Confined,milliscale unsteady laminar impinging slot jets and surface Nusselt numbers

Different modes of unsteadiness which develop within confined, laminar impinging slot jets of millimeter-scale are considered, including experimental measurements and numerical predictions of different flow characteristics, including spatially-resolved distributions of local Nusselt numbers measured on a constant heat flux surface. The effects of Reynolds number, and nozzle-to-plate distance on the local Nusselt number are investigated for a slot nozzle width B of 1.0 mm, Reynolds numbers Re from 120 to 200, nozzle-to-plate distances H/B from 0.75 to 12.5, and a nozzle aspect ratio y/B of 50. Observed are several different types of unsteady slot jet behavior, including: (i) a flow fluctuations/flapping motion mode of unsteadiness which is present for B = 1.0 mm, 4.75 ? H/B ? 5.5, and 120 ? Re ? 140, (ii) an intermittent flapping motion of the jet column which is present for B = 1.0 mm, 9 ? H/B ? 11.25, and 120 ? Re ? 200, and (iii) a continuous sinusoidal oscillation state, which is observed to be present for Re = 160 and H/B = 10. The flow fluctuations/flapping motion mode of unsteadiness, and the intermittent flapping motion of the jet column are both associated with local maxima in local, stagnation point Nusselt number distributions. The variations of these stagnation point Nusselt numbers associated with these two modes of unsteadiness are characterized by correlations which provide the dependence upon Reynolds number and normalized nozzle-to-plate distance ratio, H/B. Also described is the lateral variation of local Nusselt numbers for five nozzle-to-plate distances H/B of 2, 6, 8, 10, and 12, and Reynolds numbers from 120 to 200.     

Nonlinear flow and heat transfer dynamics of impinging jets onto slightly-curved surfaces

The nonlinear flow and heat transfer characteristics for a slot-jet impinging on slightly-curved surfaces are experimentally studied here. The effects of curved surface geometry and jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. Two different slightly-curved surface geometries of convex and concave are used as target surfaces. The nozzle geometry is a rectangular slot, and the dimensionless nozzle-to-surface distance equals to L¹ = 8. The constant heat fluxes are accordingly applied to the surfaces to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of Re = 8617, Re = 13 350 and Re = 15 415 for both curved surfaces. The velocity distributions of issuing jet from the nozzle exit to the target surface are obtained by a highly sensitive hot-wire anemometer. The T-type thermocouples are used to measure local temperatures of both the air jet and the plates. Two-dimensional velocity measurements show that the surfaces are remained out of the potential core region for all Re tested here. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported. The correlations reveal that the impinging cooling rate is higher with the concave surface and increase with increasing Re.     

Nonlinear flow and heat transfer dynamics of a slot jet impinging on a slightly curved concave surface

The nonlinear flow and heat transfer characteristics for a slot jet impinging on a slightly curved concave surface are experimentally studied here. The effects of jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. The nozzle geometry is a rectangular slot and the dimensionless nozzle-to-surface distance equals to L^⁎ = 8. The constant heat fluxes are accordingly applied to the surface to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of 8617, 13 350 and 15 415. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported.     

Numerical study of turbulent slot jet impingement cooling on a semi-circular concave surface

An investigation of the flow field and heat transfer characteristics of a slot turbulent jet impinging on a semi-circular concave surface with uniform heat flux has been carried out numerically in this study. The turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known k–ε turbulence model and its associate wall function to describe the turbulent structure. In addition, a body-fitted curvilinear coordinate system is employed to transform the physical domain into a computational domain.Numerical computations have been conducted with variations of jet exit Reynolds number Re_2B (5920 ? Re_2B ? 23,700), dimensionless jet-to-surface distance H/B (0.5 ? H/B ? 12), dimensionless jet width B/D (0.033 ? B/D ? 0.05) and the heat flux q″ (1663 W/m² ? q″ ? 5663 W/m²). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. The variations of local Nusselt numbers along the semi-circular concave surface decrease monotonically from its maximum value at the stagnation point. The numerical results show that the local Nusselt numbers are reasonably predicted with a maximum discrepancy within 15%. As the Reynolds number fixes, the effect of the impingement distance (H/B) on the average Nusselt (Nu_avg) is not significant except at low H/B = 0.5. This study provides fundamental insight into turbulent slot jet impingement cooling on the semi-circular concave surface.     

Forced convective heat transfer with impinging slot jets of meso-scale

Measurements were made to investigate the localized heat transfer behavior of submerged slot jets. The experiments were performed with kerosene jets impinging on a vertical constant-heat-flux surface from a meso-scale slot nozzle 125 μm in width with Re = 600–1200 and nozzle-to-plate spacing Z/B = 2–20. Heat transfer coefficients at the stagnation line were measured and correlated as a function of jet Reynolds numbers and Prandtl numbers. Lateral distributions of local heat transfer coefficients were also determined and correlated. Non-monotonic variations and unusual behavior of local heat transfers were observed and attributed to the possible transition from a laminar to a turbulent flow. This transition takes place within an extremely short distance of 400–500 μm.     

Effects of jet plate size and plate spacing on the stagnation Nusselt number for a confined circular air jet impinging on a flat surface

This work deals with the effects of jet plate size and plate spacing (jet height) on the heat transfer characteristics for a confined circular air jet vertically impinging on a flat plate. The jet after impingement was restricted to flow in two opposite directions. A constant surface heat flux of 1000 W/m² was arranged. Totally 88 experiments were performed. Jet orifices individually with diameter of 1.5, 3, 6 and 9 mm were adopted. Jet Reynolds number (Re) was in the range 10,000–30,000 and plate spacing-to-jet diameter ratio (H/d) was in the range 1–6. Eleven jet plate width-to-jet diameter ratios (W/d = 4.17–41.7) and seven jet plate length-to-jet diameter ratios (L/d = 5.5–166.7) were individually considered. The measured data were correlated into a simple equation. It was found that the stagnation Nusselt number is proportional to the 0.638 power of the Re and inversely proportional to the 0.3 power of the H/d. The stagnation Nusselt number was also found to be a function of exp[−0.044(W/d) − 0.011(L/d)]. Through comparisons among the present obtained data and documented results, it may infer that, for a jet impingement, the impingement-plate heating condition and flow arrangement of the jet after impingement are two important factors affecting the dependence of the stagnation Nusselt number on H/d.     

Cooling of two smooth cylinders in row by a slot jet of air with low turbulence

According to the current literature on the cooling of two cylinders in row, by a uniform flow of air, the first cylinder is always a heat transfer promoter versus the second one. The aim of the present paper is to summarize the state of art of the literature on the cooling of two cylinders in row by a slot jet of air. Additional experiments are carried on in order to investigate the possible application of jet cooling to heat transfer apparatuses, including electronics, in order to study the positions of the two cylinders in row which realize the same heat transfer on each cylinder. In the experiments a slot jet of air with low turbulence is employed with a slot height, S, equal to the impinged cylinder diameter, D, i.e. D/S = 1.0. The first cylinder is set at two distances H from the slot exit, H/S = 4 and 6, while the distance of the second cylinder from the first one, L, is variable from L/S = 2–11. The Reynolds number, Re, defined with the cylinder diameter D, spans in the range Re = 11,000–22,200. If the first cylinder is set at the dimensionless distance from the slot exit which realizes the maximum mean heat transfer on the first cylinder, i.e. H/S = 6, the second one has generally a lower mean Nusselt number. The only exception is when the second cylinder is set at the dimensionless distance L/S = 4 and the Reynolds number is at the maximum value experimented, i.e. Re = 22,200. If the first cylinder is set at the dimensionless distance H/S = 4 the mean Nusselt number on the second cylinder is greater if its distance from the first one is in the range L/S = 3.5–7 for Re = 14,300–22,200. The first cylinder acts as a heat transfer promoter, as happens in uniform flow, only for Re = 22,200.     

Experiments on impingement heat transfer with film extraction flow on the leading edge of rotating blades

A transient liquid crystal experiment was performed to study the heat transfer characteristic of impingement cooling with outflow film on the leading edge of turbine blades under rotating conditions. In the experiments, the angles between the jet direction and rotating shaft were 0°, 30°, and 45°, respectively. The impinging jet Reynolds number, based on the diameter of the impingement hole, ranged from 2000 to 12,000. The rotation number Ro (Ωd/u) ranged from 0 to 0.278. The relative impingement distance was fixed at 2. The results showed that, due to the effect of rotation, the spreading rate of the jet flow was enhanced and the heat transfer was weakened for all Reynolds numbers. For the condition of Re = 4000 and Ro = 0.139 with corresponding angles θ = 0°, 30°, 45°, the Nusselt number of the stagnation point decreased by 33%, 30%, and 35%, respectively, compared to the stationary results. Furthermore, for the corresponding angles θ = 30° and 45°, the location of the stagnation point is offset 0.6d (jet impingement hole diameter) and 0.9d down, respectively, when Ro = 0.139. The average Nusselt numbers on the suction surface and the pressure surface both decreased with increased rotating speed. Moreover, the reduction of the average Nusselt number on the pressure surface was larger than that on the suction surface. At Ro = 0.139, the average Nusselt number on the suction surface decreased less than 10% for all three angles, while on the pressure surface, the decrease was almost 20% compared to the result for Ro = 0.     

Numerical study of confined slot jet impinging on porous metallic foam heat sink

This study numerically investigates the impinging cooling of porous metallic foam heat sink. The analyzed parameters ranges comprise ε = 0.93/10 PPI Aluminum foam, L/W = 20, Pr = 0.7, H/W = 2–8, and Re = 100–40,000. The simulation results exhibit that when the Re is low (such as Re = 100), the Nu_max occurs at the stagnation point (i.e. X = 0). However, when the Reynolds number increases, the Nu_max would move downwards, i.e. the narrowest part between the recirculation zone and the heating surface. Besides, the extent to which the inlet thermal boundary condition influences the prediction accuracy of the Nusselt number increases with a decreasing H/W and forced convective effect. The application ranges of H/W and Re that the effect of the inlet thermal boundary condition can be neglected are proposed. Lastly, comparing our results with those in other studies reveals that the heat transfer performance of the Aluminum foam heat sink is 2–3 times as large as that without it. The thermal resistance is also 30% less than that of the plate fin heat sink for the same volumetric flow rate and the 5.3 mm jet nozzle width. Therefore, the porous Aluminum foam heat sink enhances the heat transfer performance of impinging cooling.     

Thermal and fluid dynamic behaviors of confined laminar impinging slot jets with nanofluids

Heat transfer enhancement technologies play an important role in research and industrial fields; thus, they have been widely applied to many applications as in refrigeration, automotive, aerospace, and process industry. For example, heat transfer can be passively enhanced by increasing the thermal conductivity of the working fluids, adopting nanofluids, or actively by employing impinging jets.In this paper a numerical analysis on confined impinging slot jets working with pure water or water/Al₂O₃ based nanofluids is presented. The flow is laminar and a constant uniform temperature is applied on the target surface. The single-phase model approach has been adopted in order to describe the nanofluid behavior and different particle volume concentrations have been considered. Moreover, simulations have been performed for different geometric ratios in order to take into account the confining effects and Reynolds numbers. The behavior of the system has been analyzed in terms of average and local convective heat transfer coefficient, Nusselt number, and required pumping power profiles. Correlations for stagnation point and average Nusselt number for 100 ≤ Re ≤ 400, 0% ≤ ϕ ≤ 5% and 4 ≤ H/W ≤ 10 are provided.     

Heat transfer of impinging jet-array over convex-dimpled surface

A detailed heat transfer measurement over a convex-dimpled surface of impinging jet-array with three eccentricities (E/H) between jet-centre and dimple-centre is performed. These surface dimples considerably modify heat transfers from smooth-walled scenarios due to different impinging topologies for jet array with modified inter-jet reactions. Heat transfer variations caused by adjusting jet Reynolds number (Re) and separation distance (S/D_j) over the ranges of 5000 ⩽ Re ⩽ 15,000 and 0.5 ⩽ S/D_j ⩽ 11 with three eccentricities of E/H = 0, 1/4 and 1/2 are examined. A selection of experimental data illustrates the isolated and interactive influences of Re, S/D_j and E/H on local and spatially averaged heat transfers. In conformity with the experimentally revealed heat transfer physics, a regression-type analysis is performed to generate a set of heat transfer correlations, which permit the evaluations of spatially averaged Nusselt numbers over central jet region of dimpled impinging surface.     

Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers

In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re = 1–40 and Richardson number, Ri = 0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re = 1–2, between Re = 2–3 and between Re = 3–4 for Ri = 0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work.     

Heat transfer in a turbulent slot jet flow impinging on concave surfaces

An experimental and numerical study is conducted to investigate turbulent slot jet impingement cooling characteristics on concave plates with varying surface curvature. Air is used as the impingement coolant. In the experimental work, a slot nozzle specially designed with a sixth degree polynomial in order to provide a uniform exit velocity profile was used. The experiments were carried out for the jet Reynolds numbers in the range of 3423 ≤ Re ≤ 9485, the dimensionless nozzle-to-surface distance range of 1 ≤ H/W ≤ 14 for dimensionless values of the curvature of impinging surfaces in the range of R/L = 0.5, 0.725, and 1.3 and a flat impingement surface. Constant heat flux was applied on the plates. Numerical computations were performed using the k-ε turbulence model with enhanced wall functions. For the ranges of the governing parameters studied, the stagnation, and local and average Nusselt numbers have been obtained both experimentally and numerically. The numerical results showed a reasonable agreement with the experimental data.     

Numerical thermal analysis and optimization of a water jet impingement cooling with VOF two-phase approach

The fluid flow and heat transfer characteristics of a free-surface liquid jet impingement cooling have been investigated numerically. The slot jet with water impinging normally on a flat plate is employed. To describe the turbulent structure, the turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known turbulence model, which are associated with wall function. Numerical computations have been conducted with variations of jet exit Reynolds number (11,000 ≤ Re_d ≤ 17,000), dimensionless jet-to-surface distance (3 ≤ H/d₀ ≤ 12), dimensionless jet width (1 ≤ B/d₀ ≤ 2), and the heat flux (140 kW/m² ≤ q″ ≤ 280 kW/m²). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. Under the studied ranges, the variations of local Nusselt numbers by hydraulic diameter Nu_d of the dimensionless jet-to-surface distance 3 ≤ H/d₀ ≤ 12 along the flat plate decrease monotonically from its maximum value at the stagnation point. In addition, the shape of the inlet area and jet-to-surface distance are optimized by using the response surface methodology (RSM) and the genetic algorithm (GA) method after solutions are carefully validated with available experimental results in the literature. Based on the optimal results, the optimum condition is in H/d₀ = 7.86 and B/d₀ = 2 for this physical model.     

Numerical study of transient conjugate heat transfer of a turbulent impinging jet

This study presents the numerical study of transient conjugate heat transfer in a high turbulence air jet impinging over a flat circular disk. The numerical simulation of transient, two-dimensional cylindrical coordinate, turbulent flow and heat transfer is adopted to test the accuracy of the theoretical model. The turbulent governing equations are resolved by the control-volume based finite-difference method with a power-low scheme, and the well-known low-Re κ–ω turbulence model to describe the turbulent structure. The SIMPLE algorithm is adopted to solve the pressure–velocity coupling. The parameters studied include turbulent flow Reynolds number (Re = 16,100–29,600), heated temperature of a circular disk (T_h = 373 K) or heat flux (q″ = 63–189 kW/m²), and orifice to heat-source spacing (H/D = 4–10). The numerical results of the transient impinging process indicate that the jet Reynolds number has a significant effect on the hydrodynamics and heat transfer, particularly in the stagnation region of an impinging jet. High turbulence values lead to greater heat transfer coefficients in the stagnation region and cause a bypass of the laminar-to-turbulent transition region in the wall jet region. Induced turbulence from the environment around the jet also influences the variation of the stagnation heat transfer. The modeling approach used here effectively captures both the stagnation region behavior and the transition to turbulence, thus forming the basis of a reliable turbulence model.     

Experimental investigation of mixed convection heat transfer for thermally developing flow in a horizontal circular cylinder

An experimental investigation is presented on mixed (free and forced) convection to study the local and average heat transfer for hydrodynamically fully developed, thermally developing and thermally fully developed laminar air flow in a horizontal circular cylinder. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L/D = 30), is subjected to a constant wall heat flux boundary condition. The investigation covers Reynolds number range from 400 to 1600, the heat flux varied from 60 W/m² to 400 W/m² and with cylinder inclination angle of θ = 0° (horizontal). The hydrodynamically fully developed condition is achieved by using an aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 180 cm (L/D = 60), another one with length of 240 cm (L/D = 80) and two short calming sections with lengths 60 cm (L/D = 20), 120 cm (L/D = 40). The surface temperature variation along the cylinder surface, the local and average Nusselt number variation with the dimensionless axial distance Z⁺ were presented. For all entrance sections, it was found an increase in the Nusselt number values as the heat flux increases. It was concluded that the free convection effects tended to decrease the heat transfer results at low Re while to increase the heat transfer results for high Re. The combined convection regime could be bounded by a suitable selection of Re number ranges and the heat flux ranges. The obtained Richardson numbers (Ri) range varied approximately from 0.13 to 7.125. The average Nusselt numbers were correlated with the (Rayleigh numbers/Reynolds numbers). The proposed correlation has been compared with available literature and showed satisfactory agreement.     

Effect of power-law fluid behavior on momentum and heat transfer characteristics of an inclined square cylinder in steady flow regime

The governing equations describing the momentum and heat transfer phenomena of power-law non-Newtonian fluids over a heated square cylinder at 45° of incidence in the two-dimensional (2-D) steady flow regime are solved numerically. Extensive results on the detailed structure of the flow and temperature fields as well as on the gross engineering parameters are presented over the following ranges of conditions: 0.2 ? n ? 1; 0.1 ? Re ? 40 and 0.7 ? Pr ? 100. At low Reynolds numbers, the flow remains attached to the surface of the cylinder. This seems to occur for all values of power-law index, at least up to about Re = 1. On the other hand, twin standing vortices were seen to form at Re = 10 for all values of power-law index considered herein. The influence of the Reynolds number and power-law index is delineated on the detailed structure of the flow field (streamlines), wake characteristics and surface pressure distribution as well as on the value of drag coefficients. Similarly, the effect of Prandtl number is studied on forced convective heat transfer for the two commonly encountered boundary conditions, namely, constant temperature or constant heat flux prescribed on the surface of the cylinder. Using the computed numerical results, simple heat transfer correlations are obtained in terms of the Nusselt number as a function of the pertinent governing parameters thereby enabling the prediction of the rate of heat transfer between the fluid and the immersed cylinder. In addition, variation of the local Nusselt number on the surface of the inclined of square cylinder and representative isotherm plots are also presented to elucidate the effect of Reynolds number, Prandtl number and power-law index on the heat transfer phenomenon.     

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in power-law fluids in the steady flow regime

The continuity, momentum and energy equations describing the flow and heat transfer of power-law fluids over a semi-circular cylinder have been solved numerically in the two-dimensional steady flow regime. The influence of the Reynolds number (Re), Prandtl number (Pr) and power-law index (n) on the local and global flow and heat characteristics have been studied over wide ranges of conditions as follows: 0.01 ? Re ? 30, 1 ? Pr ? 100 and 0.2 ? n ? 1.8. The variation of drag coefficient and Nusselt number with the Reynolds number, Prandtl number and power-law index is shown over the aforementioned ranges of conditions. In addition, streamline and isotherm profiles along with the recirculation length and distribution of pressure coefficient and Nusselt number over the surface of the semi-circular cylinder are also presented to gain further insights into the nature of the underlying kinematics. The wake size (recirculation length) shows almost linear dependence on the Reynolds number (Re ? 1) for all values of power-law index studied herein. The drag values show the classical inverse variation with the Reynolds number, especially for shear-thinning fluids at low Reynolds numbers. The point of maximum pressure coefficient is found slightly displaced from the front stagnation point for highly shear-thinning fluids, whereas for shear-thickening and Newtonian fluids, it coincides with the front stagnation point. For fixed values of the Prandtl number and Reynolds number, the rate of heat transfer decreases with the gradual increase in power-law index; this effect is particularly striking at high Prandtl numbers due to the thinning of the thermal boundary layer. Conversely, as expected, shear-thinning behavior facilitates heat transfer and shear-thickening impedes it. The effect of power-law index on both momentum and heat-transfer characteristics is seen to be appreciable at low Reynolds numbers and it gradually diminishes with the increasing Reynolds number.     

A general correlation for the stagnation point Nusselt number of an axisymmetric impinging synthetic jet

Whereas the heat transfer mechanisms in steady impinging jets are well understood, the available knowledge of heat transfer to impinging synthetic jets remains inconsistent. This paper provides an objective comparison of the stagnation point heat transfer performance of axisymmetric impinging synthetic jets versus established steady jet correlations. Furthermore, a general correlation for the stagnation point Nusselt number is proposed including the effect of all appropriate scaling parameters: Reynolds number (500 ? Re ? 1500), jet-to-surface spacing (2 ? H/D ? 16) and stroke length (2 ? L₀/D ? 40). Based on the ratio of stroke length to jet-to-surface spacing L₀/H, four heat transfer regimes are identified.     

Heat and fluid flow across a rotating cylinder dissipating uniform heat flux in 2D laminar flow regime

Free-stream flow and forced convection heat transfer across a rotating cylinder, dissipating uniform heat flux, are investigated numerically for Reynolds numbers of 20–160 and a Prandtl number of 0.7. The non-dimensional rotational velocity (α) is varied from 0 to 6. Finite volume based transient heatline formulation is proposed. For Re = 100, the reasons for the onset/suppression of vortex shedding at a critical rotational velocity is investigated using vorticity dynamics. At higher rotational velocity, the Nusselt number is almost independent of Reynolds number and thermal boundary conditions. Finally, a heat transfer correlation is proposed in the 2D laminar flow regime. Cylinder rotation is an efficient Nusselt number reduction or cylinder-surface temperature enhancement technique.