen for the analysis: Thin, triangular and V-shaped fins. Calculations are performed for various dimensionless lengths and number of fins, dimensionless temperature difference and fin angle for triangular and V-shaped fins. It is found that the number of fins and dimensionless length of the fins for both thin fins and triangular fins, and the fin angle for triangular and V-shaped fins have significant effect on both entropy generation and pumping power. Further, both entropy generation and pumping power also are influenced by dimensionless temperature difference.     

Effect of rounded corners on the secondary flow of viscoelastic fluids through non-circular ducts

The Reiner–Rivlin viscoelastic model was used to investigate numerically on the pattern and strength of the secondary flows in rounded corners square ducts. The influence of rheological properties on flow domain was studied. The governing equations for steady state, laminar fully developed flow were solved by finite difference method. It is shown the secondary flow of a Reiner–Rivlin fluid has a negligible effect on the axial flow and f.Re. Viscous and elastic behaviors as well as the rounding of the corners have important effects on the secondary flows created by viscoelastic fluid.     

A numerical study on developing laminar forced convection and entropy generation in half- and double-sine ducts

In the present paper, the developing laminar forced convection and entropy generation in both double- and half-sine ducts are investigated with numerical methods. The studied cases cover Re ranging from 86 to 2000. The duct aspect ratio (Λ/a) and the external heat flux (q^*) are varied as Λ/a=2, 4 and 8, and the values of q^* are varied as 0.0405, 0.0811 and 0.1622, respectively. The comparisons of the flow features, including the distributions of axial velocity, temperature, Nusselt number and the local entropy generation, in the double- and half-sine ducts are provided in detail in the paper. Particularly, the optimal analysis of the two-type ducts based on the minimal entropy generation principle is the major concern. Through the evaluations of the overall entropy generation in the whole flow domain, the optimal option between the double- and half-sine duct is found to be dependent on the duct aspect-ratio, external heat flux and Re. Among all the cases studied, the half-sine duct with Λ/a=2 is found to have the minimal entropy generation, and therefore is concluded as the optimal option for achieving the least irreversibility and best exergy utilization in the thermal system.     

Second law analysis of periodic heat conduction through a wall

Periodic heat conduction through a wall is a simple model for the behaviour of a building wall submitted to climatic temperature changes. Beyond the well-known definition of heat transfer, the present concern is thermodynamics, through two quantities. The first quantity is the total entropy generation (total over time period and wall thickness). Formal derivation shows that from this point of view also, the phenomenon is the superposition of stationary linear heat-conduction plus periodic heat-diffusion around a uniform temperature. The second quantity is defined by considering ideal Carnot cycles that would maintain the inner space at a prescribed temperature. Parameters that influence either quantities are explored, evidencing values of the wall thickness beyond which there does not seem to be any interest in increasing the wall thickness.     

The creeping flow of a polymeric fluid through bent square ducts with heat dissipation

The 3D non-isothermal creeping flow of nylon-6 in a bent square duct with uniform temperature is studied numerically. The non-Newtonian characteristics of this fluid polymer are represented by a differential-type non-isothermal White-Metzner model. Computational results are obtained by the elastic-viscous split-stress (EVSS) finite element method, incorporating the streamline-upwind Petrov-Galerkin (SUPG) scheme. The generated thermal field is entirely due to viscous heating. Essential flow characteristics, including temperature distribution in the flow field, are predicted. The resulting average Nusselt numbers along the walls are obtained. Subsequently, the effects of flow-rate and geometry are investigated.     

Entropy generation through hexagonal cross‐sectional duct for constant wall temperature in laminar flow

Second law analysis of heat transfer in laminar flow for hexagonal cross‐section duct was analysed analytically. Geometrical effect of hexagonal duct was considered. The variation of total entropy generation was studied along the duct length. As a working fluid water and unused engine oil were used to compare the effect of fluid in the duct. Results were compared with circular cross‐section duct. It is found that the non‐dimensional entropy generation in a hexagonal cross‐section duct can be as high as a factor of four than that for a circular duct. Further, the unused engine oil gives up to about ten times lower non‐dimensional entropy generation values than that of water but needs about ten times more pumping power to heat transfer ratio. Copyright © 2004 John Wiley & Sons, Ltd.     

Heat transfer coefficients for the laminar fully developed flow of viscoplastic liquids through annuli

Heat transfer during the laminar fully developed axial flow of viscoplastic materials through concentric annular spaces was studied experimentally. The thermal boundary conditions were insulated outer tube wall and uniform heat flux at the inner tube wall. The flowing liquids were Carbopol aqueous solutions at different concentrations, whose flow curves were well represented by the Herschel–Bulkley viscosity function. The effect of yield stress and power-law exponent on the Nusselt number is investigated. It is shown that the effect of rheological parameters on the inner-wall Nusselt number is rather small.     

Second law optimization of convective heat transfer through a duct with constant heat flux

A second law analysis is carried out on convective heat transfer from a fluid flowing in a duct with constant heat flux. The entropy generated is expressed as a function of the initial temperature difference and the frictional pressure drop. Since the loss in available energy is directly proportional to the entropy generated, an optimum value of the initial temperature difference is found where the entropy generated is the minimum. A similar optimum is found for the ratio of heat transfer to pumping power. An optimum fluid velocity which corresponds to the minimum loss of available power is recommended.     

Further finite element analyses of fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts: Heat transfer predictions

Forced convection heat transfer to hydrodynamically and thermally fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts has been studied for the H1 and T thermal boundary conditions. The solutions for the velocity and temperature fields were obtained numerically using the finite element method with quartic triangular elements. From these solutions, very accurate Nusselt number values were determined. Computations were performed over a range of power-law indices and duct aspect ratios.     

Entropy generation for compressible natural convection with high gradient temperature in a square cavity

Entropy generation due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subjected to different side wall temperatures for compressible and incompressible natural convection flows. Based on the obtained velocity and temperature values, the distributions of local entropy generation, average entropy generation and average Bejan number are determined and compared for compressible and incompressible regimes. It is found that the entropy generated for compressible flow always is more than incompressible flow. The study is performed for Ra = 10⁴–10⁸, ε = 0.01(incompressible regime) and 0.6 (compressible regime), Ge = 10⁻⁵ and Pr = 0.7.     

Mathematical optimisation of laminar forced convection heat transfer through a vascularised solid with square channels

This paper presents a three-dimensional geometric optimisation of cooling channels in forced convection of a vascularised material with the localised self-cooling property subjected to a heat flux. A square configuration was studied with different porosities. Analytical and numerical solutions were provided. The geometrical configuration was optimised in such a way that the peak temperature was minimised at every point in the solid body. The optimisation was subject to the constraint of a fixed global volume of solid material, but the elemental volume was allowed to morph. The solid material was subject to a heat flux on one side and the cooling fluid was forced through the channels from the opposite direction with a specified pressure difference. The structure had three degrees of freedom as design variables: the elemental volume, channel hydraulic diameter and channel-to-channel spacing. A gradient-based optimisation algorithm was used to determine the optimal geometry that gave the lowest thermal resistance. This optimiser adequately handled the numerical objective function obtained from numerical simulations of the fluid flow and heat transfer. The numerical results obtained were in agreement with a theoretical formulation using scale analysis and the method of intersection of asymptotes. The results obtained show that as the pressure difference increases, the minimised thermal resistance decreases. The results also show the behaviour of the applied pressure difference on the optimised geometry. The use of the optimiser made the numerical results to be more robust with respect to the optimum internal configurations of the flow systems and the dimensionless pressure difference.     

Study on friction factor of developing and developed laminar flow in annular-sector ducts

The pressure drops of laminar developing and developed flow in annular-sector ducts with small round corner have been investigated experimentally. Numerical simulation has been performed to study the effect of the small round corner on the friction factor in the developed region. It has been found that with the increase in corner radius, the value off Re decreases. In the range ofr _c/r_ofrom 0.031 to 0.12, the decrease inf Re varies from 0.048% to 0.1% for the five apex angle computed.     

3D simulation of laminar flow and heat transfer in V-baffled square channel

The article presents a numerical investigation on laminar flow and heat transfer characteristics in a three-dimensional isothermal wall square-channel fitted with inline 45° V-shaped baffles on two opposite walls. The computations based on the finite volume method with the SIMPLE algorithm have been conducted for the airflow in terms of Reynolds numbers ranging from 200 to 2000. The inline V-baffles with its V-tip pointing downstream and the attack angle (or half V-apex angle) of 45° relative to the flow direction are mounted repeatedly on the lower and upper walls. The baffled channel flow shows a fully developed periodic flow and heat transfer profile for BR = 0.2 at x/D≈ 8 downstream of the inlet. Influences of different baffle height ratios (BR) and pitch ratios, (PR) on thermal behaviors for a fully developed periodic condition are investigated. It is apparent that the longitudinal counter-rotating vortex flows created by the V-baffle can induce impingement/attachment flows over the walls resulting in greater increase in heat transfer over the test channel. Apart from speeding up the fully developed periodic flow pattern, the rise of the BR leads to the increase in Nu/Nu₀ and f/f₀ values while that of the PR provides an opposite trend. The V-baffle performs better than the angled baffle at a similar condition. The V-baffle with BR = 0.2 and PR = 1.5 yields the maximum thermal performance of about 3.8 whereas the Nu/Nu₀ is some 14 times above the smooth channel at higher Re.     

Numerical prediction on laminar heat transfer in square duct with 30° angled baffle on one wall

A numerical investigation on periodic laminar flow and heat transfer behaviors in a three-dimensional isothermal wall square duct fitted with 30° angled baffles on lower duct wall only is presented. The computations based on a finite volume method with the SIMPLE algorithm have been conducted for the fluid flow in terms of Reynolds numbers ranging from 100 to 2000. The angled baffles with attack angle of 30° are mounted periodically on the lower duct wall to generate a longitudinal vortex flow through the tested duct. Effects of different baffle height and three pitch length ratios on heat transfer and flow characteristics in the duct are investigated. The study shows that the longitudinal vortex flow created by the baffle helps to induce impinging flows over the baffle trailing end sidewall and the inter-baffle cavity wall resulting in drastic increase in heat transfer rate over the test duct. The computational results reveal that the Nusselt number ratio and the maximum thermal enhancement factor values for using the angled baffle are, respectively, found to be about 7.9 and 3.1 at Re = 2000, BR = 0.3 and PR=1.5.     

Entropy generation and mechanical efficiency in laminar peristaltic flow through an elliptical duct

Heat transfer analysis coupled with peristaltic transport is important in many real-world application areas varying from microchannels to spacecrafts. Power production, chemical, and food industries, electronics, and environmental engineering are some examples of applications. In thermal devices, the overall performance of a heat exchanger depends on heat exchanger efficiency and entropy generation. The main purpose of this paper is to study a mathematical model coupling the peristaltic pumping with the heat transfer phenomenon for an incompressible Newtonian fluid in an elliptical tube. The Navier–Stokes and energy equations have been analytically solved for long wavelength, small Reynolds, and small Peclet numbers approximations. Exact expressions of velocity profile and temperature distribution have been found in the wave frame analysis. The impacts of pertinent parameters on the physical quantities of the problem have been analyzed with the help of graphs. We concluded that the geometrical parameters (occlusion, aspect ratio) enhance the pressure rise and the mechanical efficiency. It should be noted that the best way for minimizing entropy generation is decreasing occlusion, aspect ratio, flow rate, or Brinkman number.     

A numerical study on entropy generation induced by turbulent forced convection in curved rectangular ducts with various aspect ratios

The present paper analyzes the entropy generation induced by turbulent forced convection in a curved rectangular duct with external heating by numerical methods. The problem is assumed as steady, three-dimensional and turbulent. The flow features, including the secondary flow motions, the distribution of local entropy generation as well as the overall entropy generation in the whole flow fields, are analyzed. For a baseline case with Re = 20,000, external heat flux q? = 0.112 and aspect ratio γ = 1, the results show the entropy generation induced by the frictional irreversibility concentrates within the regions adjacent to the duct walls, whereas the entropy generation resulted from the heat transfer irreversibility only significantly occurs near the outer wall of the duct where the external heat flux imposed. Except the baseline case, two additional cases with aspect ratio equal to 0.25 and 4 are calculated. Through the comparison of the three aspect-ratio cases, it is seen that the resultant entropy generations in the flow fields for the three cases are all dominated by the frictional irreversibilities. Among the three aspect-ratio cases, the resultant entropy generation is minimal in the γ = 1 case. Accordingly, the case with γ = 1 is concluded to be the optimal aspect ratio under the current flow condition based on the minimal entropy generation principle.     

Performance of solar air heater ducts with different types of ribs on the absorber plate

Repeated ribs are considered an effective technique to enhance forced convection heat transfer in channels. In order to establish the performance of rib-roughened channels, both heat transfer and friction characteristics have to be accounted for. In the present paper, heat transfer coefficients and friction factors have been experimentally investigated for a rectangular channel having one wall roughened by repeated ribs and heated at uniform flux, while the remaining three walls were smooth and insulated. Angled continuous ribs, transverse continuous and broken ribs, and discrete V-shaped ribs were considered as rib configurations. Different performance evaluation criteria, based on energy balance or entropy generation analysis, were proposed to assess the relative merit of each rib configuration. All the rib-roughened channels performed better than the reference smooth channel in the medium-low range of the investigated Reynolds number values, which is that typically encountered in solar air heater applications.     

Heat transfer enhancement for laminar flow of ethylene glycol through a square duct fitted with increasing and decreasing orders of twisted tape

The isothermal friction factor and heat transfer enhancement through a square duct fitted with increasing and decreasing order of twist ratio sets have been studied under nearly uniform wall temperature conditions. The ethylene glycol flows under laminar flow (Re = 30–1200) through a square duct and hot water flows through an annular channel formed between a square duct and circular tube, in a counter current fashion. The hot water at a very high flow rate is circulated though the annular channel to ensure a nearly uniform wall temperature condition. There is not much change in the magnitude of the heat transfer coefficient enhancement with the increasing twist ratio and with the decreasing twist ratio set, as the intensity of the swirl generated at the inlet or at the outlet in the order of increasing twist ratio or decreasing twist ratio, is the same in both the cases. Performance evaluation analysis on constant pumping power was made and a maximum performance ratio was obtained for each twist insert corresponding to a Reynolds number of 680. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20410