Spatially-averaged Nusselt Numbers Research Articles

Computational study of bubble, thin-film dynamics and heat transfer during flow boiling in non-circular microchannels

Flow boiling in multi-microchannel evaporators is one of the most efficient thermal management solutions for high-power-density applications. However, there is still a lack of understanding of the governing two-phase heat and mass transfer processes that occur in these devices, which has resulted in a limited availability of applicable boiling heat transfer prediction methods based on first principles, and of reliable thermal design tools. This article presents a systematic analysis of the dynamics of bubbles and the surrounding liquid film during flow boiling in three-side-heated non-circular microchannels. The study is performed using a custom version of ESI OpenFOAM v2106 with a geometric volume-of-fluid method to capture the interface dynamics, also incorporating conjugate heat transfer through the evaporator walls. The hydraulic diameter of the channel is fixed to Dh=0.229mm and the range of width-to-height aspect ratios ϵ=0.25−4 is examined. We investigate different fluids, namely water, HFE7100, R1233zd(E), R1234ze(E), and evaporator materials, namely copper, aluminium, silicon, stainless steel, with base heat fluxes in the range qb=50−200kW/m2. The results show that conjugate heat transfer acts to make the temperature distributions around the perimeter of the channel cross-section more uniform, and that the topography of the lubricating film and the extension of the dry vapour patches that develop while the film is depleted both depend on the cross-sectional channel shape and influence the heat transfer performance significantly. For highly wetting conditions, channels with ϵ=0.25 tend to allow enhanced heat transfer rates, with a spatially-averaged Nusselt number that is 50% higher than that obtained for ϵ=1 (square channels) and 10% higher than that for ϵ=4. This arises thanks to an extended evaporating film that covers the vertical walls which, owing to the three-side-heated configuration, contribute twice to the spatially-averaged heat transfer performance. For more hydrophobic conditions, large dry patches develop over the vertical walls for ϵ=0.25 due to the lower evaporator temperatures, leading to reduced heat transfer, with thermal performance weakly dependent on ϵ in the range ϵ=0.5−2.

Experimental study on convective heat transfer of hybrid impingement configuration by square-array continuous jets and a center-positioned synthetic jet

An experimental investigation is performed to illustrate the heat transfer characteristics for a specific hybrid-jet impingement configuration that is comprised of a square-layout continuous-jet array and a center-positioned loudspeaker-driven synthetic-jet actuator. Herein four continuous-jet Reynolds numbers (ranging from Re=3000 to Re=10,000), three hole-to-hole pitches (X/d = Y/d = 4. 5 and 6), and a series of impinging distances (H/d = 2–10) are considered while the central synthetic jet is operated at f = 250 Hz with a characteristic Reynolds number of about Re0=4500. It is identified that the integration of central synthetic jet in the array-jet unit is indeed an effective means to enhance the overall heat transfer performance, which is more suitable for the practical applications wherein the synthetic jet Reynolds number is greater than or equivalent to the array-jet Reynolds number. By the integration of central synthetic jet, a significant localized heat transfer augment is achieved at the central zone of array-jet unit, especially under small and moderate array-jet Reynolds numbers. In terms of the spatially-averaged Nusselt number, an increase of more than 100% could be achieved by the central synthetic jet integration at H/d ≥ 6 under Re=3000. The benefit of the central synthetic jet integration is also clearly demonstrated under Re=5000, wherein the spatially-averaged Nusselt number could be increased by 30%-60%, taking a monotonous increasing trend along with the impinging distance generally. Under Re=7000, a relative increase among 10%-30% still remains. When the array-jet Reynolds number is increased up to 10,000, only in the sparse continuous-jet array (X/d = Y/d = 6) the benefit of the central synthetic jet integration could behave, with a limited relative increase of less than 20%.

Geometric optimization of a lid-driven cavity with two rectangular intrusions under mixed convection heat transfer: A numerical investigation motivated by constructal design

The present work aims at the geometric optimization, by means of constructal design and exhaustive search, of two rectangular fins inserted in a lid-driven cavity subjected to unsteady, incompressible, laminar, two-dimensional mixed convective flow with stable stratification. The main purpose is to maximize the dimensionless heat transfer rate (q˜′) and time and spatial-averaged Nusselt number (NuH¯). The domain presents three constraints: cross-sectional areas for each fin and total area of the cavity. Two degrees of freedom are investigated, height/length ratios of the left and right rectangular fin (H1/L1 and H2/L2), considering three different fraction areas for fins and two different Richardson numbers Ri = 0.1 and 1.0, representing two conditions for mixed convective flow. All cases have constant Reynolds and Prandtl numbers (ReH = 400 and Pr = 6.0). The conservation equations of mass, momentum, and energy are solved using the Finite Volume Method. Recommendations for fins shapes were strongly affected by the performance indicators chosen. Results also indicated that asymmetric configurations for the fins with different fraction areas for each fin led to the best thermal performance. Moreover, the optimal shapes and the effect of degrees of freedom over performance indicators were also affected by the Richardson numbers investigated.

GEOMETRICAL EVALUATION OF RECTANGULAR FIN MOUNTED IN LATERAL SURFACE OF LID-DRIVEN CAVITY FORCED CONVECTIVE FLOWS

In this work, it is investigated the geometric effect of rectangular fin inserted in a lid-driven square cavity over thermal performance of laminar, incompressible, steady and forced convective flows. This study is performed by applying Constructal Design to maximize the heat transfer between the fin and the cavity flow. For that, the problem is subjected to two constraints: area of the cavity and area of rectangular fin, and two degrees of freedom: height/length ratio of rectangular fin (H1/L1) and its position in upstream surface of the cavity (S/A1/2). It is considered here some fixed parameters, as the ratio between the fin and cavity areas (ϕ = 0.05), the aspect ratio of the cavity dimensions (H/L = 1.0) and Prandtl number (Pr = 0.71). The fin aspect ratio (H1/L1) was varied for three different placements of the fin at the upstream cavity surface (S/A1/2 = 0.1, 0.5 and 0.9) which represents a lower, intermediate and upper positions of the fin. The effects of the fin geometry over the spatial-averaged Nusselt number ( ) is investigated for three different Reynolds numbers (ReH = 10, 102 and 103). The conservation equations of mass, momentum and energy were numerically solved with the Finite Volume Method. Results showed that both degrees of freedom (H1/L1 and S/A1/2) had a strong influence over , mainly for higher magnitudes of Reynolds number. Moreover, the best thermal performance is reached when the fin is placed near the upper surface of the cavity for an intermediate ratio between height and length of rectangular fin, more precisely when (S/A1/2)o = 0.9 and (H1/L1)oo = 2.0.

Direct numerical simulation and in-depth analysis of thermal turbulence in square annular duct

The thermal turbulence in an infinitely-long square annular duct (SAD) was studied by the direct numerical simulation with the Reynolds (Re) number Reb≈6400 based on the bulk velocity. The isothermal boundary condition was applied to the side walls in SAD with the higher and lower temperatures on the outer and inner walls, respectively. As one of the most fascinating features for the corner turbulence, the turbulent-driven secondary flow (TDSF) presented the twin counter-rotating vortex pairs symmetrically located at the outer concave and inner convex corners. The TDSF was found significantly increase the spatially-averaged Nusselt (Nu) number comparing to the laminar flow. The instantaneous vortex structures were visualized by the third-generation vortex-identification method based on Liutex. The budget analyses of the governing-equation for the turbulent boundary layer (TBL) in SAD distinguished the balancing mechanisms from the one in the traditional flat-plate TBL, which justified the necessity to classify the generic TBLs into their sub-categories of Type-A, B and C TBLs. Moreover, the current study focused on a number of issues in the thermal TBL, such as the TDSF structures with their thermal effects and the TBL law formulations. For the present TBL in SAD, it was found that the buffer layer located in between the inner and the semi-log layers tended to be wider than that in a flat-plate TBL, and an outer linear conduction layer was, for the first time, found for the Type-B temperature TBL. Based on the indicator function, the quantitative sublayer partitions were first conducted for both the velocity and temperature TBLs and then the applicable ranges for the linear and semi-log sublayers were rigorously determined. Further, the profound damping mechanism was first introduced and applied to the traditional linear and semi-log laws to derive more accurate analytical law formulations for the entire velocity and temperature TBL sublayers.

Lattice Boltzmann simulation to laminar pulsating flow past a circular cylinder with constant temperature

In order to investigate the heat transfer characteristics of pulsating flows past a circular cylinder, a Lattice Boltzmann (LB) numerical code based on a 2-dimension-9-velocity frame is developed. The local Nusselt number and the dimensionless viscous force around the cylinder surface are explored in detail. Double Particle Distribution Function model and the second order extrapolation method for the curve boundary of the cylinder are employed in the LB numerical code. Numerical results found that the spatial averaged Nusselt number of the cylinder is oscillating with the same pulsating frequency of the incoming air flows. The heat transfer enhancement is mainly located in the windward side of the cylinder, and the heat transfer enhancement only happens in one half cycle of the pulsation. Whereas the heat transfer in the leeward side of the cylinder is found to be unaffected, and the heat transfer is slightly deteriorated in the other half cycle of the pulsation. Further analysis showed that the heat transfer enhancement is proportional to the magnitude of dimensionless viscous force.

Impingement jet array heat transfer with small-scale cylinder target surface roughness arrays

The present investigation considers special small-scale roughness patterns on impingement target surfaces to increase surface heat transfer augmentation levels of impingement jet array cooling. Utilized are three different heights of cylinder small roughness elements, which are mounted on three different test surfaces. The cylinder-shaped roughness is small-scale because diameter is 7.5 percent and maximum height is 25 percent of impingement hole diameter. Associated results are compared with spatially-averaged Nusselt number ratio distributions measured on target surfaces with triangle small roughness, or rectangle small roughness. Data are obtained for impingement jet Reynolds numbers of 900, 1500, 5000, and 11,000. Nusselt number variations for the small cylinder roughness show different trends with streamwise development and changing roughness height, compared to target plates with small rectangle roughness and small triangle roughness. In general, this is because roughness elements which contain surface shapes with sharp edges generate increased magnitudes of vorticity with length scales of the order of the roughness element diameter. Such generation is not always present in an abundant fashion with the small cylinder roughness because of the smooth contours around each roughness element periphery. Such effects are illustrated by several data sets, including Nusselt numbers associated with the small cylinder roughness with a height of 0.250D at a turbulent Reynolds number of 11,000.

Numerical investigation and recurrence plot analysis of pulsating magnetohydrodynamic mixed convection over a backward facing step

In the current study, numerical investigation of pulsating magnetohydrodynamic mixed convection over a backward facing step is carried out for the range of parameters; Reynolds number (25 ⩽ Re ⩽ 100), Hartmann number (0 ⩽ Ha ⩽ 60), Strouhal number (0.1 ⩽ St ⩽ 1) and Gr number is kept at Gr = 104. The governing equations are solved with a general purpose finite element based solver. The effects of various parameters on the fluid flow and heat transfer characteristics are numerically studied. It is observed that the flow field and heat transfer rate are influenced by the variations of Reynolds, Hartmann and Strouhal numbers. Furthermore, recurrence plot analysis is applied for the analysis of the time series (spatial averaged Nusselt number along the bottom wall downstream of the step) and for a combination of different parameters, the systems are identified using recurrence quantification analysis parameters including recurrence rate, laminarity, determinism, trapping time and entropy.

Effects of phase shift on the heat transfer characteristics in pulsating mixed convection flow in a multiple vented cavity

In the current study, numerical investigation of pulsating mixed convection in a multiple vented cavity with phase shift is carried out for the range of parameters; Richardson number (0.25⩽Ri⩽4), phase shift (0⩽ϕ⩽π) and Strouhal number is fixed at 1. The governing equations are solved with a general purpose finite volume based solver. The effects of Ri number and phase shift parameters on the fluid flow and heat transfer characteristics are numerically studied. It is observed that the flow field and heat transfer enhancement are influenced by the variation of these parameters. Furthermore, recurrence plot analysis is applied for the analysis of the time series (spatial averaged Nusselt number along the vertical wall of the cavity) and for a combination of different parameters, the systems are identified using recurrence quantification analysis parameters including recurrence rate, laminarity, determinism, trapping time and entropy.

Crossflows from jet array impingement cooling: Hole spacing, target plate distance, Reynolds number effects

Data which illustrate the combined and separate effects of hole array spacing, jet-to-target plate distance, and Reynolds number on cross-flows, and the resulting heat transfer, for an impingement jet array are presented. The array of impinging jets are directed to one flat surface of a channel which is bounded on three sides. Considered are Reynolds numbers ranging from 8000 to 50,000, jet-to-target plate distances of 1.5D, 3.0D, 5.0D, and 8.0D, and steamwise and spanwise hole spacing of 5D, 8D, and 12D, where D is the impingement hole diameter. In general, the cumulative accumulations of cross-flows, from sequential rows of jets, reduce the effectiveness of each individual jet (especially for jets at larger streamwise locations). In other situations, the impingement cross-flow results in locally augmented Nusselt numbers. Such variations most often occur at larger downstream locations, as jet interactions are more vigorous, and local magnitudes of mixing and turbulent transport are augmented. This occurs in channels at lower Reynolds numbers, where impingement jets are confined by smaller hole spacing, and smaller jet-to-target plate distance. The overall result is complex dependence of local, line-averaged, and spatially-averaged Nusselt numbers on hole array spacing, jet-to-target plate distance, and impingement jet Reynolds number.

Cross-flow effects on impingement array heat transfer with varying jet-to-target plate distance and hole spacing

New impingement heat transfer data are presented for experimental conditions and configurations employed have not been previously examined, which illustrate the effects of impingement cross-flows on local, line-averaged, and spatially-averaged Nusselt numbers, as both jet-to-target distance and jet hole spacing are altered. Data are given for a constant impingement jet Reynolds number of 8000. In general, the impingement passage cross-flows which accumulate are detrimental to local Nusselt number performance, especially for denser hole arrays with 5D and 8D hole spacing, where D is impingement hole diameter. This is illustrated by periodic variations of surface Nusselt numbers, which generally decrease with streamwise development, and by local Nusselt number peak values for hole spacings of 5D, 8D, and 12D which generally become smaller at successive x/D locations for each value of Z/D. Also considered are unique situations where significant accumulation of cross-flow fluid results in an opposite trend, with local Nusselt numbers which increase with streamwise development for dense hole spacing of 5D, and smaller jet-to-target plate distances of 1.5D and 3.0D.

Numerical investigation and dynamical analysis of mixed convection in a vented cavity with pulsating flow

In the present study, numerical investigation of pulsating mixed convection in a multiple vented cavity is carried out for the range of parameters; Reynolds number (500⩽Re⩽2000), Grashof number (104⩽Gr⩽106), Strouhal number (0⩽St⩽2). The governing equations are solved with a general purpose finite volume based solver. The effects of various parameters on the fluid flow and heat transfer characteristics are numerically studied. It is observed that the flow field and heat transfer rate are influenced by the variations of Reynolds, Grashof and Strouhal numbers. Furthermore, recurrence plot analysis is applied for the analysis of the time series (spatial averaged Nusselt number along the vertical wall of the cavity) and for a combination of different parameters, the systems are identified using recurrence quantification analysis parameters including recurrence rate, laminarity, determinism, trapping time and entropy.

Pulsating nanofluids jet impingement cooling of a heated horizontal surface

In this study, a numerical study of pulsating rectangular jet with nanofluids is presented. The aim of this work is to numerically investigate the effects of various parameters such as pulsating frequency, Reynolds number, nanoparticle volume fraction on the fluid flow and heat transfer characteristics. The unsteady Navier–Stokes and energy equations are solved with a commercial finite volume based code. It is observed in the steady case, adding nanoparticles increases the peak value of the Nusselt number at the stagnation point and spatial-averaged Nusselt number along the impingement plate. Heat transfer enhancement up to 18.8% is obtained for particle volume fraction of 6% at Reynolds number of 200. In the pulsating flow case, the combined effect of pulsation and inclusion of nanoparticles is not favorable for the augmentation of the stagnation point Nusselt number at Re=200, ϕ=1%, 3% and at Re=400, ϕ=1%, 3% when compared to the steady case.

Effects of Jet-To-Target Plate Distance and Reynolds Number on Jet Array Impingement Heat Transfer

Data which illustrate the effects of jet-to-target plate distance and Reynolds number on the heat transfer from an array of jets impinging on a flat plate are presented. Considered are Reynolds numbers Rej ranging from 8200 to 52,000 with isentropic jet Mach numbers of approximately 0.1 to 0.2. Jet-to-target plate distances Z of 1.5D, 3.0D, 5.0D, and 8.0D are employed, where D is the impingement hole diameter. Streamwise and spanwise hole spacings are 8D. Local and spatially-averaged Nusselt numbers show strong dependence on the impingement jet Reynolds number for all situations examined. Experimental results also illustrate the dependence of local Nusselt numbers on normalized jet-to-target plate distance, especially for smaller values of this quantity. The observed variations are partially due to accumulating cross-flows produced as the jets advect downstream, as well as the interactions of the vortex structures, which initially form around the jets and then impact and interact as they advect away from stagnation points along the impingement target surface. The highest spatially-averaged Nusselt numbers are present for Z/D = 3.0 for Rej of 8200, 20,900, and 30,000. When Rej = 52,000, spatially-averaged Nusselt numbers increase as Z/D decreases, with the highest value present at Z/D = 1.5.

Numerical analysis of laminar pulsating flow at a backward facing step with an upper wall mounted adiabatic thin fin

The effect of an upper wall mounted adiabatic thin fin on laminar pulsating flow in a backward facing step has been investigated numerically. Study is performed for different Reynolds numbers (based on the step height) in the range of 10 and 200 and for the expansion ratio of 2. The working fluid is air with the Prandtl number of 0.71. The governing equations are solved with a general purpose finite volume based solver, FLUENT. The effects of various pertinent parameters, Reynolds number, fin length and pulsating frequency on the fluid flow and heat transfer characteristics are numerically studied. It is observed that fin alters the flow field and thermal characteristics. In the steady flow case, heat transfer enhancement is obtained with the installation of the fin on the upper wall and increases with increasing fin length and increasing Reynolds number. Heat transfer enhancement of 188% is obtained for fin length of Lf=1.5H at Reynolds number of 200. In the pulsating flow case, time-spatial averaged Nusselt number along the bottom wall downstream of the step normalized with spatial averaged Nusselt number in the steady flow case versus excitation Strouhal number shows a resonant type behavior; first an increase in the value is seen up to St=0.05, then a decrease is seen with the increasing values of the frequency of the pulsation for the case without fin. Adding a fin shifts the maximum value of the normalized Nusselt number from St=0.05 to St=0.1. Compared to steady flow with no-fin case, adding a fin is not advantageous for heat transfer enhancement in pulsating flow.

Fuzzy-based estimation of mixed convection heat transfer in a square cavity in the presence of an adiabatic inclined fin

In this study, heat transfer from a square cavity in the presence of a thin inclined adiabatic fin is estimated using inputs–outputs generated from a CFD code with a fuzzy based identification procedure. The Reynolds number based on cavity length is 300 and the Richardson number is varied between 1 and 30. The top and bottom walls of the cavity are kept at constant temperature while the vertical walls are assumed to be adiabatic. The fin height, fin inclination angle, and Richardson number are considered as the input and the spatial averaged Nusselt number is taken as the output for the fuzzy model. Two data sets are used. One data set which contains 45 cases is used for estimation and another data set which contains 10 cases (not used in estimation) is used for validation purposes. The predictions using fuzzy model compare well with the CFD computations.

Thermal performance of dimpled surfaces in laminar flows

The present study provides data which illustrate the effects of an array of dimples on local and spatially-averaged surface Nusselt number distributions, as well as on friction factors in channels with laminar flow. Trends of spatially-averaged Nusselt numbers and friction factors are provided as they vary with dimple depth, channel height, Reynolds number from 260 to 1030, and the use of protrusions on the opposite channel wall. When compared with turbulent flow results, the present laminar data illustrate changes due to the absence of turbulence transport. For example, in contrast to turbulent flows, the present laminar flow data show that there is no overall benefit from the use of a top wall with protrusions. In addition, spatially-averaged Nusselt number ratios and friction factor ratios measured on a deep dimpled surface with a smooth top wall show trends which are opposite from ones observed in turbulent flows, since lower laminar heat transfer augmentations are present for smaller channel heights when compared at the same Reynolds number.

Effects of hole spacing on spatially-resolved jet array impingement heat transfer

Data which illustrate the effects of hole spacing on spatially-resolved heat transfer from an array of jets impinging on a flat plate are presented. Considered are Reynolds numbers ranging from 8200 to 30,500, and Mach numbers from 0.1 to 0.6. The spacing of the holes used to produce the impinging jets is either 8 D or 12 D in both the streamwise and spanwise directions. Local and spatially-averaged Nusselt numbers show strong dependence on the impingement jet Reynolds number for both situations, with negligible variations between Ma = 0.1 and 0.2 at constant Reynolds number. Experimental data, taken at Mach numbers greater than 0.2, while maintaining constant Reynolds number, show that Mach number has a significant impact on overall heat transfer. For 8 D spacing, heat transfer is augmented significantly as the Mach number increases, and for hole spacing of 12 D, heat transfer also increases significantly as the Mach number increases. Also included is a new correlation, based on that of Florschuetz et al. [L.W. Florschuetz, C.R. Truman, D.E. Metzger, Streamwise flow and heat transfer distributions for jet array impingement with crossflow, ASME Trans.–J. Heat Transfer 103 (1981) 337–342], as an impingement design tool.

Free Convective Heat Transfer in Tilted Longitudinal Open Cavity

Heat transfer experiments were performed to investigate the effects of inclination and channel height-to-gap ratio on free convection in a simulated fin-passage with a strategic aim of devising a criterion for selecting the optimal fin length that could provide the maximum free convective capability. The ranges of parameters investigated include the Grashof number, up to 500,000; channel height-to-gap ratios of 1, 2, and 3; and tilt angles of 0°, 30°, 60°, 90°, 120°, 150°, and 180°. Selections of local and spatially averaged Nusselt number results demonstrate the manner by which the Grashof number, tilt angle, and channel height-to-gap ratio interactively affect the heat transfer. In conformity with the experimentally revealed heat transfer physics, the correlation of a spatially-averaged Nusselt number over two parallel walls and the bottom surface of an open-ended channel is derived that permits the individual and interactive effects of the Grashof number, tilt angle, and channel height-to-gap ratio on heat transfers to be evaluated. A criterion for selecting the optimal height-to-gap ratio of the fin channel is subsequently formulated as a design tool for maximizing the convective capability of a free convective fin assembly.

Heat transfer in a twin-blow narrow channel with two opposite walls roughened by skewed ribs arranged in staggered manner

This experimental study performs the detailed heat transfer measurements over a skewed-rib roughened surface in a rectangular narrow channel with two equal-area flow entrances located on two adjacent edges of a channel-corner. This flow configuration allows for increasing the coolant-flow fed into the narrow channel without increasing the height of assembly in order to enhance the capacity of cooling duty for electronic chipsets. At a specified total coolant mass flow rate, four test scenarios, namely the single-blow from the side or upper entrance and the twin-blow with the coolant mass flow ratio of 1 : 1 or 2 : 1 between the side and upper blows are performed. A selection of full-field heat transfer distributions over the rib-roughened surface illustrates the manner by which the flow entry condition and the Reynolds number affect the local and spatially averaged heat transfers. With fixed total coolant consumptions, the twin-blow with the coolant mass flow ratio of 2 : 1 between the side and upper blows elevates the spatially averaged heat transfers to the levels of 150–180% of the single-blow references. A regression-type analysis is subsequently performed to develop the correlation of spatially-averaged Nusselt numbers over rib-roughened surface, which permits the effect of Reynolds number on heat transfer to be determined for four test scenarios.