Laminar tube flow heat transfer in non-newtonian fluids under arbitrary wall heat flux

Analytical solutions are developed for the wall temperature profile of a power law fluid in laminar flow in a circular tube. This profile is first developed for the boundary condition involving uniformly constant heat flux at the wall. This is next extended for the boundary condition involving an arbitrarily varying heat flux at the wall. The computed results are finally compared with measured values obtained from a horizontal recirculating flow experimental unit.     

Developing flow and heat transfer to power law fluids in square,trapezoidal and pentagonal ducts

A computational method has been developed successfully to predict the developing flow and heat transfer to a power law fluid flowing in square, trapezoidal and pentagonal cross-section straight ducts. The governing three-dimensional equations are parabolized axially. An orthogonal body-fitted coordinate system is employed to handle any arbitrary simply-connected channel geometry. The transformed equations are discretized and solved by line SOR technique. The computer code is capable of handling various boundary conditions and incorporates variable fluid properties and viscous dissipation. Typical results are presented to demonstrate the applicability of the code developed.     

Finned tube performance evaluation with nanofluids and conventional heat transfer fluids

The performance of hydronic finned-tube heating units with nanofluids is compared to their performance with a conventional heat transfer fluid comprised of 60% ethylene glycol and 40% water, by mass (60% EG) using a mathematical model. The nanofluids modeled are comprised of either CuO or Al₂O₃ nanoparticles dispersed in the 60% EG solution. The finned tube configuration modeled is similar to that commonly found in building heating systems. The model employs correlations for nanoparticle thermophysical properties and heat transfer that have been previously documented in the literature. The analyses indicate that finned tube heating performance is enhanced by employing nanofluids as a heat transfer medium. The model predicts an 11.6% increase in finned-tube heating output under certain conditions with the 4% Al₂O₃/60% EG nanofluid and an 8.7% increase with the 4% CuO/60% EG nanofluid compared to heating output with the base fluid. The model predicts that pumping power required for a given heating output with a given finned tube geometry is reduced with both the Al₂O₃/60% EG and the CuO/60% EG nanofluids compared to the base fluid. The finned tube with 4% Al₂O₃/60% EG has the lowest liquid pumping power at a given heating output of all the fluids modeled.     

Laminar heat transfer to temperature-dependent Bingham fluids in tubes

This paper presents a theoretical treatment of laminar flow heat transfer in circular tubes for a temperature-dependent non-Newtonian fluid for which the relationship between the shear stress, τ, and the shear rate, ġg, can be described by an equation of the form τ=τ_y + K(T)ġgⁿ where τ_y is a yield stress, n is a constant and K(T) is a function of temperature. This model can therefore cater for both power-law and Bingham plastic behaviour. The two boundary conditions of constant wall temperature and constant wall heat flux are considered for both heating and cooling situations. The computed results are presented by plotting a Nusselt number as a function of the Graetz number with dimensionless groups specifying the temperature dependence effect, the rheological properties and the wall conditions as parameters. This method of presentation is convenient for engineering design purposes. Temperature profiles, velocity profiles and the pressure drop can also be determined.     

Turbulent heat transfer in a horizontal helically coiled tube

An experiment has been conducted in detail to study the turbulent heat transfer in horizontal helically coiled tubes over a wide range of experimental parameters. We found that the enhancement of heat transfer in the coils results from the effects of turbulent and secondary flows. With Reynolds number increasing to a high level, the contribution of the secondary flow becomes less to enhance heat transfer, and the average heat transfer coefficient of the coil is closer to that in straight tubes under the same conditions. The local heat transfer coefficients are not evenly distributed along both the tube axis and the periphery on the cross section. The local heat transfer coefficients on the outside are three or four times those on the inside, which is half of the average heat transfer. A correlation is proposed to describe the distribution of the heat transfer coefficients at a cross section. The average cross-section heat transfer coefficients are distributed along the tube axis. The average value at the outlet section should not be taken as the average heat transfer coefficient. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 395–403, 1999     

Suitable Heat Transfer Model for Self-Similar Laminar Boundary Layer in Power Law Fluids

The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.     

Experimental investigation of heat transfer in a triple tube heat exchanger with coiled spring inserts

Experiments have been performed to investigate the effect of coiled spring inserts on heat transfer, pressure drop, and performance parameters of a triple tube heat exchanger (TTHX). Three different spring inserts having a pitch of 5, 10, and 15 mm are used and the diameter of the spring wire is taken as 1 mm. The experiments were carried out under a turbulent flow regime, with water as a working medium in parallel and counter flow configurations. The variation in different performance characteristics like heat transfer coefficient, Nusselt number, and effectiveness have been compared at various Reynolds numbers ranging between 4000 and 16,000 in the considered flow patterns. The Nusselt number of TTHX with the lowest pitch spring is found to be higher than that of the plain TTHX by 57.27% at Re = 4000 for the counter flow configuration. Both the thermal performance factor and effectiveness increased as the pitch of the spring insert was decreased. The effectiveness of TTHX with the lowest pitch spring insert is found higher than that of the plain TTHX by 43.84% in the counter flow pattern.     

A heat transfer correlation of flow boiling in micro-finned helically coiled tube

Two main mechanisms, nucleate boiling and convective boiling, are widely accepted for in-tube flow boiling. Since the active nuclei on the heated wall are dominant for nucleate boiling and flow pattern governs the convective boiling, the heat transfer coefficient is strongly influenced by the wall heat flux, mass flux and vapor quality, respectively. In practical industrial applications, for example, the evaporators in refrigeration, forced convective evaporation is the dominant process and high heat transfer efficiency can be obtained under smaller temperature difference between wall and liquid. Therefore, it is of importance to develop a correlation of convective boiling heat transfer with a good accuracy. In this paper, a new kind of micro-finned helically coiled tube was developed and the flow boiling heat transfer characteristics were experimentally studied with R134a. Based on the analysis of the mechanisms of flow boiling, heat transfer correlations of the specific micro-finned helically coiled tubes are obtained.     

Laminar Natural Convective Heat Transfer in the Enclosed Evacuated Collector Tube with East—West Symmetric Heat Input

INTR0DUCTI0NNaturalconvectioninenclosureshasbeenfoundinavariety0fapplications,suchassolarcollectors,nu-cleartechn0logies,thecoolingofelectronicalcircuits,etc.Amongthemnaturalconvectioninsideanen-closedrectangularcavityisthemostclassicalproblem.Correspondinglyagreatdealofexperimentalandnumericalworkhasbeendoneinsuchafieldwiththe"clean"boundaryCPnditi0nsofuniformwalltem-perature(UWT)anduniformheatflch(UHF).Re-celltlymoreattelltionispaidontheconvectioninthecirculartube.HwangandLai[11inves…     

Laminar forced convection heat transfer of a non-newtonian fluid in a square duct

Numerical solutions for laminar heat transfer of a non-Newtonian fluid in the thermal entrance region of a square duct are presented for three thermal boundary conditions. The power-law model characterises the non-Newtonian behavior. The numerical results show that for each flow behavior index the Nusselt number decreases from a maximum value at the entry plane to a limiting value when both velocity and temperature profiles are fully developed. The results are compared with the available solutions for Newtonian fluid and excellent agreement is found.     

Numerical solution of power law fluids flow and heat transfer with a magnetic field in a rectangular duct

The steady laminar flow and heat transfer of an incompressible, electrically conducting, power law non-Newtonian fluids in a rectangular duct are studied in the presence of an external uniform magnetic field. The momentum and energy equations are solved iteratively using a finite difference method. Two cases of the thermal boundary conditions are considered; (1) T thermal boundary condition “constant temperature at the wall” and (2) H2 thermal boundary condition “constant heat flux at the wall”. The viscous and Joule dissipations are taken into consideration in the energy equation. A numerical solution for the governing partial differential equations is developed and the influence of the magnetic field on the velocity distribution, the friction factor and the average Nusselt number are discussed.     

Momentum and heat transfer from a square cylinder in power-law fluids

Numerical solutions are sought, using FLUENT, to the mass, momentum and thermal energy equations for the 2-D flow of power-law fluids over a cylinder of square cross-section. The major thrust of this work is to delineate the values of the Reynolds number denoting the onset of flow separation and the limits of the steady flow regime for both shear-thinning and shear-thickening type fluids. Extensive results are reported on streamline and vorticity contours over wide ranges of power-law index (0.2–1.4) corroborating the occurrence of these two transitions. Having established the limits of the steady flow regime, drag and Nusselt number results are obtained in this regime as functions of the Reynolds number (0.1–40), of Prandtl number (0.7–100) for highly shear-thinning fluids (power-law index < 0.5) thereby extending the range of currently available results to that encountered in practical applications. The Nusselt number shows positive dependence on both the Reynolds and Prandtl numbers. Also, shear-thinning characteristics can augment the rate of heat transfer by up to 100% under appropriate conditions.     

Laminar flow heat transfer from an argon plasma in a circular tube

The laminar flow of a plasma in the entrance region of a circular tube has been analyzed using an implicit finite-difference scheme. The solution is based upon the boundary-layer equations with the plasma radiation term retained in the energy equation, and the transverse convection term retained in both the momentum and energy equations. Numerical results have been obtained for an argon plasma having a linear enthalpy and cubic velocity profile at the tube entrance. At the low temperature limit of the analysis, the friction factor is in agreement with previously published results; and in all but a very small region near the tube entrance the local Nusselt number agrees with the Nusselt number for constant property, fully-developed flow to within approximately 17 per cent.     

恒热流工况下强化传热管传(火用)性能的评价

通过对管内对流换热过程的灯用传递分析,提出用强化前后的传灯用Nu或传灯用量差ΔNue或ΔE作为强化传热性能评价指标。以工程上常用的螺旋槽管为例,讨论了Re、量纲1热通量、不同结构参数等对强化管传灯用性能的影响。分析结果表明,对于所选螺纹管结构参数,ΔNue随Re增加而增大;随量纲1热通量、量纲1长度的增加而递减。算式可有效评价强化管传灯用效果,以便选取最佳结构参数。     

Laminar flow of viscoelastic fluids in rectangular ducts with heat transfer: A finite element analysis

A numerical study on the laminar flow and heat transfer behavior of viscoelastic fluids in rectangular ducts is conducted using the finite element approach. A Criminale-Ericksen-Fibley relation is applied to describe the viscoelastic character of the fluid, and a hydrodynamically and thermally fully developed flow with the H1 thermal boundary condition is considered. The finite element procedure employed yields essentially mesh-independent predictions with a fairly moderate computational effort. Computed results are presented and discussed in terms of the secondary flow field, the temperature field, the friction factor and the Nusselt number. In particular it is shown that the presence of a secondary flow markedly alters the temperature field and results in a substantial heat transfer enhancement with all duct aspect ratios considered.     

Turbulent convective heat transfer of methane at supercritical pressure in a helical coiled tube

The heat transfer of methane at supercritical pressure in a helically coiled tube was numerically investigated using the Reynolds Stress Model under constant wall temperature. The effects of mass flux (G), inlet pressure (P_in) and buoyancy force on the heat transfer behaviors were discussed in detail. Results show that the light fluid with higher temperature appears near the inner wall of the helically coiled tube. When the bulk temperature is less than or approach to the pseudocritical temperature (T _pc ), the combined effects of buoyancy force and centrifugal force make heavy fluid with lower temperature appear near the outer-right of the helically coiled tube. Beyond the T _pc , the heavy fluid with lower temperature moves from the outer-right region to the outer region owing to the centrifugal force. The buoyancy force caused by density variation, which can be characterized by Gr/Re² and Gr/Re^2.7, enhances the heat transfer coefficient (h) when the bulk temperature is less than or near the T _pc , and the h experiences oscillation due to the buoyancy force. The oscillation is reduced progressively with the increase of G. Moreover, h reaches its peak value near the T _pc . Higher G could improve the heat transfer performance in the whole temperature range. The peak value of h depends on P_in. A new correlation was proposed for methane at supercritical pressure convective heat transfer in the helical tube, which shows a good agreement with the present simulated results.     

Heat transfer characteristics of a temperature-dependent-property fluid in shell and coiled tube heat exchangers

An experimental investigation was performed to study the heat transfer characteristics of temperature-dependent-property engine-oil inside shell and coiled tube heat exchangers. For this purpose, a well-instrumented set-up was designed and constructed. Three heat exchangers with different coil pitches were selected as the test section for counter-flow configuration. Engine-oil was circulated inside the inner coiled tube, while coolant water flowed in the shell. All the required parameters like inlet and outlet temperatures of tube-side and shell-side fluids, flow rate of fluids, etc were measured using appropriate instruments. An empirical correlation existed in the previous literature for evaluating the shell-side Nusselt number was invoked to calculate the heat transfer coefficients of the temperature-dependent-property fluid flowing in the tube-side of the heat exchangers. Using the data of the present study, an empirical correlation was developed to predict the heat transfer coefficients of the temperature-dependent-property fluid flowing inside the shell and coiled tube heat exchangers.     

Exergoeconomic performance of an endoreversible Carnot heat pump with complex heat transfer law

The finite-time exergoeconomic performance of an endoreversible Carnot heat pump with a complex heat transfer law, including generalized convective heat transfer law and generalized radiative heat transfer law q∝ (Δ T ⁿ ) ^m , is investigated in this paper. The focus of this paper is to obtain the compromised optimization between economics (profit) and the energy utilization factor (coefficient of performance, COP) for the endoreversible Carnot heat pump, by searching the optimum COP at maximum profit, which is termed as the finite-time exergoeconomic performance bound. The obtained results include those obtained in much of the literature and can provide some theoretical guidance for the design of practical heat pumps.     

Numerical investigation on conjugate heat transfer to supercritical CO2 in membrane helical coiled tube heat exchangers

ABSTRACT

Conjugate heat transfer to supercritical CO₂ in membrane helical coiled tube heat exchangers has been numerically investigated in the present study. The purpose is to provide detailed information on the conjugate heat transfer behavior for a better understanding of the abnormal heat transfer mechanism of supercritical fluid. It could be concluded that the supercritical fluid mass flux and vertical/horizontal placement would significantly affect the abnormal heat transfer phenomenon in the tube side. The flow field of supercritical fluid is affected by both the buoyancy and centrifugal force in the conjugate heat transfer process. The local wall temperature and heat transfer coefficient in the tube side would rise and fall periodically for the horizontal heat exchanger, but this phenomenon will gradually disappear with the increase of the mass flow rate or fluid temperature in the tube side. The dual effects of buoyancy force and centrifugal force lead to the deflection of the second flow direction for the vertical placement, which further results in the heat transfer deterioration region on the top-generatrix wall for the downward flow being larger than that for the upward flow.