Heat Transfer In Entrance Region Research Articles

A heat transfer correlation of Poiseuille-Rayleigh-Bénard convection in the thermal entrance region of a horizontal rectangular channel

In order to understand heat transfer characteristics and obtain a heat transfer correlation of Poiseuille-Rayleigh-Bénard (P-R-B) convection in the thermal entrance region of a horizontal rectangular channel, we performed a series of the direct numerical simulations. The working fluid is water, and the spanwise aspect ratio of the rectangular channel ranges from 2 to 10. The results show that the thermal entrance length for the onset of buoyancy-driven convection extends with the decreasing Rayleigh number and the increasing Reynolds number. The average Nusselt number in the thermal entrance region increases with the increase of Rayleigh number and Reynolds number. Furthermore, a smaller aspect ratio and a shorter length of the channel contributes to enhanced heat transfer in the thermal entrance region. Based on the simulation results, the heat transfer correlation in the thermal entrance region is established, which can be used as a reference for the engineering design on P-R-B convection.

Characterization of an Apparatus to Study Solid Deposit Formation in Lubricating Oils at High Temperatures

Abstract When exposed to excessively high temperatures, the lubricating oils in turbines undergo extreme oxidation and thermal degradation processes that eventually result in the formation of solid deposits that can, in turn, cause operational problems. This work describes the testing and characterization process of a newly constructed test rig that studies the propensity of lubricants to form such deposits. In the test rig, the lubricant flows through a heated tube, thermally degrades or oxidizes, and forms solid deposits that adhere to the heated surface. An oil flow rate calibration curve as a function of pump speed was developed using two oils, Castrol GTX 20W-50 and Mobil DTE 732. The steady-state axial temperature distribution along the heated tube was measured for temperature settings of up to 475 °C and flow rates of 10.4, 12.2, and 13.9 mL/min using Mobil DTE 732. The results showed that the surface temperature is not uniform, but that it varies axially as is expected from the heat transfer in the thermal entrance region of a pipe with laminar flow. Examples of the results of tests performed with the apparatus using Mobil DTE 732 and Castrol GTX 20W-50 flowing at 10.4 mL/min with surface temperatures between 328 and 489 °C are presented. Based on these tests, it is clear that the induction time for solid-deposit formation can be unambiguously determined using the experimental apparatus. The induction times of the sample tests described were found to be 638 ± 10 min and 86 ± 10 min for Mobil DTE 732 and Castrol GTX 20W-50, respectively.

Application of four-equation closure for turbulent heat flux in prediction of convective heat transfer to hydrocarbon fuels at supercritical pressures

Accurate modelling of the turbulent thermal fields is of great importance for simulations of convective heat transfer to fluids at supercritical pressures. The widely adopted Reynolds analogy between turbulent momentum transfer and turbulent heat transfer may fail for variable property flows under certain conditions, especially as the fluid approaches the pseudo-critical temperature (Tpc). In order to accurately predict the flow and heat transfer behaviors, the two-equation turbulence model for the thermal field by Hattori, Nagano, and Tagawa (HNT kt−εt) in association with the low-Reynolds number model for the velocity field by Myong and Kasagi (MK k−ε) were incorporated in an in-house code developed within the framework of OpenFOAM. Numerical simulations of convective heat transfer to supercritical pressure hydrocarbon fuels (RP-3 aviation kerosene and n-decane) in vertical heated tubes were performed using the MK-HNT model, MK k−ε model with Prt set as 1.0, and SST k−ω model with Prt set as 1.0. The validity of the models was examined through comparisons with the available experimental data under a variety of operating conditions. All three models performed reasonably well for the cases of normal heat transfer regime. Meanwhile, improvements in the prediction of inner wall temperature could be obtained by the use of the MK-HNT model for cases of heat transfer in the thermal entrance region, heat transfer enhancement (HTE) under forced convection conditions, and heat transfer deterioration (HTD) under mixed convection conditions. Moreover, the different heat transfer mechanisms were investigated by analyzing the predicted turbulent flow and thermal fields. The results indicated that the development of the thermal boundary layer in the entrance region and the drastic variation of specific heat and density in the trans-pseudo-critical region would have considerable effects on the distributions of the Reynolds stress and turbulent heat flux. In addition, it was found that the computational cost was not severely increased by solving two additional turbulence equations.

Smart role of Al2O3-water suspension on laminar heat transfer in entrance region of a channel with transverse in-line baffles

This study aims to two dimensionally evaluate laminar flow and heat transfer characteristics of Al2O3-water nanofluid in the entrance region of a baffled parallel plate channel. The mixture model, based on a single fluid two phase approach, with temperature-dependent properties is adopted to simulate nanofluid. A constant heat flux is imposed on the walls. The effect of Reynolds number, nanoparticle volume fraction and heat flux on wall temperature, velocity and pressure fields, and thermal-hydraulic performance are numerically investigated. It is found that the intensity and length of recirculation regions of flow in the baffled channel increases and decreases, respectively, as nanofluid is applied. The results reveal more uniform wall temperature profiles are obtained using nanofluid, especially for lower Reynolds number and higher volume fraction. Using nanofluid has more remarkable effect on reducing temperature in front of baffles in which hot spots occur. Because of this superior feature, the nanofluid under study plays an intelligent role in cooling applications of baffled channel. Both heat transfer and pressure drop increase when nanoparticles are dispersed in basefluid. The baffled channel shows better cooling performance at the presence of nanoparticle while imposed heat flux is increased. This potential of nanofluids proves that it can be called “smart fluid”. It means that nanfluid plays automatically more effective role as heat transfer medium when temperature increases and then higher heat dissipation is required. It is also found that the effect of nanofluid on both heat transfer and pressure drop is approximately independent from baffle shape and the baffled channel presents a better thermal-hydraulic performance under the condition of constant inlet velocity.

Entrance Region Heat Transfer in a Channel With a Ribbed Wall

Direct numerical simulation was performed for the heat transfer of airflow in the entrance region of a channel with repeated rib protrusions. The rib-pitch to rib-height ratio (Pi/H) was increased from 2.0 to 16.0 by four steps. The rib-height ratio (H/δ) was maintained constant at 0.20. The distribution of heat transfer coefficient numerically simulated agreed with the experiment by Kattchee and Mackewicz (1963, “Effects of Boundary Layer Turbulence Promoters on the Local Film Coefficients of ML-1 Fuel Elements,” Nucl. Sci. Eng., 16, pp. 31–38). The enhancement parameter was used to evaluate the heat transfer performance by a ribbed channel. This parameter was defined as the ratio of the mean Nusselt number for the ribbed channel against the smooth channel consuming the same pumping power. The simulation result revealed that the enhancement parameter was maximized for Pi/H = 2 to 4 over the upstream ribs (x/δ < 2) and was remained high for Pi/H = 4, 8, and 16 over the downstream ribs (x/δ > 4). Therefore, the optimal rib pitch was smaller for the upstream ribs, and increased to the developed region. The mechanisms underlying this trend were discussed through observation of the streamlines, mean temperature, turbulence statistics, and instantaneous structures. The turbulence was increased over the ribbed wall for the cases of medium to wide rib pitch (Pi/H = 4, 8, and 16), whereas the turbulence increase appeared only over the upstream ribs (x/δ < 2) for the cases of narrow rib pitch (Pi/H = 2). The excellent performance of the wider rib pitch (Pi/H = 4, 8, and 16) at the downstream ribs (x/δ > 2) was resulted from the turbulence increase activating the turbulent heat transport. Whereas, the superiority by the narrower rib pitch (Pi/H = 2, 4) comes from the turbulence activation, and the renewed thin boundary layer which continues due to the densely allocated ribs.

Effect of Entry Temperature on Forced Convection Heat Transfer With Viscous Dissipation in Thermally Developing Region of Concentric Annuli

Steady laminar forced convection heat transfer in the thermal entrance region of concentric annuli has been studied considering viscous dissipation characterized by the Brinkman number. The inner and outer pipes have been kept at constant and equal temperature. Two cases of entry temperatures have been considered, case 1: an entry temperature that varies with the radial coordinate, obtained by an adiabatically prepared fluid, i.e., attained by the fluid due to viscous dissipation in an adiabatic concentric annular duct and case 2: the conventional uniform entry temperature. The numerical results presented include the nondimensional temperature profiles, Nusselt numbers, and heat transferred from (or to) the inner and outer pipes. It has been shown from the numerical solutions that it is necessary to employ the dissipative entry temperature in place of conventional uniform entry temperature for higher Brinkman numbers. The results for circular pipes follow when the radius ratio takes the limiting value of zero.

A Theoretical Investigation on Thermal Entrance Region Heat Transfer in a Conduit Filled with Nanofluids

A theoretical analysis has been made to explore thermal entrance region heat transfer in nanofluids. The nu- merical model used in this paper is based on the Buongiorno model for convective heat transfer in nanofluids with modi- fications to fully account for the effects of nanoparticles volume fraction distributions on the continuity, momentum and energy equations. Numerical investigations have been conducted for developing laminar forced convection flows in a cir- cular tube subject to a uniform wall heat flux. From the results, it has been concluded that, for certain cases of alumina- water nanofluids and titania-water nanofluids, in most entrance region, anomalous heat transfer enhancement (that ex- ceeding the rate expected from the increase in thermal conductivity) is possible, whereas, close to the edge of the en- trance, no anomalous heat transfer enhancement is observed.

Heat transfer analysis in thermal entrance region under turbulent flow conditions

ABSTRACTTurbulent heat transfer in the thermal entrance region of the pipe was studied by numerical solution of the energy equation using finite difference technique under different operating conditions. The turbulence effect was accounted for by introducing thermal eddy diffusivity term in the energy equation in both axial and radial directions. The axial and radial temperature profiles, the local heat transfer coefficient in the entrance and fully developed regions, and the entrance lengths were obtained and discussed. In addition, the role of thermal eddy diffusivity in the thermal entrance region and fully developed region was investigated. The finite difference numerical solution was also commented on. The theoretical results were compared with previous experimental works, and a reasonably good agreement was found. It was found that the temperature gradient in axial direction is very steep, close to the leading edge near the pipe's surface and becomes almost negligible after a distance equals few pipe diameters, depending on Reynolds number (Re), Prandtl number (Pr), and heat flux (q). The radial temperature profile was very steep, close to the pipe's surface near the leading edge and becomes almost constant at a very short distance from the pipe surface, depending on Re, Pr, and q. The entrance length (Lt) was found to be reached after 0.5–3.5 pipe diameters distance for the investigated ranges of Re, Pr, and q. Thermal eddy diffusivity plays an important role in axial and radial transport. Ignoring it, causes underestimation in the heat transfer coefficient and overestimation in the entrance length. © 2012 Curtin University of Technology and John Wiley & Sons, Ltd.

Heat transfer in the thermal entrance region for drag reduction surfactant solutions in pipe flow

Experimental results relating to heat transfer for a flow of surfactant solutions in the thermal entrance region of a pipe were discussed. Aqueous solutions of hexadecyltrimethylammonium chloride with addition of sodium salicylate were used as model fluids. It was observed that the effect of buoyancy on the heat transfer process was less pronounced in the entrance region of a pipe than in the scope of a fully developed flow. It was demonstrated that it was possible to correlate experimental results for the flow of drag-reducing surfactant solutions, based on the dependence of Nusselt number on a dimensionless longitudinal coordinate. In addition, simple empirical equations were proposed which enable the local and mean values of the heat transfer coefficient to be calculated.

Heat transfer in trapezoidal microchannels of various aspect ratios

Heat transfer in the thermal entrance region of trapezoidal microchannels is investigated for hydrodynamically fully developed, single-phase, laminar flow with no-slip conditions. Three-dimensional numerical simulations were performed using a finite-volume approach for trapezoidal channels with a wide range of aspect ratios. The sidewall angles of 54.7° and 45° are chosen to correspond to etch-resistant planes in the crystal structure of silicon. Local and average Nusselt numbers are reported as a function of dimensionless length and aspect ratio. The effect of Prandtl number upon the thermal entrance condition is explored. The fully developed friction factors are computed and correlated as a function of channel aspect ratio. Correlations are also developed for the local and average Nusselt numbers in the thermal entrance region as a function of a dimensionless axial length variable.

A boundary layer analysis for entrance region heat transfer in vertical microchannels within the slip flow regime

A boundary layer integral analysis has been executed to investigate the heat transfer characteristics of natural convection gas flows in symmetrically heated vertical microchannels, under the conditions of large channel aspect ratios, in the slip flow regime. It has been revealed that for low values of Rayleigh number, the entrance region length is only a small fraction of the total channel extent. For higher values of Rayleigh number, however, effects of the developing region are non-trivial, and two counteracting heat transfer mechanisms need to be aptly taken into consideration for interpreting the Nusselt number values. In the present study, the proportionate enhancement in the average Nusselt number with wall-slip effects has been observed to become more prominent for higher values of Knudsen number. However, the relative augmentation in the rate of heat transfer tends to get somewhat arrested for higher values of Rayleigh number, as attributable to the counteracting influences of augmented rates of advective transport and reduced wall-adjacent temperature gradients. For all cases, the boundary layer theory based predictions have been found to agree excellently with the corresponding results obtained from full-scale numerical predictions.

Convective heat transfer in the thermal entrance region of finned double-pipe

Numerical simulation of the steady and laminar convection in the thermal entry region of the finned annulus is carried out for the case of hydrodynamically fully developed flow when subjected to uniform heat flux thermal boundary condition. Finite difference based marching procedure is used to compute the numerical solution of the energy equation. The results to be presented include Nusselt number, as a function of dimensionless axial length and thermal entrance length for various configurations of the finned double-pipe. The numerical results show that Nusselt number has complex dependence on the geometric variables like ratio of radii, fin height, and number of fins. A comparison of the computed results for certain limiting cases with the results available in the literature validates the numerical procedure used in this work.

Heat transfer in the thermal entrance region for flow through rectangular porous passages

The study of heat transfer in rectangular passages with prescribed wall heat flux is of practical interest. These passages could be open or filled with saturated porous materials. A solution that uses the Green’s function can accommodate the inclusion of heat flux over the entire surface area or over isolated sections of the boundary. Also, this solution permits the inclusion of frictional heating. Two different boundary conditions are considered: constant wall temperature and constant wall heat flux. The computed heat transfer coefficients show that the thermally fully developed condition may not be attainable in practical applications for very narrow passages with prescribed wall heat flux.

Study on coordinative optimization of convection in tubes with variable heat flux

The laminar heat transfer in the thermal entrance region in round tubes, which has a variable surface heat flux boundary condition, is analytically studied. The results show that the heat transfer coefficient is closely related to the wall temperature gradient along the tube axis. The greater the gradient, the higher the heat transfer rate. Furthermore, the coordination of the velocity and the temperature gradient fields is also analysed under different surface heat fluxes. The validity of the field coordination principle is verified by checking the correlation of heat transfer coefficient and the coordination degree. The results also demonstrate that optimizing the thermal boundary condition is a way to enhance heat transfer.

Numerical analysis of laminar heat transfer in entrance region of a horizontal channel with transverse fins

In the present work, a numerical investigation of the laminar fluid flow and heat transfer in the entrance region of a two dimensional horizontal channel, with in-line ribs, is carried out. The computations are based on the Finite Volume method and the SIMPLE algorithm has been implemented. Both sides of the channel are assumed at a constant temperature and physical properties of the fluid are assumed as constant. Computations are performed for the Reynolds number in the range of 100 to 500, Prandtl number of 0.7 and blockage ratio of 0.1, 0.2 and 0.3. The present results show that the ribs interrupt the boundary layers. Flow detaches from the channel wall and it forms a recirculation zone in front of the rib. The reattachment point has the maximum local Nusselt number. The precise location of periodically fully developed region depends on the Reynolds number from the third to the sixth rib. Increasing the rib pitch causes a marginal increase in the local Nusselt number and a decrease in the friction factor. Increasing the blockage ratio results in a moderate decrease in the local Nusselt number.

Laminar convection of non-Newtonian fluids in the thermal entrance region of coiled circular tubes

The governing equations for fully developed laminar flow and heat transfer in the thermal entrance region of circular curved tubes are solved numerically for power law fluids. Detailed descriptions of the secondary velocity profiles and temperature profiles as a function of Dean number, Prandtl number and power law index are provided to elucidate the significant role of secondary convection. Results for friction factors, asymptotic Nusselt numbers and Nusselt numbers in the thermal entrance region are computed and compared with the published experimental and theoretical results for Newtonian and power law fluids. Satisfactory agreement is found. For a given Prandtl and Dean number the Nusselt number increases with increases in power law index and the thermal entrance length is found to be shortened for dilatant fluids in comparison with the pseudoplastic fluids.

The extended Graetz problem with piecewise constant wall heat flux for pipe and channel flows

Heat transfer in the thermal entrance region of a pipe or a parallel plate channel has been analysed for laminar and turbulent internal flow taking into account axial heat conduction effects in the fluid. The present paper shows an analytical solution for the problem of a piecewise uniform wall heat flux. The obtained exact analytical solutions for the extended Graetz problem are as simple and efficient to compute as the related solutions of the parabolic problem. The obtained results show the effect of axial heat conduction in the fluid for a semi-infinite as well as for a finite length of the heated sections.

Buoyancy-assisted flow reversal and convective heat transfer in entrance region of a vertical rectangular duct

Abstract In this study, predictions of buoyancy-assisted flow reversal and convective heat transfer in the entrance region of a vertical rectangular duct are reported for the first time. In line with the current trend toward the use of computationally efficient numerical methods, the present study is based on the use of a three-dimensional parabolic, boundary-layer model and the FLARE approximation. Physical situations investigated include cases with various asymmetric heating conditions over wide ranges of parameters. Analytical solutions for the fully developed flows are also presented, and the criteria for the flow reversal to occur are predicted. Solutions for the developing flow obtained in this study agree closely with the elliptic-model solutions, and precisely approach the fully developed solutions downstream.

TURBULENT FLUID FLOWS AND HEAT TRANSFER CHARACTERISTICS IN FLOW CHANNELS WITH DISTRIBUTED CHIP MODULES

A study is carried out to investigate the characteristics of turbulent fluid flow and heat transfer in the entrance region of a flow channel containing heat-generating modules of different sizes and distributions. The flow is described by Reynolds averaged Navier–Stokes equations and k-e model with wall function treatment. The prediction for flow and heat transfer characteristics has been made and compared with published experimental results. The computational results showed good agreement for performance parameters such as Nusselt numbers and Coefficient of pressure with experiments. The investigation is performed for Reynolds number values of 5000 and 15,000, and for two different geometrical configurations. Flow and heat transfer characteristics with varying parameters are also discussed.

Three dimensional laminar non-Newtonian fluid flow and heat transfer in the entrance region of a cross-shaped duct

The Galerkin finite element is used to solve the three dimensional momentum and energy equations for laminar non-Newtonian flow in cross-shaped straight duct. Both flow and heat transfer develop simultaneously from the entrance of the channel. Uniform wall temperature (T) and also constant wall heat flux both axially and peripherally (H2) are used as thermal boundary conditions. The power-law model is chosen to characterize the non-Newtonian behaviour of the fluid. The effect of power-law index and geometric parameter on the apparent friction factor as well as Nusselt number are presented and discussed.