Global Nusselt Number Research Articles

Heat transfer fluctuation in a pipe caused by axially non-uniform heat distribution

This paper numerically investigates the impact of non-uniform boundary heat fluxes on the local and global Nusselt numbers of a circular pipe in fully developed turbulent flow regime. The numerical study is carried out basing on a validated three-dimensional CFD model under a series of prescribed sinusoidal wall heat fluxes. Results show that local Nusselt number fluctuation is remarkable under the heat flux with large non-uniformity and the local fluctuation ratio relatives to the uniform boundary condition is within the range of −26% to +15%. The phase-difference between heat flux profile and Nusselt number profile is expounded via mathematical treatment. To explore the underlying mechanism of the foregoing phenomenon, the analytical tool of field synergy principle is employed and is executed in a more rigorous way. It indicates that the local heat transfer fluctuation attributes to the local synergy-angle change in the very near-wall region. Besides, the average Nusselt number is also investigated. It is shown that, for a fixed amount of total heat flux, the average Nusselt number slightly decreases when the boundary heat flux changes into non-uniform, which dues to the global enlargement of synergy angle as well as the global augmentation of entropy generation increment.

Thermal and flow characteristics of a single-row circular-finned tube heat exchanger under elevated free-stream turbulence

The thermal performance of single-row heat exchangers is generally considered to be inferior to multi-row heat exchangers. It is therefore desirable to optimize the former; especially for those cases which cannot accommodate an alternative. In this study, the heat transfer performance of a single-row circular-finned tube heat exchanger was investigated experimentally under elevated disturbance levels. Specifically, grid-generated turbulence (GGT)—the characteristics of which had been measured beforehand with a hot-wire anemometer—was applied to a clean-flow benchmark case and measurements taken at the heat exchanger outlet. It was shown that when the grid is positioned appropriately, a mean enhancement (in global Nusselt number) of up to 11% can be achieved. Flow visualizations revealed the flow structures responsible for the increase in heat transfer.

Convection Heat Transfer Enhancement on Recirculating Flows in a Backward Facing Step: The Effects of a Small Square Turbulence Promoter

This work addresses the numerical simulation of incompressible turbulent recirculating channel flows in a backward-facing step. The effects of a small square turbulence promoter on convection heat transfer are evaluated through a parametric study. The governing equations comprise the time-averaged mass, linear momentum, and energy conservation principles in conjunction with the two-equation k–epsilon turbulence model. The study is focused on the assessment of the local and global Nusselt numbers at the channel stepped wall. The main results indicate that a maximum increment around 15% on the average Nusselt number can be achieved by using a small turbulence promoter to disturb the flow. Furthermore, it was found that the peak of the local Nusselt number on the stepped wall is located in the region where the turbulent diffusion is maximum in the near wall region.

Radiation effects on natural convection in a vertical channel with an auxiliary plate

In this experimental study the effects of unheated auxiliary plate positions along the centerline of a vertical channel on combined natural convective in air and radiative heat transfer are investigated. The vertical channel is symmetrically heated and a uniform heat flux along the principal walls of the channel is assumed. Comparisons between experimental data carried out from different positions of the auxiliary plate and two surfaces emissivity values are given in terms of heated wall temperatures and radiative heat transfer. Average Nusselt numbers by means of experimental data are evaluated. Results are given for different thermal and geometrical dimensionless parameters. Results show that the lowest maximum channel wall temperatures are attained for the auxiliary plate placed at the channel exit for high channel Rayleigh numbers and heat flux values. Correlations for average Nusselt numbers, global average Nusselt numbers and dimensionless maximum wall temperatures in terms of channel Rayleigh numbers and auxiliary plate-to-channel height ratio, h/L, are evaluated in the ranges: 20 < Ra'< 1.5 × 105, 22 <Ra′∗ < 1.7 × 105 and 0 ≤ h/L ≤ 0.5 for inlet and outlet positions and walls emissivity equal to 0.9. The proposed correlations are in good agreement with correlation for simple channel.

Computational Fluid Dynamics and Experimental Studies of a New Mixing Element in a Static Mixer as a Heat Exchanger

Abstract The main aim of this work is to study the thermal efficiency of a new type of a static mixer and to analyse the flow and temperature patterns and heat transfer efficiency. The measurements were carried out for the static mixer equipped with a new mixing insert. The heat transfer enhancement was determined by measuring the temperature profiles on each side of the heating pipe as well as the temperature field inside the static mixer. All experiments were carried out with varying operating parameters for four liquids: water, glycerol, transformer oil and an aqueous solution of molasses. Numerical CFD simulations were carried out using the two-equation turbulence k-ω model, provided by ANSYS Workbench 14.5 software. The proposed CFD model was validated by comparing the predicted numerical results against experimental thermal database obtained from the investigations. Local and global convective heat transfer coefficients and Nusselt numbers were detrmined. The relationship between heat transfer process and hydrodynamics in the static mixer was also presented. Moreover, a comparison of the thermal performance between the tested static mixer and a conventional empty tube was carried out. The relative enhancement of heat transfer was characterised by the rate of relative heat transfer intensification.

Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection

AbstractWe present high-resolution numerical investigations of heat transport by two-dimensional (2D) turbulent Rayleigh–Bénard (RB) convection over the Rayleigh number range$1{0}^{8} \leqslant Ra\leqslant 1{0}^{10} $and the Prandtl number range$0. 7\leqslant Pr\leqslant 10$. We find that there exists strong counter-gradient local heat flux with magnitude much larger than the global Nusselt number$Nu$of the system. Two mechanisms for generating counter-gradient heat transport are identified: one is due to the bulk dynamics and the other is due to the competition between the corner-flow rolls and the large-scale circulation (LSC). While the magnitude of the former is found to increase with increasing Prandtl number, that of the latter maximizes at medium$Pr$. We further reveal that the corner–LSC competition leads to the anomalous$Nu$–$Pr$relation in 2D RB convection, i.e. $Nu(Pr)$minimizes, rather than maximizes as in the three-dimensional cylindrical case, at$Pr\approx 2\sim 3$for moderate$Ra$.

Comparative study on performance of a zigzag printed circuit heat exchanger with various channel shapes and configurations

Comparative study has been performed with various channel cross-sectional shapes and channel configurations of a zigzag printed circuit heat exchanger (PCHE), which has been considered as a heat exchanging device for the gas turbine based generation systems. Three-dimensional Reynolds-averaged Navier–Stokes equations and heat transfer equations are solved to analyze conjugate heat transfer in the zigzag channels. The shear stress transport model with a low Reynolds number wall treatment is used as a turbulence closure. The global Nusselt number, Colburn j-factor, effectiveness, and friction factor are used to estimate the thermal–hydraulic performance of the PCHE. Four different shapes of channel cross section (semicircular, rectangular, trapezoidal, and circular) and four different channel configurations are tested to determine their effects on thermal–hydraulic performance. The rectangular channel shows the best thermal performance but the worst hydraulic performance, while the circular channel shows the worst thermal performance. The Colburn j-factor and friction factor are found to be inversely proportional to the Reynolds number in cold channels, while the effectiveness and global Nusselt number are proportional to the Reynolds number.

Investigations of flow and temperature field development in bare and wire-wrapped reactor fuel pin bundles cooled by sodium

Simultaneous development of liquid sodium flow and temperature fields in the heat generating pin bundles of reactor has been investigated. Development characteristics are seen to be strongly influenced by pin diameter, number of pins, helical wire-wrap, ligament gap between the last row of pins and hexcan wall and Reynolds number. Flow development is achieved within an axial length of ∼125 hydraulic diameters, for all the pin bundle configurations considered. But temperature development is attained only if the pin diameter is small or the number of pins is less. In the case of large pin diameter with more pins, temperature development could not be achieved even after a length of ∼1000 hydraulic diameters. The reason for this behavior is traced to be the weak communication among sub-channels in tightly packed bundles. It is seen that the pin Nusselt number decreases from center to periphery in a bundle. Also, if the ligament gap is narrow, the Nusselt number is large and more uniform. Flow development length is short if the Reynolds number is large and the converse is true for thermal development length. Helical wire-wrap shortens the thermal entry length and significantly enhances the global Nusselt number. But, its influence on hydrodynamic entry length is not significant.

Air Cooling of Mini-Channel Heat Sink in Electronic Devices

Heat transfer experiments were conducted to investigate the thermal performance of air cooling through mini-channel heat sink with various configurations. Two types of channels have been used, one has a rectangular cross section area of 5 × 18 mm2 and the other is triangular with dimension of 5 × 9 mm2. Four channels of each configuration have been etched on copper block of 40 mm width,30 mm height, and 200 mm length. The measurements were performed in steady state with air flow rates of 0.002 - 0.005 m3/s, heating powers of 80 - 200 W and channel base temperatures of 48°C, 51°C, 55°C and 60°C. The results showed that the heat transfer to air stream is increased with increasing both of air mass flow rate and channel base temperature. The rectangular channels have better thermal performance than trian- gular ones at the same conditions. Analytical fin approach of 1-D and 2-D model were used to predict the heat transfer rate and outlet air temperature from channels heat sink. Theoretical results have been compared with experimental data. The predicted values for outlet air temperatures using the two models agree well with a deviation less than ±10%. But for the heat transfer data, the deviation is about +30% to –60% for 1-D model, and –5% to –80% for 2-D model. The global Nusselt number of the present experimental data is empirically correlated as with accuracy of ±20% for and compared with other literature correlations.

관군 배열에서의 종간 간격이 열전달에 미치는 영향에 대한 수치 해석적 연구

In this study, a longitudinal pitch effect on in-line tube bank heat transfer has been analyzed numerically. To verify the accuracy of the solver model and boundary conditions, global Nusselt number(Nu) and pressure drop across the 2 row tube bank are compared with the existing experimental correlations under 500 ~ 2,000 Reynolds number(Re) range. By changing transverse pitch(<TEX>$S_T$</TEX>) or longitudinal pitch(<TEX>$S_L$</TEX>) separately in tube bank, we're trying to identify the each effect on heat transfer. We found that the effect of transverse pitch can be accounted for Reynolds number evaluated with maximum velocity(<TEX>$V_{max}$</TEX>) at the smallest flow area similar to most existing correlations. Variation of the longitudinal pitch(<TEX>$S_L$</TEX>) has a greater impact on the heat transfer compared to the transverse pitch(<TEX>$S_T$</TEX>). Overall Nusselt number increases with larger longitudinal pitch(<TEX>$S_L$</TEX>), however individual Nusselt number of the tube row has significant difference after the first row.

Mixed convection in an inclined channel with heated porous blocks

PurposeThe purpose of this paper is to study numerically the fluid flow and heat transfer in an inclined channel provided with heated porous blocks on its lower plate.Design/methodology/approachThe Brinkman‐Forchheimer extended Darcy model with the Boussinesq approximation is adopted for the flow in the porous regions. The governing equations with the appropriate boundary conditions are solved by the control volume method. The effect of some pertinent parameters such as the buoyancy force intensity, the porous blocks shape and height, the porous medium permeability and the Reynolds number are analyzed for various inclination angles ranging from −90° to +90°.FindingsThe results reveal, essentially, that the inclination angle of the channel can alter substantially the fluid flow and heat transfer mechanisms, especially at high Richardson and Darcy numbers. In this case, the maximum and minimum global Nusselt numbers are reached for α=+90° and α=−90°, respectively.Research limitations/implicationsThe results obtained in this work are valid for an inclined channel with porous blocks attached on the heated parts of the lower plate, whereas the upper wall is thermally insulated.Practical implicationsThe results obtained in this worky can be used in the thermal control of electronic components. The use of porous blocks mounted on the heat sources will increase the rate of heat removal in order to maintain the electronic components at an acceptable operating temperature.Originality/valueThe paper provides an interesting method to improve the cooling of electronic devices by use of a porous medium.

Forced convection heat transfer of polymer melt flow inside channels with contraction/expansion sections

Polymer melt flow inside channels with contraction/expansion sections is commonly found in numerous forming applications. Due to high polymer viscosity, this flow presents laminar behaviour, high pressure drop and relevant viscous heating effect. The analysis presented in this work comprises the numerical simulation of a set of equations (mass, linear momentum and energy conservation principles) that models this class of flow. The generalized Newtonian formulation is employed, being the apparent polymer viscosity computed as a function of temperature and shear strain rate. The governing equations are discretized using the finite difference method with central formulae (for both diffusion and convection terms). The work is focused on the assessment of the local and global Nusselt numbers based upon a parametric study of the effects of the contraction/expansion aspect ratio and entrance flow velocity. The main findings indicate that, similarly to Newtonian flows, the Nusselt number presents a good correlation with Reynolds, Prandtl and Eckert numbers.

Thermal convection in double glazed windows with structured gap

Convective heat transfer inside the gap of double glazed windows is studied numerically using a commercial CFD code (Fluent v6.3), for different Rayleigh numbers and aspect ratios. A reference window with empty gap is compared with windows where the gap contains fins arranged in such a way as to reduce heat transfer. The effects of convective air flow inside the cavities were estimated both at the onset of convection and at steady-state in real environmental conditions. The global Nusselt numbers were calculated for different configurations of the fins in the window gap, in order to apply the standard heat loss estimation method to this type of windows.

Measurements of the instantaneous local heat flux in turbulent Rayleigh–Bénard convection

We present measurements of the instantaneous local heat flux in highly turbulent Rayleigh–Bénard (RB) convection in air (Pr=0.7) for aspect ratios in the range 1.13⩽Γ⩽9.00 and for Rayleigh numbers in the range 1.3×109⩽Ra⩽9.6×1011. The measurements have been carried out simultaneously at the surfaces of the heating and the cooling plate using a commercial sensor whose diameter is 360 times smaller than the diameter of the RB facility. We find that for all investigated values of Ra and Γ the time-averaged local heat flux at the centres of the heating and cooling plates is significantly higher than the global heat flux obtained in previous measurements. In particular, for the smallest investigated aspect ratio, Γ=1.13, the scaling exponents of the local heat fluxes as functions of the Rayleigh number are found to be considerably below those of the global heat flux obtained in experiments with cryogenic helium at Γ=1 by Niemela and Sreenivasan (2003 J. Fluid Mech.481 355–84). Our measurements indicate that the spatial distribution of the heat flux at the heating and cooling plates is strongly nonuniform and that this nonuniformity decreases with increasing Ra and Γ. Our investigations of the time dependence of the local heat fluxes show that these quantities undergo fluctuations up to ±15% of their time-averaged values. Our work suggests that local heat flux measurements at different positions along heating and cooling plates are useful for a deeper understanding of the scaling properties of the (global) Nusselt number in RB convection.

Turbulent direct-contact heat transfer between two immiscible fluids

Heat transfer between two immiscible liquid phases in turbulent flow is of great interest in improving the residence time, compactness, and energy cost of cooling and heating processes. The high-efficiency vortex (HEV) device used here as a direct-contact heat exchanger (DCHE) is a generic multifunctional exchanger/reactor in which wall tabs generate longitudinal vortices responsible for convective radial transfer that enhance macro-mixing, phase dispersion and fast temperature homogenization in the flow. The experiments reported here concern a continuous flow of water in which an immiscible mineral oil is injected. The inlet water temperature ranges from 11 to 13 °C, and the inlet oil temperature from 40 to 48 °C; the flow Reynolds number varies between 7500 and 15 000. An algebraic one-dimensional thermal model accounting for the axial evolution of the phase temperatures coupled with drop breakup is developed and validated by the experimental thermal results in the DCHE. This model requires knowledge of the turbulent field in single-phase conditions; it can be adapted to other flow geometries and can be used as a sizing tool for engineering design. Despite the phase separation at the outlet, the DCHE is more efficient than a double-jacketed heat exchanger in terms of global Nusselt number. In addition, the HEV heat exchanger is energetically less costly than the other DCHE for the same heat-transfer capacity.

Thermal hydraulic performance analysis of the printed circuit heat exchanger using a helium test facility and CFD simulations

The thermal-hydraulic performance of the PCHE was investigated using the KAIST helium test loop. Experiments were performed in the helium laminar region with 350 < Re < 1200. The hot/cold side inlet conditions were 25–550 °C/25–100 °C over the operating pressure of 1.5–1.9 MPa, respectively. Mass flow rates were controlled in the range of 40–100 kg/h. Pressure drop and temperature difference were measured at the inlet and outlet of the hot and cold sides. A global Fanning factor correlation and a global Nusselt number correlation were proposed using information only at the inlet and outlet of the hot and cold sides. A three-dimensional (3-D) numerical simulation was performed using FLUENT, a commercial computational fluid dynamics (CFD) code, to compare simulation results to the KAIST helium test data and to obtain the local Nusselt number in the PCHE. CFD predictions showed good agreement with experimental data. A local pitch-averaged Nusselt number correlation was proposed using local temperature, pressure, surface heat fluxes, and properties provided by CFD simulations. The system analysis code, GAMMA, was also utilized to identify which correlation was more applicable for system analysis. It turns out that the proposed local pitch-averaged Nusselt number correlation from CFD simulations is more appropriate than the global Nusselt number correlation developed from experimental data.

One-Dimensional Model of Natural Convection in Differentially Heated Partitioned Enclosures With Conducting External Walls and Vertical Partitions

Natural convection in partitioned enclosures is extensively investigated due to its importance in many applications. Real enclosures have diffusive walls and partitions. A method has been developed to evaluate the global natural convection Nusselt number for a differentially heated (heated from sides) partitioned enclosure with walls and vertical partitions of finite thickness. A formula has been elaborated, giving the global Nusselt number as a function of the global Rayleigh number, global aspect ratio of the whole enclosure, and two other dimensionless parameters: the conductive thermal resistance ratio and the porosity. After validation of the method by comparison of our results with those from both the literature studies and the numerical simulation, a parametric study is carried out to show the influence of the dimensionless parameters. The method is a helpful tool for thermal engineers and scientists to design such a common system.

Heat transfer in a mechanical face seal

This paper presents a numerical analysis of heat transfer in an experimental inner pressurized mechanical face seal, using CFD. The configuration is similar to the laminar flow between a static and a rotating disc bounded by a co-rotating sidewall. A series of simulations allow the authors to propose a correlation for the global Nusselt number for the rotating ring and the static disc. The Nusselt number is a function of the Reynolds number of the flow and the Prandtl number, as well as of the ratio of the fluid and material thermal conductivities. This last conclusion arises from the fact that the heat source is located in the contact between the rotor and the stator and depends on the temperature distribution in the solids. The cooling oil flow appears not to affect the Nusselt number. The numerical results were validated by comparison with measurements carried out on the experimental seal by means of an infrared camera.

Multiple steady states in a porous enclosure partially heated and fully salted from below

The Darcy model with the Boussinesq approximation is used to study natural convection in a porous medium saturated by a binary fluid. The geometry considered is a square cavity whose portion of the bottom surface is isothermally heated, the upper surface is cooled at a constant temperature and all other surface are adiabatic. The solutal buoyancy forces are assumed to be induced by the imposition of uniform concentration on the upper and lower boundaries. The governing parameters for the problem are the thermal Rayleigh number, R T , the Lewis number, Le, the buoyancy ratio, φ, the dimensionless length of the bottom plate, B T , the aspect ratio of the cavity A, the normalized porosity of the porous medium, ε, and the relative position of the heating element with respect to the vertical centerline of the cavity, δ T . Two main convective modes are studied, namely single and double-cell convection, and their features are described. Also the possible existence of tricellular flows is demonstrated. Maximum streamfunction and global Nusselt and Sherwood number are presented as functions of the external parameters. The existence of up to three steady-state solutions for a given set of the governing parameters is demonstrated.

Experimental study of temperature distribution and local heat flux for turbulent Rayleigh–Bénard convection of air in a long rectangular enclosure

Measurements of temperature distribution and local heat flux were performed in a rectangular Rayleigh–Bénard (RB) cell with aspect ratios Γ x = 5 and Γ y = 1 using air as the working fluid. The range of Rayleigh numbers was from Ra ≈ 6 × 10 7 up to Ra ≈ 6 × 10 8 and the measurements were taken at four different positions on the cooling and heating plates. The structure of the temperature profiles was analysed with the scaling to the temperature gradient at the wall γ , calculated from both global Nusselt number ( γ glob ) and the measured local heat flux density q ( γ loc ) . The measured local Nusselt number in the center of Rayleigh–Bénard cell is found to be significantly higher than the global Nusselt number, which was calculated from a heat transfer law, based on asymptotic considerations from Hoelling and Herwig [M. Hoelling, H. Herwig, Asymptotic analysis of heat transfer in turbulent RB-convection, Int. J. Heat Mass Transfer 49 (2006) 1129–1136]. Profiles scaled with γ glob agree very well with the universal asymptotic temperature profile for Ra → ∞ . Conversely, profiles scaled with γ loc have another structure. The results clearly show the difference between the temperature profiles from the theoretical model with walls of infinite extend and from the real RB-cell. In contrast to common opinion the structure of the temperature profile was found to consist of three different behaviors. It has been observed for all profiles a linear behavior in the viscous sublayer directly on the wall, a power law in the boundary layer and a logarithmic function in the overlap layer.