Heat transfer correlations of perpendicularly impinging jets on a hemispherical-dimpled surface

Heat transfer results of an inline array of round jets impinging on a staggered array of hemispherical dimples are reported with the consideration of various parametric effects such as Reynolds number (Re_Dj), jet-to-plate spacing (H/D_j), dimple depth (d/D_d) and ratio of jet diameter to dimple projected diameter (D_j/D_d) for both impinging on dimples and impinging on flat portions. The results were normalized against those from a flat plate. The heat transfer was measured by using transient wideband liquid crystal method. Our previous work (Kanokjaruvijit and Martinez-Botas (2005) [1]) on the effect of crossflow scheme suggested that jet impingement coupled with channel-like flow formed by the crossflow helped enhance heat transfer on a dimpled surface; hence three sidewalls were installed to constrain the spent air to leave in one direction. Throughout the study, the pitch of the nozzle holes was kept constant at 4 jet diameters. The Reynolds number (Re_Dj) ranging from 5000 to 11,500, jet-to-plate spacing (H/D_j) varying from 1 to 12 jet diameters, dimple depths (d/D_d) of 0.15, 0.25 and 0.29, and dimple curvature (D_j/D_d) of 0.25, 0.50 and 1.15 were examined. The shallow dimples (d/D_d = 0.15) improved heat transfer significantly by 70% at H/D_j = 2 compared to that of the flat surface, while this value was 30% for the deep ones (d/D_d = 0.25). The improvement also occurred to the moderate and high D_j/D_d. Thereafter, the heat transfer results were correlated in dimensionless form by using logarithmic multiple regression. The correlations were reported with necessary statistics.     

An experimental study of pressure loss and heat transfer in the pin fin-dimple channels with various dimple depths

An experimental study was conducted to investigate the effects of dimple depth on the pressure loss and heat transfer characteristics in a pin fin-dimple channel, where dimples are located on the endwall transversely between the pin fins. The pin fin-dimple channels considered consist of ten rows of pin fin-dimple combined structure. The pin fin transverse spacing-to-diameter ratio S/D = 2.5, the streamwise spacing-to-diameter ratio X/D = 2.5, the pin fin height-to-diameter ratio H/D = 1.0. The dimples have a print diameter the same with the pin fins, but have three different dimple depth-to-diameter ratios, i.e. δ/D = 0.1, 0.2 and 0.3. The experimental results, mainly the average Nusselt number and friction factor, for the pin fin-dimple channels with various dimple depths have been obtained and compared with each other for the Reynolds number range of 8200–50,500. The study showed that, compared to the baseline pin fin channel, the pin fin-dimple channels have further improved convective heat transfer performance by up to 19.0%, and the pin fin-dimple channel with deeper dimples shows relatively higher Nusselt number values. The study still showed dimple depth-dependent pressure loss behaviors for the pin fin-dimple channels compared to the pin fin channel, and the pin fin-dimple channel with shallower dimples shows relatively lower friction factors by up to 17.6% over the studied Reynolds number range. Furthermore, three-dimensional conjugate computations have been carried out for similar experimental conditions, and the computations showed the detailed characteristics in the distribution of the velocity and turbulence level in the flow, which revealed the underlying mechanisms for the associated dimple depth-dependent pressure loss and heat transfer characteristics in the pin fin-dimple channels.     

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 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.     

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.     

Investigation of coated tubes in cross-flow boiling

The boiling in cross-flow is investigated for coated tubes (low-porosity, flame-sprayed) in this paper. The effect of surface roughness on flow boiling heat transfer for a horizontal tube surface in cross-flow is studied for saturated boiling of water at atmospheric pressure. The parameters varied were for flow velocity up to 3.24 kg/s (G = 258.49 kg/m² s), heat flux from 12 to 45 kW/m², surface roughness (Ra) from 0.3296 to 4.731 μm. Nominal enhancement in heat transfer coefficient at higher mass flux may be attributed to the continued nucleation at the uppermost surfaces (in the wake region of the flow) of the rougher tubes thereby increasing the overall heat transfer rate. The flow boiling data was found to best fit the Kutateladze asymptotic equation h = h_l[1 + (h_npb/h_l)ⁿ]^1/n with the value of n = 2.258 (which is close to the value of n = 2 suggested by Kutateladze).     

Experimental study of evaporation heat transfer characteristics of refrigerants R-134a and R-407C in horizontal small tubes

An experiment is carried out here to investigate the characteristics of the evaporation heat transfer for refrigerants R-134a and R-407C flowing in horizontal small tubes having the same inside diameter of 0.83 or 2.0 mm. In the experiment for the 2.0-mm tubes, the refrigerant mass flux G is varied from 200 to 400 kg/m² s, imposed heat flux q from 5 to 15 kW/m², inlet vapor quality x_in from 0.2 to 0.8 and refrigerant saturation temperature T_sat from 5 to 15 °C. While for the 0.83-mm tubes, G is varied from 800 to 1500 kg/m² s with the other parameters varied in the same ranges as those for D_i = 2.0 mm. In the study the effects of the refrigerant vapor quality, mass flux, saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient h_r are examined in detail. The experimental data clearly show that both the R-134a and R-407C evaporation heat transfer coefficients increase almost linearly and significantly with the vapor quality of the refrigerant, except at low mass flux and high heat flux. Besides, the evaporation heat transfer coefficients also increase substantially with the rises in the imposed heat flux, refrigerant mass flux and saturation temperature. At low R-134a mass flux and high imposed heat flux the evaporation heat transfer coefficient in the smaller tubes (D_i = 0.83 mm) may decline at increasing vapor quality when the quality is high, due to the partial dryout of the refrigerant flow in the smaller tubes at these conditions. We also note that under the same x_in, T_sat, G, q and D_i, refrigerant R-407C has a higher h_r when compared with that for R-134a. Finally, an empirical correlation for the R-134a and R-407C evaporation heat transfer coefficients in the small tubes is proposed.     

The particle thermal conductivity influence of nanofluids on thermal performance of the microtubes

The paper presents the numerical analysis on microchannel laminar heat transfer and fluid flow of nanofluids in order to evaluate the suitable thermal conductivity of the nanoparticles that results in superior thermal performances compared to the base fluid. The diameter ratio of the micro-tube was D_i/D_o = 0.3/0.5 mm with a tube length L = 100 mm in order to avoid the heat dissipation effect. The heat transfer rate was fixed to Q = 2 W. The water based Al₂O₃, TiO₂ and Cu nanofluids were considered with various volume concentrations ϕ = 1,3 and 5% and two diameters of the particles d_p = 13 nm and 36 nm. The analysis is based on a fixed Re and pumping power Π, in terms of average heat transfer coefficient and maximum temperature of the substrate. The results reveal that only the nanofluids with particles having very high thermal conductivity (λ_Cu = 401 W/m K) are justified for using in microcooling systems. Moreover, the analysis is sensitive to both the comparison criteria (Re or Π) and heat transfer parameters (h_ave or t_max).     

Experimental study of evaporation heat transfer of R-134a inside a corrugated tube with different tube inclinations

Experimental heat transfer studies during evaporation of R-134a inside a corrugated tube have been carried out. The corrugated tube has been provided with different tube inclination angles of the direction of fluid flow from horizontal, α. The experiments were performed for seven different tube inclinations, α, in a range of − 90° to + 90° and four mass velocities of 46, 81, 110 and 136 kg m^− 2 s^− 1 for each tube inclination angle during evaporation of R-134a. Data analysis demonstrate that the tube inclination angle, α, affects the boiling heat transfer coefficient in a significant manner. The effect of tube inclination angle, α, on heat transfer coefficient, h, is more prominent at low vapor quality and mass velocity. In the low vapor quality region, the heat transfer coefficient, h, for the + 90° inclined tube is about 62% more than that of the − 90° inclined tube. The results also showed that at all mass velocities, the highest average heat transfer coefficient were achieved for α = + 90°. An empirical correlation has also been developed to predict the heat transfer coefficient during flow boiling inside a corrugated tube with different tube inclinations.     

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 study of R-134a evaporation heat transfer in a narrow annular duct

An experiment is carried out here to investigate the evaporation heat transfer and associated evaporating flow pattern for refrigerant R-134a flowing in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm. In the experiment, the effects of the duct gap, refrigerant vapor quality, mass flux and saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient h_r are examined in detail. For the duct gap of 2.0 mm, the refrigerant mass flux G is varied from 300 to 500 kg/m² s, imposed heat flux q from 5 to 15 kW/m², vapor quality x_m from 0.05 to 0.95, and refrigerant saturation temperature T_sat from 5 to 15 °C. While for the gap of 1.0 mm, G is varied from 500 to 700 kg/m² s with the other parameters varied in the same ranges as that for δ = 2.0 mm. The experimental data clearly show that the evaporation heat transfer coefficient increases almost linearly with the vapor quality of the refrigerant and the increase is more significant at a higher G. Besides, the evaporation heat transfer coefficient also rises substantially at increasing q. Moreover, a significant increase in the evaporation heat transfer coefficient results for a rise in T_sat, but the effects are less pronounced in the narrower duct at a low imposed heat flux and a high refrigerant mass flux. Furthermore, the evaporation heat transfer coefficient increases substantially with the refrigerant mass flux except at low vapor quality. We also note that reducing the duct gap causes a significant increase in h_r. In addition to the heat transfer data, photos of R-134a evaporating flow taken from the duct side show the change of the dominant two-phase flow pattern in the duct with the experimental parameters. Finally, an empirical correlation for the present measured heat transfer coefficient for the R-134a evaporation in the narrow annular ducts is proposed.     

Heat transfer enhancement by flow bifurcations in asymmetric wavy wall channels

The enhancement characteristics of heat transfer, through a transition scenario of flow bifurcations, in asymmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element method. The heat transfer characteristics, flow bifurcation and transition scenarios are determined by increasing the Reynolds numbers for three geometrical aspect ratios r = 0.25, 0.375, and 0.5, and Prandtl numbers 1.0 and 9.4. The transition scenarios to transitional flow regimes depend on the aspect ratio. For the aspect ratios r = 0.25 and 0.5, the transition scenario is characterized by one Hopf flow bifurcation. For the aspect ratio r = 0.375, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a periodic flow, and a second Hopf flow bifurcation from a periodic to quasi-periodic flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω₁, and ω₁ and ω₂, respectively. For all the aspect ratios and Prandtl numbers, the time-average mean Nusselt number and heat transfer enhancement increases with the Reynolds number as the flow evolves from a laminar to a transitional regime. For both Prandtl numbers, the highest increase in the Nusselt number occurs for the aspect ratio r = 0.5; whereas, the lowest increases happen to r = 0.25. The increase of the Nusselt number occurs at the expense of a higher pumping power, which, for both Prandtl numbers, grows as the aspect ratio increases from r = 0.25 to r = 0.5 for reaching a specific Nusselt number. This enhancement is obtained without the necessity of high volumetric flow rates associated with turbulent flow regimes, which demand much higher pumping powers. Significant heat transfer enhancements are obtained when the asymmetric wavy channel is operated in the appropriate transitional Reynolds number range.     

The performance evaluation of Al2O3/water nanofluid flow and heat transfer in microchannel heat sink

The numerical modeling of the conjugate heat transfer and fluid flow of Al₂O₃/water nanofluid through the microchannel heat sink is presented in the paper. The laminar flow regime was considered along with viscous dissipation effect. The microchannel heat sink with square microchannels and D_h = 50 μm is considered. The heat flux was fixed to q = 35 W/m² with heating and cooling cases. The water based Al₂O₃ nanofluid was encountered with various volume concentrations of Al₂O₃ particles $?=1''–''9\%$ and three diameters of the particle d_p = 13, 28 and 47 nm. The analysis is performed on the results obtained for the local heat transfer coefficients based on a fixed pumping power. The results reveal a different local heat transfer behavior compared to the analysis made on a basis of the constant Re.     

Regularities of flow and heat transfer at the surface of transversely finned tubes

A great number of experimental investigations allowing one to reveal the physical mechanism of processes responsible for their thermal and hydraulic performance are carried out in attempt to solve problems of updating constructions and methods of thermal design of heating surfaces of transversely finned tubes widespread in power engineering. Results of flow visualization and investigation of pressure fields and local heat transfer at the fin surface over the Reynolds number range Re = (1.0 ? 6.6) · 10⁴ are presented for the case of a wide variation of geometric characteristics of finned tubes and parameters of their arrangement in a bundle. Regularities substantially changing the existing concept of transfer processes in the interfin space and in the wake behind a finned tube are revealed. It is found that the flow behavior and the distribution of local heat transfer coefficients over the fin surface change significantly at the fin height-to-finned tube diameter h/d approximately equal to 0.4. The results obtained are generalized in the form of the patterns of flow and heat transfer at the finned tube surface, including seven characteristic regions and four types of flow separation.     

A numerical study on the forced convection heat transfer from an isothermal and isoflux sphere in the steady symmetric flow regime

The effects of Reynolds and Prandtl numbers on the heat transfer characteristics of an unconfined sphere for different thermal boundary conditions (isothermal and isoflux) on the sphere surface have been investigated numerically by using a finite volume method for the range of conditions as 5 ⩽ Re ⩽ 200 and 0.7 ⩽ Pr ⩽ 400 (the maximum value of Peclet number being 2000). Based on the numerical results obtained herein, heat transfer correlations are developed for the constant temperature and the constant heat flux boundary conditions on the solid sphere surface in the steady symmetric flow regime. The variation of local Nusselt number on the sphere surface shows the effect of Prandtl number on heat transfer from a sphere in this flow regime. In addition, this work also demonstrates an approach to solve such flow problems using the Cartesian form of the field equations.     

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.     

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.     

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.     

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.     

The effect of different inlet geometries on laminar flow combined convection heat transfer inside a horizontal circular pipe

The effect of different inlet geometries on laminar air flow combined convection heat transfer inside a horizontal circular pipe has been experimentally investigated for Reynolds number range of 400–1600, and the Grashof number range from 3.12 × 10⁵ to 1.72 × 10⁶. The experimental setup consists of an aluminum circular pipe as a heated section with 30 mm inside diameter and 900 mm heated length (L/D = 30) with different inlet geometries. A wall boundary heating condition of a uniform heat flux was imposed. The inlet configurations used in this paper are calming sections having the same inside diameter as the heated pipe but with variable lengths of L_calm. = 600 mm (L/D = 20), L_calm. = 1200 mm (L/D = 40), L_calm. = 1800 mm (L/D = 60), L_calm. = 2400 mm (L/D = 80), sharp-edged and bell-mouth. It was found that the surface temperature values for calming section length corresponding to (L/D = 80) were higher than other inlet geometries due to the lower mass flow rate and higher flow resistance. It was also observed that the Nusselt number values for bell-mouth inlet geometry were higher than other inlet geometries due to the differences in the average temperatures and densities of the air. The average heat transfer results were correlated with an empirical correlation in terms of dependent parameters of Grashof, Prandtl and Reynolds numbers. The proposed correlation was compared with available literature and it shows reasonable agreement.