Thermal Entrance Region Research Articles

Upstream heating history effects on heat transfer of supercritical R134a in transcritical organic Rankine cycle

A comprehensive understanding on the heat transfer of supercritical working fluid is critical for the design of vapor generator in transcritical Organic Rankine Cycles. The thermal entrance region under supercritical pressure conditions is relatively complex and remains unresolved. To this end, this study investigates heat transfer to supercritical fluids in heated horizontal flow, focusing on the impact of upstream heating history which has been rarely discussed. The Abe-Kondoh-Nagano (AKN) low Rek–ε turbulence model was employed, covering a wide range of upstream conditions: upstream heating length ranging from 10d (d is tube diameter) to 200d, and upstream heat flux up to 4.5 times that of the downstream test section. The results revealed that heating history didn't matter when upstream Grq/Grth < 5. For upstream mixed convection of Grq/Grth = 10–220, heating history had a significant effect on the downstream flow, causing a maximum 50 %–60 % increase in heat transfer coefficients within an affected length up to 100d. When the downstream flow was forced convection, thermophysical property variations mainly contributed to the above enhancement. Meanwhile for downstream mixed convection, upstream heating history notably enhanced turbulent intensity, further improving heat transfer. The upstream heating length was identified as a crucial factor influencing both forced and mixed convections downstream. Negligible differences were observed when the heating length was less than 20d. On the other hand, the radial distribution of flow and thermal fields remained constant beyond a critical heating length, indicating the achievement of a pseudo-fully-developed state with identical heat transfer behavior. Results of this work confirm that the effect of upstream heating history is closely tied to thermal developing length and holds significant importance in the thermal design of vapor generators.

CFD simulation of the inundation effect for saturated propane vapor condensation on the surface of a horizontal tube using the volume of fluid method

The inundation of the lower tubes in a tube bundle with condensate formed on the upper tubes is among the major causes of reduced condensation rate. Experimental methods can hardly be used to get detailed information on the inundation effect, since each factor that controls the condensation process should be considered individually. However, CFD modelling using direct interface-tracking methods is an effective tool for analyzing such processes. This paper reports the results of simulation of the saturated propane vapor condensation on the surface of a horizontal tube using the Volume of Fluid method with the modified Lee model. The study presents, for the first time, the characteristics of saturated vapor condensation including the effect of inundation predicted using a 3D model. The interphase surface and the distribution of instantaneous heat transfer coefficients over the surface of the inundated pipe are presented. It has been shown that increasing the temperature of the condensate flow can substantially affect the distribution of the heat transfer rate over the tube surface due to the formation of a thermal entrance region. These results may become a starting point for modelling condensation in a tube bundle that enjoys current interest in practice.

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.

Thermally developing combined electroosmotic and pressure-driven flow of Phan–Thien–Tanner fluids in a microchannel

We present semi-analytical solutions for the hydrodynamically developed and thermally developing flow of a non-Newtonian fluid through an isothermal rectangular microchannel. The fluid motion is actuated by the combined consequences of the electroosmotic and pressure-gradient forces. For the rheological behavior of the non-Newtonian fluid, we have used the simplified Phan–Thien–Tanner viscoelastic model. Going beyond the Debye Hückel linearization approximation, we have used the full-scale solution for the electrical double-layer potential equation to obtain the exact analytical solutions for the velocity, flow rate, and shear rate parameters. In contrast, the temperature distribution and heat transfer for the thermally developing flow have been obtained by solving the energy equation numerically considering the effects of volumetric heat generation due to Joule heating and viscous dissipation. We find that a larger value of the viscoelastic set ε̃Wĩk2 contributes toward the net gain in flow rate. Both the normal and shear stress increase for increasing ε̃Wĩk2, while the shear viscosity reduces with a degree of surface charging. The average shear viscosity reduces with the degree of surface charging and at higher ε̃Wĩk2 values. The heat transfer is enhanced for augmenting ε̃Wĩk2, although the thermal entrance region gets contracted for a pure electroosmotic flow at higher Peclet numbers. Our study reveals that the heat transfer rate can be amplified by effectively modulating the degree of surface charging and ε̃Wĩk2. We have also carried out an entropy generation analysis, which shows the dominance of heat transfer irreversibility over fluid friction irreversibility. We believe that the present research will offer essential approaches for designing advanced energy-efficient microchannels appropriate to modern industrial applications using viscoelastic fluids.

Local heat and mass transfer in a rotor-stator system with hub inflow: Thermal boundary layer and superposition effect

Improving the cooling performance of a gas turbine rotor-stator system can have a significant impact on the efficiency of a gas turbine engine. In this study, we investigated the local heat and mass transfer (HMT) of a rotor-stator system with hub inflow considering the thermal boundary layer and superposition effect. A rotor-stator system test facility capable of analyzing HMT characteristics was constructed. Measurements of local HMT coefficients were carried out using the naphthalene sublimation method. First, the development of local HMT was investigated using discontinuous boundary condition experiments. Quantitative evaluation of the high HMT in the windward area revealed the thermal entrance regions. Then, to assess individual and combined effects, the local HMT characteristics were analyzed under three conditions: hub inflow-only, rotating-only, and a combination of hub inflow and rotating flows. Hub inflow dominated in regions below local rotational Reynolds number (Rer) of 1.25 × 105, and the enhancement region appeared above Rer of 2.0 × 105. Our study described for the first time the boundaries of HMT in a rotor-stator system based on the dominant influence of superposed flow. We expect our results to aid the development of cooling designs for rotor-stator systems in gas turbine engines.

Numerical study on heat transfer characteristics of molten salt in a flat tube with circular helical wire

The combination of a new type of irregular-shaped helical wire and flat tube is used to further enhance heat transfer of molten salt for the first time due to the demands of efficient utilization of molten salt. The thermo-hydraulic performance of turbulent flow in a flat tube with irregular-shaped helical wire under constant wall temperature condition is investigated using Fluent software. The effects of helical pitch, wire diameter, gap width between the tube wall and helical wire, different fluids and inlet Reynolds number ranging from 1500 to 8500 are evaluated. It is found that adding irregular-shaped helical wire insert in flat tube can reduce greatly the lengths of flow and thermal entrance regions. The maximum heat transfer performance of flat tube with irregular-shaped helical wire is 400% that of smooth flat tube. The heat transfer performance increases with the wire diameter and decreases with the gap width and helical pitch. The maximum thermal performance factor with a value of 1.72 is observed based on a constant pumping power. Besides, the heat transfer performance of flat tube with irregular-shaped helical wire is 24.0%-40.2% larger than that of circular pipe with helical wire at low Reynolds number.

Hydrodynamic and thermal entrance region assessment of turbulent flow through a circular tube with a tight-fit twisted tape insert, considering multifarious operating conditions and pitch ratios

Hydrodynamic and thermal entrance region assessment of turbulent flow through a circular tube with a tight-fit twisted tape insert, considering multifarious operating conditions and pitch ratios

Development of the hydrodynamic and thermal boundary layers of forced convective laminar flow through a horizontal tube with a constant heat flux

The development of the thermal and hydrodynamic boundary layers of laminar flow through a smooth horizontal tube was investigated for forced convective conditions. The tube was heated at a constant heat flux and had an inner diameter of 4 mm and a length of 6 m. Numerical simulations were conducted using ANSYS Fluent 19.3 with a highly structured mesh and accurate temperature-dependent thermophysical properties. Laminar flow of air, water, and a mixture of 75% ethylene glycol (by weight fraction) in water was simulated, which covered a Reynolds number range of 630 to 2000 and Prandtl number range of 0.7–70. Theoretical methods were also used to obtain the relevant boundary layer growth parameters, such as velocity profiles, velocity gradient, vorticity, temperature profiles, Nusselt numbers, as well as hydrodynamic and thermal boundary layer thicknesses. Subsequently, methods were proposed to determine the development of both boundary layers in the entrance region, the locations at which the boundary layers merged, and the location at which the flow became fully developed. By analysing the velocity and temperature profiles, it was found that our conventional understanding of the merging of the boundary layers in internal tube flows had to be modified. Three distinct regions were identified in the hydrodynamic entrance region of laminar forced convective tube flow: (1) hydrodynamic inlet region, (2) shear stress developing region, and (3) vorticity adjustment region. Furthermore, three distinct regions were identified in the thermal entrance region: (1) thermal inlet region, (2) convective diffusion region, and (3) conductive diffusion region.

The effect of different carrier fluids on heat transfer performance in a microfluidic serpentine device

In this work, the efficiency of heat transfer and the related fluid-mechanic performance inside a microfluidic device are investigated by varying the type of carrier fluid at different flow rates. The experimental analysis has been conducted on a serpentine channel configuration by considering five different fluid mixtures. The results displayed and emphasized the relevant role of viscosity on thermal performance in the laminar regime. The corresponding Nusselt number values have been identified in terms of Reynolds and Prandtl numbers. Specifically, high-viscosity mixtures exhibited Nusselt number values strongly correlated with Prandtl number. So far, heat transfer for these mixtures is improved as a result of the greater extent of the thermal entrance region and of the higher thermal gradient. Nusselt-Reynolds trends for such mixtures also presented a consistent rate of increase, this increment being however severely limited by the action of viscous dissipation as Reynolds number increases. On the other hand, mixtures with low viscosity showed high correlation between Nusselt and Reynolds numbers. The importance of local turbulence phenomena for such low-viscosity fluids becomes one of the main factors in heat transfer enhancement, also for small-scale thermal sinks in laminar regime. In fact, for such mixtures, thermal performances are incremented by the combining effects of local mixing phenomena at each bend of the serpentine and by the increasing extension of the thermo-hydraulic development region.

Thermal-hydraulic characteristics of FLiBe in annuli with helical wire

A fully tight-fitting triangular wire coil is used to enhance heat transfer of FLiBe in the annular channel for the first time. The numerical simulations of annular channels with triangular wire coil were performed with three helical pitches, three annular widths, and one equilateral triangle corresponding to Reynolds number of 4000–10000. It is found that adding triangular wire coil generates a vortex and reduces significantly the lengths of flow and thermal entrance regions of the annular channel. The local Nusselt number for peripheral point is extremely non-uniform. The Nusselt number decreases with annular width and helical pitch increase. The Nusselt number of enhanced annular channel is 1.45–1.98 times that of smooth annular channel. The overall performance of annular channel with helical pitch of 15 mm and annular width of 10 mm is best by using the principle of entropy generation. However, by using the performance evaluation criteria, the annular channel with helical pitch of 15 mm and annular width of 19.4 mm is best when the Reynolds number is less than or equal to 5500. And the annular channel with helical pitch of 20 mm and annular width of 19.4 mm is best at the high Reynolds number.

A Novel Way to Control Wall Temperature Distribution by Grading Blowing Rate

Abstract The Graetz problem in a transpiration-cooled channel was analytically attacked so as to explore the developing temperature field due to a sudden change in wall temperature of the channel subject to an arbitrary distribution of the local mass flux over the porous wall. Analytical expressions for the developments of the thermal boundary layer thickness, wall temperature, and Nusselt number were obtained for the thermal entrance region, assuming hydrodynamically forced convective flow in a channel with a locally variable blowing mass flux. When the blowing mass flux is kept constant over the wall surface, the cooling by the coolant is less effective near the entrance, thus, exposing to danger of thermal damage. This study reveals that the blowing mass flux graded inversely proportional to one-third power of the axial distance is quite effective to keep the wall temperature uniform. Numerical calculations based on finite volume method were also carried out to verify the analysis. The findings from this study can be applied to possible thermal managements of heat generating stacks such as in EV batteries and PEMFC, in which temperature uniformity is essential for product longevity.

Analysis of heat transfer for simultaneously developing temperature profile and fluid flow of power-law fluids in the entrance region of a tube

• Simultaneously developing power-law fluid flow and heat transfer in a tube is addressed. • The model is based on the inlet-filled region concept. • The heat transfer solution is obtained using an integral method. • The model is validated against published results, and asymptotically against the fully developed solution. • Results include Nusselt number profiles and entrance region length for different values of the power-law fluid index and Prandtl number. Developing heat transfer in a tube subjected to a constant heat flux is investigated in the case of simultaneously developing fluid flow of a power law fluid in a circular duct using an integral boundary layer model. The inlet-filled region concept is used to solve the heat transfer problem with the velocity profile determined from a previously published and validated hydrodynamic model. The thermal entrance region is divided into a thermal inlet-hydrodynamic inlet zone, followed by a thermal inlet-hydrodynamic filled zone, and last a thermally filled-hydrodynamic filled zone. The heat transfer results are validated against published power-law Nusselt number profiles, and published thermal boundary layer thickness and local Nusselt number profiles for Newtonian fluids as a special case. Furthermore, the asymptotically reached values are validated against the fully developed values. The model presented is predominantly analytical and requires minor computational work.

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.

Experimental study of the performance of two water-based nanofluids in the thermal entrance region of a pipe

Experimental study of the performance of two water-based nanofluids in the thermal entrance region of a pipe

Numerical study of thermally developing turbulent internal flows

The effect of fluid Prandtl number on the thermal characteristics of the flow at the thermal-entry region of a hydrodynamically fully developed turbulent channel flow at a friction Reynolds number of Reτ=180 is investigated using direct numerical simulation. Four test cases with molecular Prandtl numbers of Pr = 0.71, 1, 3, 7 are considered. The numerical results confirm that in contrast to laminar flows, where the thermal entry length increases with the increase of the Prandtl number, for turbulent flows the increase of the Prandtl number accelerates the thermal development of the flow toward its asymptotic fully developed state. The variations of the Nusselt number, and the mean and rms temperature profiles are reported in the streamwise direction. It is shown that at highest Prandtl number considered in this study (Pr =7 ), while the mean temperature profile in the logarithmic region is still developing, the temperature profile in the conductive sublayer and the Nusselt number approach their fully developed values, confirming the dependence of the Nusselt number of turbulent flows to the development of the conductive sublayer. The development of the rms temperature profiles in the streamwise direction is also shown to be a good indicator for the flow reaching its thermally fully developed condition. The temperature-velocity correlations, temperature variance budgets, and contours of temperature are also reported at different streamwise locations for different Prandtl numbers.

Leveque-Type Similarity Transformation for a Thermally Developing Viscous Dissipative Flow in a Parallel Plate Channel

Compared to the existing more elaborate eigenvalues-eigenfunction analytical solution where the solution of a thermally developing forced convection problem converges very slowly at the beginning of thermal entrant region, Leveque-type similarity transformation method provides a more convenient way to look into the insights of the problem. Assuming that the wall heat flux and viscous dissipation only has an effect within the thin thermal boundary layer at the beginning of the thermal entrance region, this study intends to solve the governing thermal energy equation for a thermally developing flow in a parallel plate channel, subjected to uniform heat flux, by means of Leveque-type similarity transformation. The resulting ordinary differential equation, is subsequently solved by a fourth order Runge Kutta method. A comparison of the Nusselt number along the axial direction, at the beginning of the thermally developing region with the literature, reveals less than 10% discrepancy for Brinkman number less than one, which is a commonly acceptable range for practical applications. Although its accuracy depletes downstream the channel, similarity transformation provides sufficiently accurate temperature distribution, and captures the heat transfer insights for a thermally developing viscous dissipative forced convection.

Numerical Investigation of Thermally Developing and Fully Developed Electro-Osmotic Flow in Channels with Rounded Corners

Electro-osmotic flow, that is, the motion of a polar fluid in microducts induced by an external electric field, is one micro-effect which allows fluid circulation without the use of mechanical pumping. This is of interest in the thermal management of electronic devices, as microchannels with cross sections of almost arbitrary shape can easily be integrated on the chips. It is therefore important to assess how the geometry of the channel influences the heat transfer performance. In this paper, the thermal entry region and the fully developed electro-osmotic flow in a microchannel of rectangular cross section with smoothed corners is investigated for uniform wall temperature. For the fully developed region, correlations for the Poiseuille and Nusselt numbers considering the aspect ratio and nondimensional smoothing radius are given, which can be used for practical design purposes. For thermally developing flow, it is highlighted how smoothing the corners increases the value of the local Nusselt number, with increases up to 18% over sharp corners, but that it also shortens the thermal entry length. It is also found that Joule heating in the fluid may cause a reversal of the heat flux, and that the thermal entry length has a linear dependence on the Reynolds number and the hydraulic diameter and on the logarithm of the nondimensional Joule heating.

Predicting heat transfer coefficient of a shell-and-plate, moving packed-bed particle-to-sCO2 heat exchanger for concentrating solar power

The particle-to-sCO2 heat exchanger plays a significant role in coupling the high temperature particle receiver to supercritical carbon dioxide Brayton cycle in concentrating solar power plants. In this work, heat transfer characteristics of a shell-and-plate, moving packed-bed heat exchanger are numerically evaluated through continuum modeling. It is found that the local heat transfer coefficient h for different input parameters have a similar shape: h quickly drops at the thermal entry region and then remains as a constant. The asymptotic value of h increases with the particle flow velocity but decreases with particle channel width. A universal correlation between the local heat transfer coefficient and the particle flow properties in terms of the dimensionless Nusselt number is then proposed. Moreover, by calculating the overall heat transfer coefficient and performing a sensitivity analysis, we show that the heat exchanger has a two-regime behavior: in the regime with low particle flow rate, the performance mostly depends on the particle flow velocity and the channel width, and is restricted by the small amount of energy stored in the particle flow. In the high flow rate regime, the effective conductivity of the particle flow becomes the determining factor on the performance of the heat exchanger.

Analytical solution and numerical simulation of the generalized Levèque equation to predict the thermal boundary layer

In this paper, the implicit assumptions in Levesque’s approximation are re-examined, and the dimensionless temperature distribution and the thermal boundary layer thickness were illustrated using the developed solution. By defining a similarity variable, the governing equations and boundary conditions are reduced to a typical dimensionless form in order to achieve an analytic solution in the entrance region. A relatively simple mathematical scheme was proposed by which the entrance-region temperature solution for laminar flow heat transfer with the similarity variable can be rigorously obtained The analytical solutions are then, checked against numerical solutions which were programmed under FORTRAN code using fourth-order Runge–Kutta method (RK4). Finally, other important thermal results obtained from this analysis, such as; approximate Nusselt number for the thermal entrance region which was discussed in detail. Analytical results were compared with the published data available in the literature for limiting cases, and good agreement was noticed.

Heat transfer characteristics of thermally developing flow in rectangular microchannels with constant wall temperature

Heat transfer at the thermal entrance region of rectangular microchannels is investigated for hydrodynamically fully developed but thermally developing flow with constant wall temperature. The effects of Reynolds number and aspect ratio on heat transfer properties have been calculated numerically. The local Nusselt number is found to be quite sensitive to the Reynolds number, especially for small Reynolds numbers. The slope of the Nusselt number curve is steeper with a lower Reynolds number when close to the inlet. It is found that the local Nusselt number is independent of the cross-sectional geometry at the channel inlet and the discrepancy of the local Nusselt number for different aspect ratios is gradually magnified along the streamwise direction. In consideration of the effects of Reynolds number and aspect ratio, new correlations are developed for actual Nusselt number and thermal entrance length of rectangular channels. A peak value of thermal entrance lengths can be discovered with the aspect ratio near 3. The present results may provide guidance for thermal design and optimization.