Optimal Reynolds number for the fully developed laminar forced convection in a helical coiled tube

This paper analyzes the optimal Re for the steady, laminar, fully developed forced convection in a helical coiled tube with constant wall heat flux based on minimal entropy generation principle. Two working fluids, water and air, are considered. It is found that the entropy generation distributions are relatively insensitive to coil pitch, λ. Through the entropy generation analysis for cases of coil curvature ratio, δ ranging from 0.01 to 0.3, and two dimensionless duty parameters, η₁ from 0.1 to 3.0, and η₂/10²⁰ from 0.01 to 1.0, the optimal Re for cases with various combinations of the design parameters is reported. In addition, a correlation equation for the optimal Re, δ, η₁, and η₂ is proposed after a least-square-error analysis. The optimal Re should be adopted as the operating condition according to the relevant design parameters of the helical coils so that the thermal system can have the best exergy utilization with the least irreversibility.     

Investigation of potential of improvement of helical coils based on avoidable and unavoidable exergy destruction concepts

An inevitable problem challenges heat exchanger designers is that the heat transfer augmentation in a thermal system is always achieved at the expense of an increase in pressure loss. Thus, the trade-off by choosing the most proper configuration and best flow condition has become the critical problem for design work. The brief survey on literature shows that optimal Reynolds number of laminar forced convection in a helical tube, was specified based on minimum entropy generation. Therefore, the present study analyzes the thermodynamic potential of improvement for steady, laminar, fully developed, forced convection in a helical coiled tube subjected to uniform wall temperature based on the concept of avoidable and unavoidable exergy destruction. The influence of various parameters such as coil curvature ratio, dimensionless inlet temperature difference, dimensionless passage length of the coil, and fluid properties on avoidable exergy destruction have been investigated for water as working fluid. Results show considerable potential of thermodynamic optimization of helical coil tubes. In addition, a relation for determining the amount of optimum Dean Number is proposed for the range considered in the present study.     

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.     

Experimental investigation on the convective heat transfer in straight and coiled corrugated tubes for highly viscous fluids: Preliminary results

The forced convective heat transfer in straight and coiled tubes, having smooth and corrugated wall, was experimentally investigated in two ranges of the Reynolds number: a lower one (5 < Re < 13) obtained with Glycerol and a higher one (150 < Re < 1500) obtained with Ethylene Glycol. The aim of the research was to verify the effectiveness of these passive heat transfer enhancement techniques when highly viscous fluids are treated. This issue is particularly crucial in applications in which the thermal processing of high Prandtl number fluids is required, such as in the food, chemical, pharmaceutical and cosmetics industries. In the present note, preliminary results, obtained by considering a given geometrical configuration characterized by a tube diameter of 14 mm, a curvature ratio of 0.06, a corrugation depth of 1 mm and a corrugation pitch of 16 mm, are presented. The main conclusion is that the wall curvature enhances heat transfer at all Re, whereas the wall corrugation enhances heat transfer only in the higher Re range; moreover the wall corrugation is totally ineffective in the low Re range and, if helical coils are present, it also destroys the benefit induced by the wall curvature. The largest increment in heat transfer rates is thus obtained by using smooth helical coils at low Re, and corrugated helical coils at larger Re. The results, although of preliminary nature, suggest interesting applications of the passive heat transfer enhancement technique based on smooth wall coiled tubes in the very low Reynolds number values range, while the combined passive technique based on wall corrugation and curvature represents an interesting solution for Reynolds number values in the range 150–1500.     

Second law optimization of a solar air heater having chamfered rib–groove roughness on absorber plate

Artificially roughened solar air heaters perform better than the plane ones under the same operating conditions. However, artificial roughness leads to even more fluid pressure thereby increasing the pumping power. The entropy generation in the duct of solar air heater having repeated transverse chamfered rib–groove roughness on one broad wall is studied numerically. Roughness parameters, viz., relative roughness pitch P/e, relative roughness height e/D_h relative groove position g/P, chamfer angle φ and flow Reynolds number Re have a combined effect on the heat transfer as well as fluid friction. The entropy generation is minimized and reasonably optimized designs of roughness are found.     

Second law based optimization of free convection film-wise condensation on a horizontal tube

This study uses the entropy generation minimization (EGM) method to optimize a saturated vapor flowing slowly onto and condensed on an isothermal horizontal tube. The result shows that the optimal group Rayleigh parameter exists over the parametric range investigated for horizontal tube at which the entropy generated at a minimum rate. The minimum entropy generation number in condensation heat transfer for optimal diameter, D_OPT of tube is expressed in terms of the group Brinkman parameter (Br/ψ). The result provides an immediate estimate of the relative increase in irreversibility associated with using a tube of diameter D ≠ D_OPT.     

Hydrogen storage system based on hydride materials incorporating a helical-coil heat exchanger

Metal hydrides offer the potential to store hydrogen at modest pressures and temperatures with high volumetric efficiencies. The process of charging hydrogen into a metal powder to form the hydride is exothermic. The heat released by the reaction must be removed quickly in order to maintain a rapid charging rate. An effective method for heat removal is to embed a heat exchanger within the metal hydride bed. Here, we investigate the effectiveness of a helical coil heat exchanger tube to remove the heat generated during the absorption process. This paper presents a three-dimensional mathematical model formulated in Ansys Fluent 12.1 to evaluate the transient heat and mass transfer in a cylindrical metal hydride tank embedded with a helical-coil cooling tube. We present results from a parametric study of hydrogen storage efficiency as a function of helical coil pitch and convective heat transfer coefficient (h) within the cooling tube. We also explore the effect of adding aluminum foam to enhance the thermal conductivity of the metal hydride. The parametric study reveals that the mass of stored hydrogen is less sensitive to the coil pitch when aluminum foam is added. It is also found that the absorption rate increases with h as expected, although the rate of improvement diminishes at high values of h. Results were examined at filling times of 3 and 6 min to draw conclusions about the overall effectiveness of this hydrogen storage system. At 3 min, it is found that the addition of 5% Al foam is optimal, and h = 1000 W/m²-K is sufficient to bring the metal hydride to saturation; under these conditions a non-dimensional pitch of 0.5 maximizes the hydrogen absorption. Adding Al foam beyond 5% does not improve volumetric efficiency as the Al foam begins to displace the active hydrogen-absorbing material.     

An experimental study of thermal performance of shell-and-coil heat exchangers

In the present study an experimental investigation of the mixed convection heat transfer in a coil-in-shell heat exchanger is reported for various Reynolds and Rayleigh numbers, various tube-to-coil diameter ratios and dimensionless coil pitch. The purpose of this article is to assess the influence of the tube diameter, coil pitch, shell-side and tube-side mass flow rate over the performance coefficient and modified effectiveness of vertical helical coiled tube heat exchangers. The calculations have been performed for the steady-state and the experiments were conducted for both laminar and turbulent flow inside coil. It was found that the mass flow rate of tube-side to shell-side ratio was effective on the axial temperature profiles of heat exchanger. The results also indicate that the ? − NTU relation of the mixed convection heat exchangers was the same as that of a pure counter-flow heat exchanger.     

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.     

A semi-empirical model for estimating permeability and inertial coefficient of pin-fin heat sinks

This work presents a novel semi-empirical model for estimating the permeability and inertial coefficient of pin-fin heat sinks that are set as porous media. The forms of correlations for the permeability and inertial coefficient of pin-fin heat sinks are firstly derived theoretically, then a series of pressure drop tests are performed for modifying those correlations. The variable parameters of pin-fins studied herein are the relative longitudinal pitch, the relative transverse pitch, the relative fin height and the relative fin length. The present correlations are reasonable by comparing with the data of other tests. Additionally, within the range of Reynolds number (Re_d = 676-11,252), at a given Re_d, the effect of the relative fin height on the pressure drop is negligible. The pressure drop declines as the relative fin length increases, especially as the relative transverse pitch and the relative longitudinal pitch increase. It increases as the relative transverse pitch declines or the relative longitudinal pitch increases.     

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.     

A thermal model for prediction of the Nusselt number in a pipe with chaotic flow

It is currently well established that Lagrangian chaos intensifies heat transfer significantly [J. Fluid Mech. 209 (1989) 335]. It thus appears to be a promising technique for the design of compact, high-performance heat exchangers and heat exchanger-reactors. However, the design of such apparatus requires extensive calculations. The objective of this work is to implement a simplified thermal model with which to simulate heat transfer in a twisted pipe (of a shell and tube heat exchanger) of two tube configurations, helically coiled or chaotic, without requiring the heavy calculations needed in the numerical resolution of the Navier–Stokes and energy equations. The large database obtained from the parametric study of the variation of the Nusselt number using the heat transfer model developed here, allows one to correlate Nu with Re, Pr, N_bends: Nu=1.045Re^0.303Pr^0.287N_bends^−0.033. This correlation is valid for coil geometry with alternating planes of curvature, i.e. chaotic configuration and the range of validity of the correlation is Re∈[100;300], Pr∈[30;100] and N_bends∈[3;13].     

Entropy flow and generation in radiative transfer between surfaces

Entropy of radiation has been used to derive the laws of blackbody radiation and determine the maximum efficiency of solar energy conversion. Along with the advancement in thermophotovoltaic technologies and nanoscale heat radiation, there is an urgent need to determine the entropy flow and generation in radiative transfer between nonideal surfaces when multiple reflections are significant. This paper investigates entropy flow and generation when incoherent multiple reflections are included, without considering the effects of interference and photon tunneling. The concept of partial equilibrium is applied to interpret the monochromatic radiation temperature of thermal radiation, T_λ(λ, Ω), which is dependent on both wavelength λ and direction Ω. The entropy flux and generation can thus be evaluated for nonideal surfaces. It is shown that several approximate expressions found in the literature can result in significant errors in entropy analysis even for diffuse-gray surfaces. The present study advances the thermodynamics of nonequilibrium thermal radiation and will have a significant impact on the future development of thermophotovoltaic and other radiative energy conversion devices.     

Entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes

The entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes was numerically performed by using a Reynolds stress model. The simulations were conducted for a smooth tube and five cases of corrugated tubes with Reynolds number (Re) ranging from 10,020 to 40,060 at a constant wall temperature condition. The effects of corrugation pitch and height on the flow patterns as well as local thermal and frictional entropy generation are detailed in the near wall region. The results indicate that the local heat transfer entropy generation is significantly evident at the sub-layer region and the detached vortex region, and the local thermal entropy is improved with increases in the secondary flow. Local friction entropy generation is mainly located at the windward of the corrugation and the severely turbulent fluctuation region and is mainly induced by the velocity gradient. The average friction entropy generation exhibits an exponential growth, while the average heat transfer and the total entropy generation display a linear growth trend with increased Re. The average Bejan number (Be) exhibits an exponential decline, and the minimum value can reach 0.69. From a comprehensive viewpoint, it is optimal for the Re to be lower than 30,050. When Re <20,030, higher and dense corrugations are beneficial. When 20,030?Hl/D?=?0.08 is not recommended.     

Numerical Simulation and Optimization of Enhanced Heat Transfer in Helical Oval Tubes: Effect of Helical Oval Tube Modification,Pitch Ratio,and Depth Ratio

ABSTRACT

Flow and heat transfer behaviors in the helical oval tube, alternate-twisted-direction helical oval tube and regularly spaced helical oval tubes were numerically investigated. The helical oval tubes with eight oval tube depth ratios (0.03, 0.04, 0.05, 0.06, 0.07, 0.10, 0.15, and 0.20) and nine oval tube pitch ratios (0.6, 0.8, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0) were examined in turbulent regime, Reynolds number ranged from 5000 to 20,000. The computational results showed that fully developed periodic flow and heat transfer in helical oval tubes commenced at around entrance length to characteristic diameter of 8–9. The decreasing depth ratio and increasing pitch ratio helped to reduce the pressure loss of the tube heat exchanger. The maximum thermal performance of 1.30 was obtained by the use of the helical oval tube with depth ratio of 0.05 and pitch ratio of 0.6 at the lowest Reynolds number of 5000. At similar conditions, typical helical oval tubes offered better heat transfer rate and thermal performance than helical oval tubes with alternate axes and regularly spaced helical oval tubes.     

Entropy generation in impinging flow confined by planar opposing jets

In this paper, entropy generation in impinging flow confined by planar opposing jets is investigated systematically for the first time. Different from previous works on entropy generation for practical flows, in this study the lattice Boltzmann method, which is more suitable for massive parallel computing, is used to solve the governing equations for flow field as well as the entropy generation equation, instead of traditional numerical methods. The effects of the Reynolds number 10 ≤ Re ≤ 500 and the distance ratio between opposing jets 2/5 ≤ W/L ≤ 4/5 on entropy generation are revealed. It is found that the local entropy generation number is more sensitive to the variation of W/L than Re when Re > 50. The total entropy generation number increases exponentially with Re but decreases as a power function of W/L. In addition, the entropy generation will receive significant influence from the damping traveling pressure wave during the transient state and the maximum emerges when the gas ejected from the top and bottom jets begins meeting and impinging.     

Thermo-Hydrodynamics of a Helical Coil Heat Exchanger Operated with a Phase-Change Ice Slurry as a Refrigerant

The thermal performance of helical-coil heat exchangers can be significantly enhanced when operated with ice slurry as a phase-change refrigerant. It is essential to also consider the hydrodynamics of ice slurry flow to determine the overall performance of the heat exchanger. This study presents a detailed numerical investigation of the thermo-hydrodynamic performance of a helical coil heat exchanger operated with a laminar and non-Newtonian flow of ethyl-alcohol ice slurry subject to phase change. The Bingham plastic model is used to reflect the non-Newtonian behavior of ice slurry. The phase change of ice slurry is modelled using the enthalpy-porosity method. The pressure drop and heat transfer of ice slurry in a double-turn helical coil are determined in terms of ice mass fraction and Dean number. The results show that an increase in the ice mass fraction and Dean number results in an increase of the heat transfer rate. This is, however, associated with an increase in pressure drop. The entropy generation analysis is introduced to evaluate the overall performance of the heat exchanger, taking into account the opposing effects of heat transfer and pressure drop. It is evident that, at certain ice mass fractions, there exists an optimal value of the Dean number that leads to minimum irreversibility and maximum overall performance.     

Heat transfer and pressure drop for low Reynolds turbulent flow in helically dimpled tubes

Three-dimensional helically dimpled tubes have been experimentally studied in order to obtain their heat transfer and isothermal friction characteristics. Using water and ethylene glycol as test fluids, a wide range of fluid flow conditions was covered: 2000<Re<100,000 and 2.5<Pr<100. An experimental study of 10 tubes with different geometric forms (dimple height h/d ranging from 0.08 to 0.12 and helical pitch p/d, from 0.65 to 1.1) offers insight into the influence of manufacturing parameters on tube thermohydraulic behaviour. The large amount of experimental data have been correlated so as to obtain easy to use expressions for Fanning friction factors and Nusselt numbers as functions of flow and geometry non-dimensional parameters. Performance evaluation criteria, commonly used in the enhanced heat transfer literature, were calculated in order to assess the real benefits offered by dimpled tubes.     

Optimal Reynolds number of laminar forced convection in a helical tube subjected to uniform wall temperature

In this study, fully developed laminar flow and heat transfer in a helically coiled tube with uniform wall temperature have been investigated analytically based on minimal entropy generation principle. The influence of coil curvature ratio and fluid properties, β₁ and β₂ on the optimum Reynolds number have been investigated for two well-known fluids viz. air and water. It was revealed that optimum Reynolds numbers decrease as curvature ratio increases except in the low ranges of curvature ratio where transition to turbulent flow occurs. In the range of the present study, a correlation predicting optimal Reynolds number was proposed for each fluid using least square analysis.     

Optimisation of heat transfer enhancement devices in a bayonet tube heat exchanger

This paper considers the assessment and analysis of heat transfer enhancement devices which can be considered for a bayonet tube heat exchanger. Due to restraining conditions, such as material selection, manufacturing complexity, etc., simple rib roughened surfaces in the form of rings were used on the air side flow, in the annulus. Analysis of the effect of the rings were studied, starting from cited geometries, using computational fluid dynamics. Validation was carried out using laser diagnostics. For the range of Reynolds numbers (Re_ave=160,000) considered the optimal ring configuration was a ring to annulus height ratio of 0.37 with a pitch to ring height ratio of 10. This provided the optimal heat flux to pressure drop for the given conditions.