Development of correlations for Nusselt number and friction factor for solar air heater with roughened duct having multi v-shaped with gap rib as artificial roughness

This paper presents the results of an experimental investigation of heat transfer and friction in the flow of air in rectangular ducts having multi v-shaped rib with gap roughness on one broad wall. The investigation encompassed Reynolds number (Re) from 2000 to 20,000, relative gap distance (G_d/L_v) values of 0.24–0.80, relative gap width (g/e) values of 0.5–1.5, relative roughness height (e/D) values of 0.022–0.043, relative roughness pitch (P/e) values of 6–12, relative roughness width ratio (W/w) values of 1–10, angle of attack (α) range of 30°–75°. The optimum values of geometrical parameters of roughness have been obtained and discussed. For Nusselt number (Nu), the maximum enhancement of the order of 6.74 times of the corresponding value of the smooth duct has been obtained, however the friction factor (f) has also been seen to increase by 6.37 times of that of the smooth duct. The rib parameters corresponding to maximum increase in Nu and f were G_d/L_v = 0.69, g/e = 1.0, e/D = 0.043, P/e = 8, W/w = 6 and α = 60°. Based on the experimental data, correlations for Nu and f have been developed as function of roughness parameters of multi v-shaped with gap rib and flow Reynolds number.     

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.     

Thermal performance of plate-fin heat sinks under confined impinging jet conditions

This paper utilizes the infrared thermography technique to investigate the thermal performance of plate-fin heat sinks under confined impinging jet conditions. The parameters in this study include the Reynolds number (Re), the impingement distance (Y/D), the width (W/L) and the height (H/L) of the fins, which cover the range Re = 5000–25,000, Y/D = 4–28, W/L = 0.08125–0.15625 and H/L = 0.375–0.625. The influences of these parameters on the thermal performance of the plate-fin heat sinks are discussed. The experimental results show that the thermal resistance of the heat sink apparently decreases as the Reynolds number increases; however, the decreasing rate of the thermal resistance declines with the increase of the Reynolds number. An appropriate impingement distance can decrease the thermal resistance effectively, and the optimal impingement distance is increased as the Reynolds number increases. Moreover, the influence of the impingement distance on the thermal resistance at high Reynolds numbers becomes less conspicuous because the magnitude of the thermal resistance decreases with the Reynolds number. An increase of the fin width reduces the thermal resistance initially. Nevertheless, the thermal resistance rises sharply when the fin width is larger than a certain value. Increasing the fin height can increase the heat transfer area which lowers the thermal resistance. Moreover, the influence of the fin height on the thermal resistance seems less obvious than that of the fin width. To sum up all experimental results, Reynolds number Re = 20,000, impingement distant Y/D = 16, fin width W/L = 0.1375, and fin height H/L = 0.625 are the suggested parameters in this study.     

Effect of rib spacing on heat transfer and friction in a rectangular channel with 45° angled rib turbulators on one/two walls

An experimental investigation of forced convection heat transfer in a rectangular channel (aspect ratio AR = 5) with angled rib turbulators, inclined at 45°, is presented. The angled ribs were deployed with parallel orientations on one or two surfaces of the channel. The convective fluid was air, and the Reynolds number varied from 9000 to 35,500. The ratio of rib height to hydraulic diameter (e/D) was 0.09, while four rib pitch-to-height ratios (p/e) were studied: 6.66, 10.0, 13.33, and 20.0. The aim of the work was to study the effect of rib spacing on the thermal performance of the ribbed channel. The maps of local heat transfer coefficient in the inter-rib regions have been reconstructed by liquid crystal thermography. The thermal performance of each ribbed channel is identified by the average Nusselt number and by the friction factor. Superior heat transfer performance was found at the optimal rib pitch-to-height ratio of 13.33 for the one-ribbed wall channel and at p/e = 6.66–10 for the two-ribbed wall channel.     

Measurement of detailed heat transfer along rib-roughened surface under arrays of impinging elliptic jets

The objective of the present study is to examine the detailed heat transfer coefficient distributions over a ribbed-surface under impingement of elliptic jet arrays using a liquid crystal thermograph technique. Both continuous and broken V-shaped-rib configurations with different exit flow orientations were considered. To examine the angled rib effects, three angled ribs were discussed under jet-to-plate spacing Z = 3 for different Reynolds numbers. Measured results show that the local heat transfer rates over the ribbed-surface are characterized by obvious periodic-type variation of Nusselt number distributions. The downstream peaks are diminished for increasing crossflow effect. Compared to the results without ribs, the heat transfer over the ribbed-surface may be enhanced or retarded. Whereas, among the test angled-rib arrangements, the best heat transfer performance is obtained with a surface with 45° V-shape ribs. In addition, the surface with continuous ribs provides a better impingement heat transfer than that with broken ribs.     

Experimental investigation of flow boiling heat transfer of jet impingement on smooth and micro structured surfaces

Flow boiling heat transfer experiments using R134a were carried out for jet impingement on smooth and enhanced surfaces. The enhanced surfaces were circular micro pin fins, hydrofoil micro pin fins, and square micro pin fins. The effects of saturation pressure, heat flux, Reynolds number, pin fin geometry, pin fin array configuration, and surface aging on flow boiling heat transfer characteristics were investigated. Flow boiling experiments were carried out for two different saturation pressures, 820 kPa and 1090 kPa. Four jet exit velocities ranging from 1.1–4.05 m/s were investigated. Flow boiling jet impingement on smooth surfaces was characterized by large temperature overshoots, exhibiting boiling hysteresis. Flow boiling jet impingement on micro pin fins displayed large heat transfer coefficients. Heat transfer coefficients as high as 150,000 W/m² K were observed at a relatively low velocity of 2.2 m/s with the large (D = 125 μm) circular micro pin fins. Jet velocity, surface aging, and saturation pressure were found to have significant effects on the two-phase heat transfer characteristics. Subcooled nucleate boiling was found to be the dominant heat transfer mechanism.     

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.     

Heat transfer and friction factor correlation for artificially roughened duct with metal grit ribs

This paper presents the results of an experimental investigation of heat transfer to the airflow in the rectangular duct of an aspect ratio 10:1. The top wall surface is made rough with metal ribs of circular cross section in staggered manner to form defined grid. The roughened wall is uniformly heated and the other walls are insulated. This geometry of duct closely corresponds to that used in solar air heaters. The effect of grit geometry [i.e., relative roughness height of grid (e/D_h), relative roughness pitch of grit (p/e), relative length of grit (l/s)] on the heat transfer coefficient and friction factor is investigated. The range of variation of system parameters and operating parameters is investigated within the limits, as e/D_h: 0.035 to 0.044, p/e: 12.5–36 and l/s: 1.72–1, against variation of Reynolds number: 4000–17,000. It is observed that the plate of roughness parameters l/s = 1.72, e/D_h = 0.044, p/e = 17.5 shows optimum performance. Correlations for Nusselt number and friction factor in terms of above parameters are developed which reasonably correlate the experimental data.     

Optimised mixing and flow resistance during shear flow over a rib roughened boundary

A series of numerical investigations has been performed to study the effect of lower boundary roughness on turbulent flow in a two-dimensional channel. The roughness spacing to height ratio, w/k, has been investigated over the range 0.12 to 402 by varying the horizontal rib spacing. The square roughness elements each have a cross-sectional area of (0.05 H)², where H is the full channel height. The Reynolds number, Re_τ is fixed based on the value of the imposed pressure gradient, dp/dx, and is in the range 6.3 × 10³ − 4.5 × 10⁴. A Reynolds Averaged Navier–Stokes (RANS) based turbulence modelling approach is adopted using a commercial CFD code, ANSYS-CFX 14.0. Measurements of eddy viscosity and friction factor have been made over this range to establish the optimum spacings to produce maximum turbulence enhancement, mixing and resistance to flow. These occur when w/k is approximately 7. It is found that this value is only weakly dependent on Reynolds number, and the decay rate of turbulence enhancement as a function of w/k ratio beyond this optimum spacing is slow. The implications for heat transfer design optimisation and particle transport are considered.     

Heat transfer enhancement from micro pin fins subjected to an impinging jet

An experimental investigation was carried out to study the single-phase stagnation point jet impingement heat transfer on smooth and micro pin fin structures using water and R134a. The experiments were carried out for a single jet (d_j = 2.0 mm) impinging on a 2 × 2 mm micro-heater over a wide range of Reynolds numbers. Both an unfinned and a micro structured impingement surfaces were investigated. The micro structures consisted of an array of 64 circular micro pin fins fabricated using MEMS microfabrication. The micro pin fins had diameters of 125 μm, heights of 230 μm, and pitches of 250 μm with an area enhancement of A_total/A_base = 2.44. The jet stand-off ratio and area ratio (A_j/A_base) were 0.86 and 0.785, respectively. Nusselt numbers were found to increase with increasing Reynolds numbers. Correlations from the literature for impingement zone Nusselt numbers were found to underpredict the experimental results. Significant enhancement of the heat transfer coefficients were observed as a result of the presence of the micro pin fins on the impingement surface. Enhancement factors as high as 3.03 or about 200% increase in the heat transfer coefficients were demonstrated. Enhancements are attributed to flow mixing, interruption of the boundary layers, and augmentation of turbulent transport.     

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.     

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.     

Heat transfer from a spinning disk during semi-confined axial impingement from a rotating nozzle

Conjugate heat transfer from a uniformly heated spinning solid disk of finite thickness and radius during a semi-confined liquid jet impingement from a rotating nozzle is studied. The model covers the entire fluid region including the impinging jet on a flat circular disk and flow spreading out downstream under the spinning confinement plate and free surface flow after exposure to the ambient gaseous medium. The model examines how the heat transfer is affected by adding a secondary rotational flow under semi-confined jet impingement. The solution is made under steady state and laminar conditions. The study considered various plate materials such as aluminum, copper, silver, constantan and silicon. Ammonia, water, flouroinert FC-77 and MIL-7808 oil were used as working fluids. The range of parameters covered included Reynolds number (220–900), Ekman number (7.08 × 10^?5–∞), nozzle-to-target spacing (β = 0.25–1.0), disk thicknesses to nozzle diameter ratio (b/d_n = 0.25–1.67), Prandtl number (1.29–124.44) and solid to fluid thermal conductivity ratio (36.91–2222). It was found that a higher Reynolds number increased local heat transfer coefficient reducing the interface temperature difference over the entire disk surface. The rotational rate also increased local heat transfer coefficient under most conditions. An engineering correlation relating the Nusselt number with other dimensionless parameters was developed for the prediction of the system performance.     

The effect of inclination on impinging jets at small nozzle-to-plate spacing

The effect of inclination on heat transfer characteristics of an impinging slot air jet is experimentally investigated. The effects of inclination angle (0° ? θ ? 40°) and dimensionless pumping power on the Nusselt number are considered. The focus is on cases where the nozzle-to-plate spacing is equal to or less than one nozzle diameter (H/d_h ? 1.0). The results show that the heat transfer characteristics of small nozzle-to-plate spacings are significantly different from those of large nozzle-to-plate spacings. In the cases of fixed flow rate conditions, the impingement point and average Nusselt numbers at small nozzle-to-plate spacing (H/d_h ? 1.0) increase as the inclination angle increases due to an increase in the pumping power, while the impingement point and average Nusselt numbers at large nozzle-to-plate spacing (H/d_h > 1.0) decrease as the inclination angle increases due to momentum loss of the wall jet. In the cases of fixed pumping power conditions, the impingement point and average Nusselt numbers at both of small and large nozzle-to-plate spacings are independent of the inclination angle. Based on the experimental results, correlations for the impingement point and average Nusselt numbers of the impinging jet are suggested as a function of the pumping power alone.     

Influences of nozzle-plate spacing on boiling heat transfer of confined planar dielectric liquid impinging jet

We have investigated the single-phase and boiling heat transfer of dielectric liquid under the Reynolds numbers (2000, 3000 and 5000) and under nozzle-plate spacing (H/W; 0.5, 1.0 and 4.0) in a submerged impinging jet system. The boiling incipience increases in proportion to the Reynolds number and in inverse proportion to the nozzle-to-surface spacing. The critical heat flux at H/W = 1.0 is lower than those of outer spacings, such as H/W = 0.5 and 4.0, due to the characteristics of the jet impingement heat transfer distribution. We suggest a correlation equation of nozzle-plate spacing (H/W) having the lowest CHF for various jet velocities.     

Experimental investigations on heat transfer and frictional characteristics of a turbulator roughened solar air heater duct

An experimental investigation has been carried out to study the heat transfer coefficient and friction factor by using artificial roughness in the form of specially prepared inverted U-shaped turbulators on the absorber surface of an air heater duct. The roughened wall is uniformly heated while the remaining three walls are insulated. These boundary conditions correspond closely to those found in solar air heaters.The experiments encompassed the Reynolds number range from 3800 to 18000; ratio of turbulator height to duct hydraulic mean diameter is varied from, e/D_h = 0.0186 to 0.03986 (D_h = 37.63 mm and e = 0.7 to 1.5 mm) and turbulator pitch to height ratio is varied from, p/e = 6.67 to 57.14 (p = 10 to 40 mm). The angle of attack of flow on turbulators, α = 90° kept constant during the whole experimentation. The heat transfer and friction factor data obtained is compared with the data obtained from smooth duct under similar geometrical and flow conditions. As compared to the smooth duct, the turbulator roughened duct enhances the heat transfer and friction factor by 2.82 and 3.72 times, respectively. The correlations have been developed for area averaged Nusselt number and friction factor for turbulator roughened duct.     

Measurement of local heat/mass transfer coefficients on a dimple using naphthalene sublimation

Local and average heat/mass transfer characteristics on a single dimple were investigated using a naphthalene sublimation technique. The dimple depth in this study ranged from 20% to 40% of the channel height. The experimental conditions covered the range from laminar to low-velocity turbulent flow regimes, 500 ? Re_H ? 5000. Secondary flows from the dimple were clearly observed in the transient flow regime of Re_H = 2000–3000. The velocity fluctuation in the mixing layer over the dimple increased with the dimple depth and the Reynolds number. The impingement of the mixing layer and the induced secondary flows augmented the Sherwood number around the rear rim of the dimple and in the rear plateau region, respectively. For a Reynolds number of 3000, the Sherwood number increased significantly due to the increased fluctuation in the mixing layer and the intensified secondary flows from the dimple. The heat/mass transfer augmentation factors increased as the Reynolds number increased, reaching 1.5 at a Reynolds number of 5000.     

Heat transfer of rectangular narrow channel with two opposite scale-roughened walls

An experimental study of heat transfer and pressure drop in a rectangular channel roughened by scaled surfaces on two opposite walls with flows directed in the forward and downward directions for Reynolds numbers (Re) in the range of 1500 ⩽ Re ⩽ 15,000 was performed. Nusselt number ratios between the scale-roughened and smooth-walled ducted flows (Nu/Nu_∞) were in the range of 7.4–9.2 and 6.2–7.4 for laminar forward and downward flows respectively. The Nu/Nu_∞ values for turbulent developed flows in the scale-roughened channel with forward and downward flows were about 4.5 and 3 respectively. A comparison of present data with reported results using different types of surface roughness demonstrated the better thermal performances of present scale-roughened channel with forward flow at conditions of Re > 10,000. Experimental correlations of heat transfer and friction coefficient were derived for the present scale-roughened rectangular channel.     

Effect of jet direction on heat/mass transfer of rotating impingement jet

The objective of this study is to investigate the heat/mass transfer characteristics on various impinging jets under rotating condition. Two cooling schemes related to impingement jet are considered; array impingement jet cooling and impingement/effusion cooling. The test duct rotates at Ro = 0.075 with two different jet orientations and the jet Reynolds number is fixed at 5000. Two H/d configurations of 2.0 and 6.0 are conducted. The detailed heat/mass transfer coefficients on the target plate are measured by a naphthalene sublimation technique. The rotation changes the local heat/mass transfer characteristics due to the jet deflection and spreading phenomenon. For H/d = 6.0, the jet is strongly deflected at the leading orientation, resulting in the significant decrease in heat/mass transfer. At the axial orientation, the momentum of jet core decreases slightly due to jet spreading into the radial direction and consequently, the value of stagnation peak is a little lower than that of the stationary case. However, reduction of heat/mass transfer due to rotation disappears at a low H/d of 2.0. In the averaged Sh, the leading orientation with H/d = 6.0 shows 35% lower value than that of the stationary case whereas the other rotating cases lead to a similar value of the stationary case.     

Flow structures and heat transfer of swirling jet impinging on a flat surface with micro-vibrations

This study focuses on the changes in the flow characteristics of a round jet issuing from a straight tube inserted with longitudinal swirling strips and impinging on a constant-heat-flux flat surface undergoing forced vibrations in the vertical plane. Smoke flow visualization is used to investigate the nature of the complicated flow phenomena under the swirling-flow jet for this impingement cooling. Effects of flow Reynolds number (440 ⩽ Re ⩽ 27 000), the geometries of the nozzle (BR, LSS and CSS), jet-to-test plate placement (3 ⩽ H/d ⩽ 16), and surface vibration frequencies, f [0.3–10.19 Hz (the relative amplitude of the flat surface ranged from 0.5 to 8.1 mm)] are examined. In addition, correlations were developed to predict the Nusselt number for the vibration using the results of Wen and Jang [An impingement cooling on a flat surface by using circular jet with longitudinal swirling strips, Int. J. Heat Mass Transfer 46 (2003) 4657–4667] for the no-vibration case of the present study.