Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow

An experimental study of the forced convection heat transfer for non-Newtonian fluid flow in a pipe is presented. We focus particularly on the transitional regime. A wall boundary heating condition of heat flux is imposed. The non-Newtonian fluid used is Carbopol (polyacrylic acid) aqueous solutions. Detailed rheology as well as the variation of the rheological parameters with temperature are reported. Newtonian and shear thinning fluids are also tested for comparative purposes. The characterization of the flow and the thermal convection is made via the pressure drop and the wall temperature measurements over a range of Reynolds number from laminar to turbulent regime. Our measurements show that the non-Newtonian character stabilizes the flow, i.e., the critical Reynolds number to transitional flow increases with shear thinning and yield stress. The heat transfer coefficients are given and compared with heat transfer laws for different regime flows. Details when the heat transfer coefficient loses rapidly its local dependence on the Reynolds number are analyzed.     

EXPERIMENTAL STUDIES ON FLOW IN CONVERGENT AND DIVERGENT DUCTS OF RECTANGULAR CROSS SECTION

This paper describes the experimental examination of the pressure drop and heat transfer of the flow in convergent and divergent ducts of rectangular cross section. The aspect ratio based on the dimensions of the large end of the duct was 0⋅1. It has been found that at a given convergent or divergent angle pressure drop decreases while heat transfer increases with increasing Reynolds number. Along a given duct of small convergent angle, pressure drop increases while heat transfer decreases along the duct. However, heat transfer may increase near the downstream end of ducts of high convergent angle. At a given Reynolds number, both pressure drop and heat transfer increase with increasing convergent angle. As for flow in divergent ducts, the effects of Reynolds number on pressure drop and heat transfer are somewhat similar to those of flow in a convergent duct. © 1997 by John Wiley & Sons, Ltd.     

Performance of Microchannel Heat Sinks with Newtonian and Non-Newtonian Fluids

In this paper, the flow behavior and heat transfer performance of a microchannel heat sink is examined. Microchannel heat sink is a heat exchanger that is used to control the temperature of electronic devices with high heat flux capacity. A comprehensive thermal model for a microchannel should include a three-dimensional conduction analysis in the solid parts, followed by an extensive three-dimensional developing flow in the fluid region. The heat transfer analysis in the transition region of the fluid section is a crucial matter. Hydrodynamic and thermal entrance lengths are two important parameters, among others, which are studied in the solution. To examine the potential of using a non-Newtonian fluid, the power law model was used for both Newtonian and non-Newtonian fluids. The numerical solution of the problem was based on a finite difference approach using a control volume with staggered grid system. The SIMPLE algorithm was applied to the problem, and convection terms were estimated using QUICK method. A comparison of the Newtonian and non-Newtonian results showed that for shear thinning fluids, the pressure drop could reduce up to 45%, while for shear thickening fluids, it can increase up to 48%. The same comparison for the Nusselt number showed about a 160% increase with shear thinning fluids and a 43% decrease with shear thickening fluids. The thermal resistance at a Reynolds number of 50 will reduce approximately 25% with shear thinning fluids and will increase approximately 5% with shear thickening fluids. At higher values of the Reynolds number, the changes in the value of the thermal resistance are more pronounced.     

Thermally dependent viscosity and non-Newtonian flow in a double-pipe helical heat exchanger

A double-pipe helical heat exchanger was numerically studied to determine the effects of thermally dependent viscosity and non-Newtonian flows on heat transfer and pressure drop for laminar flow. Thermally dependent viscosities were found to have very little effect on the Nusselt number correlations for Newtonian fluids; however significant effects on the pressure drop in the heat exchanger were predicted. Changing the flow rate in the annulus can significantly affect the pressure drop in the inner tube, since the average viscosity of the fluid in the inner tube would change due to the change in the average temperature.The effects of non-Newtonian power law fluids on the heat transfer and the pressure drop were determined for laminar flow in the inner tube and in the annulus. The Nusselt number was correlated with the Péclet number for heat transfer in the inner tube. For the annulus, the Nusselt number was found to correlate best with the Péclet number and the curvature ratio. Pressure drop data were compared by using ratios of the pressure drop of the non-Newtonian fluid to a Newtonian fluid at identical mass flow rates and consistency indices.     

Thermal Enhancement of Triangular Ducts Using Compound of Vortex Generators and Nanofluids

Laminar flow and heat transfer of three different types of nanofluids; Al₂O₃, CuO, and SiO₂ suspended in ethylene glycol, in a triangular duct using delta-winglet pair of vortex generator are numerically simulated in three dimensions. The governing equations of mass, momentum and energy are solved using the finite volume method. The effects of types, concentrations, and diameter of solid nanoparticles and Reynolds number on thermal and hydraulic performance of triangular duct are examined. The range of Reynolds number, volume fraction and nanoparticles diameters is 100–1200, 1–4%, and 25–85 nm, respectively. The results indicate that the average Nusselt number increases with the particles volume fraction and Reynolds number associated with an increase in the pressure drop. The heat transfer enhancement and pressure drop penalty reduce with increasing the particles diameters. However, a reduction in the pumping power required is observed to force the nanofluids when the volume fraction increases, assuming the heat transfer coefficient remains constant.     

Heat transfer and pressure drop characteristics of flow in convergent and divergent ducts

The heat transfer and pressure drop characteristics of the flow in convergent and divergent ducts of rectangular crosssection are obtained through the simulation of the flow by a three-dimensional parabolic model. The results show that in both convergent and divergent flows heat transfer decreases and pressure drop increases sharply near the entrance region of the ducts. Generally, the Nusselt number increases with increasing convergent/divergent angle, aspect ratio, or Reynolds number, and the pressure drop increases with increasing convergent/divergent angle or decreasing aspect ratio or Reynolds number in both flows. However, an increasing convergent/divergent angle may also result in a lower pressure drop owing to the recovery of static pressure from dynamic pressure. Furthermore, the pressure drop in a divergent flow is generally lower than that in a convergent flow except in the entrance region. For divergent flows with high divergent angle or high Reynolds number, flow separation may occur.     

Experiments and modeling of the hydraulic resistance and heat transfer of in-line square pin fin heat sinks with top by-pass flow

In pin-fin heat sinks, the flow within the core exhibits separation and hence does not lend itself to simple analytical boundary layer or duct flow analysis of the wall friction. In this paper, we present some findings from an experimental and modeling study aimed at obtaining physical insight into the behavior of square, in-line pin fin heat sinks. In addition to the detailed pressure measurements, the overall thermal resistance was measured as a function of Reynolds number and by-pass height. A “two-branch by-pass model” was developed, in which a one-dimensional difference approach was used to model the fluid flow through the heat sink and its top by-pass duct. Inlet and exit pressure losses were as important as the core pressure drop in establishing the overall flow and pressure drop. Comparisons were made with the data using friction and heat transfer coefficients available in the literature for infinitely long tube bundles of circular cross-section. It was shown that there is a good agreement between the temperature predictions based on the model and the experimental data at high approach velocities for tall heat sinks, however the discrepancy increases as the approach velocity and heat sink height decrease. The validated model was used to identify optimum pin spacing as a function of clearance ratio.     

Exact solution of two phase stratified flow through the pipes for non-Newtonian Herschel–Bulkley fluids

Steady state, laminar and fully developed stratified two phase flow including two immiscible fluids through the pipe has been studied analytically. One of the phases is Newtonian and the other one is non-Newtonian which obeys the Herschel–Bulkley fluid model. The dimensionless velocity distribution, Martinelli correction factor and non-Newtonian liquid holdup have been reported. The effect of interface curvature and wide range of viscosity ratio of two phases on flow behavior has been investigated. The results illustrate that the non-Newtonian rheological properties have significant effects on dimensionless velocity and consequently on two phase flow pressure drop specially for larger viscosity ratio.     

圆管内对流换热过程中潜热型功能流体流动阻力特性的实验研究

实验研究了由正十四烷和尿素甲醛树脂制成的相变微胶囊和水混合制成的潜热型功能流体在流过恒热流圆管进行对流换热时的流动阻力特性,获得了压降随流速的变化关系、摩擦阻力系数和表观黏度随R e的变化关系。并在同样条件下用单相水进行了对比实验。相变微胶囊的加入导致流体流动阻力较单相流体有显著增大。管路中扰动件导致单相流体的流动阻力特性在低R e条件下呈湍流特征;功能流体则呈不同规律,扰动仅导致流动阻力进一步增大,而流动阻力特性仍呈层流特征。     

Thermohydraulic performance of a periodic trapezoidal channel with a triangular cross-section

Simulations are performed to study the heat transfer behaviour of an equilateral triangular section duct following a tortuous path for fully-developed laminar flows with Reynolds numbers below 200. The enhancement of heat transfer and the increase in pressure drop are compared with those for ducts of circular, semi-circular and square section following the same serpentine path. For this flow regime, the triangular duct is shown to be the optimum choice (best heat transfer augmentation compared with increased pressure drop) amongst those studied. The effects of changing the path shape, the apex angle for an isosceles triangular cross-section and rounding of a corner of the equilateral triangular duct are also considered.     

Effect of Serpentine Grooves on Heat Transfer Characteristics of Microchannel Heat Sink with Different Nanofluids

An experimental and numerical investigation of the thermal performance of three different nanofluids ethylene glycol‐based CuO, water‐based CuO, and Al₂O₃ is done in a serpentine‐shaped micorchannel heat sink. The microchannels considered ranged from 810 μm to 890 μm in hydraulic diameter and were made of copper material. The experiments were conducted with the Reynolds number ranging from approximately 100 to 1300. The forced convective heat transfer coefficient of nanofluids shows that there is an improved heat transfer rate compared to base fluids water and ethylene glycol. The experimental results also confirm that there is an earlier transition from laminar to turbulent flow in microchannels. The results prove that as the hydraulic diameter decreases there is increased pressure drop and the heat transfer coefficient increases for both the base fluids and nanofluids. The flow characteristics are discussed based on the pressure drop. While investigating the heat transfer coefficient of the three different nanofluids the nanofluid CuO/EG has the highest heat transfer coefficient as a result of the material's property. This research also will encourage young researchers to work on nanofluids of varying nanoparticle size and concentration to discover new results.     

Frottements et pertes de charge des fluides viscoélastiques dans des conduites rectangulaires

RésuméPour les fluides newtoniens dans des configurations simples, la définition du nombre de Reynolds ne présente aucune difficulté, par contre dans le cas d'écoulement de fluides non newtoniens dans des conduites de formes quelconques, la variation de la viscosité avec la vitesse de cisaillement nécessite une généralisation de ce nombre adimensionnel. Malheureusement plusieurs définitions différentes ont été proposées dans la littérature. Ce travail propose une méthode générale valable pour une large classe de fluides non newtoniens et pour toutes les formes de conduite. Une application est développée pour un fluide viscoélastique s'écoulant dans une conduite de forme rectangulaire. Les résultats obtenus par cette étude sont en bon accord avec les corrélations connues.For Newtonian fluids in simple configurations, the definition of the Reynolds number is quite a standard problem, but for non-Newtonian fluid flows in ducts with arbitrary shape of cross section, the dependence of the viscosity with the shear rate requires a generalization of this dimensionless number, unfortunately several different definitions have been proposed in the literature. This work proposes a general method valid for a large class of non-Newtonian fluids and for all duct shapes. Application is developed for a viscoelastic flow through a rectangular duct. Results obtained in the present investigation are in a good agreement with available correlations.     

Laminar Flow and Heat Transfer to a Non-Newtonian Fluid in an Entrance Region of a Square Duct with Prescribed Constant Axial Wall Heat Flux

Abstract

Forced-convection heat transfer information as a function of the pertinent nondimensional numbers is obtained numerically for laminar incompressible non-Newtonian fluid flow in the entrance region of a square duct with simultaneously developing temperature and velocity profiles for constant axial wall heat flux with uniform peripheral wall temperature. The power-law model characterizes the non-Newtonian behavior.

Finite-difference representations are developed for the equations of the mathematical model, and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Results are presented for local and mean Nusselt numbers as functions of the Graetz number and the Prandtl number in the entrance region. Comparisons are made with previous analytical work for Newtonian fluids. The results show a strong effect of the Prandtl number on the Nusselt numbers with fully developed and uniform velocity profiles representing the lower and upper limits, respectively. The results provide a new insight into the true three-dimensional character of the pseudoplastlc fluid flow in the entrance region of a square duct and are accurate.     

Pressure drop predictions for laminar flows of extended modified power law fluids in rectangular ducts

This paper reports on a numerical study of the friction factor-modified Reynolds number product, f × Re_M, for fully developed, laminar flows of pseudoplastic and dilatant fluids in rectangular ducts. Constitutive equations for the apparent viscosity that span from the low shear rate Newtonian region through the high shear rate Newtonian region were utilized, and a shear rate parameter was defined that determines the flow regime where the duct is operating. Numerical results for f × Re_M in all flow regimes are included along with correlation equations. Errors associated with applying power law solutions to flows of weakly non-Newtonian fluids are discussed.     

Thermal and hydraulic characteristics of a triangular duct using an Al2O 3 nanofluid in a turbulent flow regime

This paper presents the computational analysis of convective heat transfer characteristics, pressure drop, and entropy generation characteristics of Al₂O₃/water nanofluids in a noncircular duct (triangular) using a single phase approach under a turbulent flow regime. The thermal and pressure drop characteristics of different concentrations of Al₂O₃ nanoparticles (NPs) and the analysis were carried out in Fluent software using a k‐ε approach under constant wall heat flux around the boundary. The results show that there is an increase in pressure drop and thereby an increase in friction by 20% for the smooth condition. The total pressure drop between the entry and exit section of the duct is increased to approximately 84.2% and 85.6% for a higher Reynolds number (Re = 10 000) compared with that of base fluid. Similarly, the entropy generation of water is increased by 40% as compared with 0.05% and 0.1% Al₂O₃ NPs. There is also a decrease in entropy generation identified while there is an increase in the Reynolds number. The convective heat transfer of 0.05% and 0.1% nanofluid has a similar trend with increased Reynolds number. The maximum performance is observed at the Reynolds number (Re = 4000) and found to be 1.29 for 0.1% concentration, whereas, the fluid at 0.05% is observed to be at 1.23. At a higher Reynolds number (Re = 10 000) the performance index decreased to approximately 1.19 and 1.25 for 0.05% and 0.1%, respectively.     

Viscous dissipation and heat transfer in pulsatile flows of a yield-stress fluid

The convective heat transfer phenomenon due to viscous dissipation associated with the low Reynolds number pulsatile flow of a non-Newtonian inelastic fluid exhibiting a yield-stress (Bingham fluid) through a circular pipe is studied numerically. The problem is of interest in a number of industrial applications such as the processing of industrial slurries and plastic melts. The singularities due to the infinite value attained by the effective viscosity at zero rates of deformation is avoided by adopting a bi-viscosity model. The flow enhancement characteristic of the pulsatile flows of non-Newtonian fluids affects the associated heat transfer rates in the case of non-isothermal flows. The emphasis in this study is on investigating the effects of the fluid rheology, characterized by the yield number, as well as the frequency of the imposed pulsatile pressure gradient on the fluid flow and its heat transfer characteristics. The presented results reveal the instataneous as well as the time averaged characteristics of the flow and heat transfer phenomena.     

Numerical investigations of flow and heat transfer enhancement in a corrugated channel using nanofluid

In this paper, heat transfer and pressure drop characteristics of copper–water nanofluid flow through isothermally heated corrugated channel are numerically studied. A numerical simulation is carried out by solving the governing continuity, momentum and energy equations for laminar flow in curvilinear coordinates using the Finite Difference (FD) approach. The investigation covers Reynolds number and nanoparticle volume fraction in the ranges of 100–1000 and 0–0.05 respectively. The effects of using the nanofluid on the heat transfer and pressure drop inside the channel are investigated. It is found that the heat transfer enhancement increases with increase in the volume fraction of the nanoparticle and Reynolds number, while there is slight increase in pressure drop. Comparisons of the present results with those available in literature are presented and discussed.     

Experimental Study on the Air-Side Performance of a Multipass Parallel and Counter Cross-Flow L-Footed Spiral Fin-and-Tube Heat Exchanger

This study conducted experiments on the air-side performance of novel L-footed spiral fin-and-tube heat exchangers that were faced with airflow at high Reynolds numbers (3500–13,000). The examined heat exchangers have a multipass parallel-and-counter cross-flow type of water flow arrangement. This flow arrangement is a combination of the parallel cross-flow and the counter cross-flow. This type of water flow arrangement may be the best fit for the reverse-flow system, because it can provide constant heat-exchange effectiveness for every flow reversal direction at the same airflow rate. Ambient air was used as a working fluid on the air side and hot water for the tube side. This way the effect of the number of tube rows on the heat transfer and friction characteristics of L-footed spiral fin-and-tube heat exchangers was clearly observed. The effect of the fin's outside diameter on the pressure drop was also studied. The results show that the number of tube rows has no significant effect on the air-side heat transfer or on friction characteristics at high Reynolds numbers. However, the fin's outside diameter shows a significant effect on the pressure drop. The pressure drop increases as the fin's outside diameter increases for the same number of tube rows.     

高浓度水煤浆直管内流动的数值模拟

通过管流法试验得出质量浓度为65.3%的兖州煤水煤浆为剪切增稠的幂流体。将试验得出的流变模型和参数作为计算的依据,运用FLUENT软件提供的非牛顿流体模块,对水煤浆在直管中的流动进行了数值模拟。计算得出水煤浆在管道中流动产生滑移的临界速度,并得到临界速度与管径的变化关系。提出滑移速度新的定义方法,计算得出三个管径中不同平均流速下的滑移速度均为0.02 m/s,表明水煤浆的滑移速度与平均流速和管径呈弱相关。通过对滑移速度进行修正,得出滑移修正后的单位长度压差与实测值相吻合,表明计算模型是正确的。计算得到管道截面水煤浆的表观粘度变化曲线,从管壁到管道中心先缓慢减少再急剧降低。     

Thermally Developing Forced Convection of Non-Newtonian Fluids Inside Elliptical Ducts

Laminar-forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a non-Newtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various cross-section aspect ratios.