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.     

Experimental study on laminar flow forced-convection in a channel with upper V-corrugated plate heated by radiation

Experimental study of the effects of the operating parameters on laminar flow forced-convection heat transfer for air flowing in a channel having a V-corrugated upper plate heated by radiation heat flux while the other walls are thermally insulated has been carried out. The parameters studied and their ranges were as follows: flow Reynolds number (Re) ranging from 750 to 2050, incident radiation fluxes (q_inc) of 400, 700, and 1000 W/m², inlet air bulk temperatures (T_b,in) ranging from 12.4 to 59.4 °C and tilting angles of the channel (β) of 0°, 15°, 30°, 45°, and 60°. The results show that, the effect of Re on local Nusselt number (Nu_x) are clear and more significant at the channel entrance region. While, changing β from 0° to 60° leads to an increase in Nu_x by a ratio ranging from 33% to 67.3% depending on Re values and other operating parameters. Increasing the q_inc values by 175% and 250% leads to an increase in Nu_x values by 26% and 50%, respectively. In addition, the results indicate that there are significant increases in Nu_x in the channel entrance region due to the increase in inlet air bulk temperature and this influence diminishes downstream.     

Mixed convection on jet impingement cooling of a constant heat flux horizontal porous layer

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions, and the Darcian and non-Darcian effects are evaluated. The unsteady stream function-vorticity formulation is used to solve the governing equations. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Reynolds number (1 ≤ Re ≤ 1000), modified Grashof number (10 ≤ Gr¹ ≤ 100), half jet width (0.1 ≤ D ≤ 1.0), Darcy number (1 × 10^?6 ≤ Da ≤ 1 × 10^?2), and the distance between the jet and the heated portion (0.1 ≤ H ≤ 1.0). It is found that the average Nusselt number (Nu_avg) increases with increase in either modified Grashof number or jet width for high values of Reynolds number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The average Nusselt number decreases with the increase in Da for the non-Darcy regime when Re is low whereas Nu_avg increases when Re is high. It is shown that mixed convection mode can cause minimum heat transfer unfavorably due to counteraction of jet flow against buoyancy driven flow. Minimum Nu_avg occurs more obviously at higher values of H. Hence the design of jet impingement cooling through porous medium should be carefully considered in the mixed convection regimes.     

High rotation number heat transfer of a 45° rib-roughened rectangular duct with two channel orientations

An experimental study of heat transfer in a radially rotating rectangular channel of aspect ratio 1/2 with two opposite walls roughened by 45° staggered ribs is performed. Heat transfer distributions along centerlines of two rib-roughened surfaces are measured for the radially outward airflow at test conditions of Reynolds number (Re), rotation number (Ro) and density ratio (Δρ/ρ) in the ranges of 5000–15,000, 0–2 and 0.07–0.28. The rotating test rig permits the generation of heat transfer data with Ro considerably higher than previous data ranges. A selection of experimental data illustrates the individual and interactive influences of Re, Ro and buoyancy number (Bu) on local heat transfer with two channel orientations of 0° and 45°. With Ro varying from 0.1 to 2, heat transfer ratios between rotating and static channels on the stable and unstable rib-roughened surfaces with 0° (45°) of channel orientation are in the ranges of 0.5–1.42 (0.5–1.49) and 1.08–2.73 (1.06–2.21) respectively. A set of heat transfer correlations for the test geometry with channel orientations of 0° is derived to evaluate the local Nusselt number (Nu) in the periodically developed region with Re, Ro and Bu as the controlling flow parameters.     

Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity

The development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom heated open enclosure has been numerically studied. The enclosure considered has rectangular horizontal lower surface and vertical side surfaces. The lower surface is at a uniform temperature T_h while other sides of the cavity along with the channel walls are adiabatic. The governing two-dimensional flow equations have been solved by using Galarkin weighted residual finite element technique. The investigations are conducted for different values of Rayleigh number (Ra), Reynolds number (Re) and Hartmann number (Ha). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt number (Nu), the Drag force (D) and average bulk temperature (θ_av) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity whereas in the channel these effects are less significant.     

Heat transfer characteristics in steam-cooled rectangular channels with two opposite rib-roughened walls

An experimental study of heat transfer characteristics in steam-cooled rectangular channels with two opposite rib-roughened walls for Reynolds number (Re) in the range of 10,000–80,000 was conducted. To simulate the actual geometry and heat transfer structure of turbine blade/vane internal cooling passage, each of the test channels was made by welding four stainless steel plates. The pitch-to-rib height ratio p/e was kept at 10 and the channel length L was kept at 1000 mm. The channel aspect ratios (W/H) were 0.25, 0.5 and 1, respectively. The channel blockage ratios were 0.047 for W/H = 1, 0.5 and 0.078 for W/H = 0.25. We have found that the average Nusselt number (Nu) for the channel with α = 45° is about 15–25 percent higher than that for the channel with α = 60°. For the channels with W/H = 0.5 or 1, the average Nu decreases along the rib axes because of the rib-induced secondary flow that moves from the left-hand side to the right-hand side. In addition, based on the heat transfer results, we have developed the semi-empirical correlations for the two test channels with the highest and the lowest heat transfer. The correlations can be used in the design of the internal cooling passage of new-generation steam-cooled gas turbine blade/vane.     

Fluid flow characteristics and convective heat transfer improvement on a gas turbine blade

The flow field features and heat transfer enhancement are investigated on a gas turbine blade by applying the jet impingement cooling method. The distribution of the flow field and the Nusselt number (Nu) was determined on the targeted surface in the cooling channel. The injection holes of different shapes, such as circular, square, and rectangular were considered. The Reynolds numbers (Re) of the airflow in the range of 2000–5000 and aspect ratios of 0.5–2 were particularly focused. The flow vortices and recirculation in the cooling channel and their influence on the heat transfer enhancement were analyzed in detail under different airflow and geometric conditions. Decreasing the ratio of the distance between jet-to-target plate to the diameter of the jet orifice (H/d) increased the heat transfer rate and produced high-intensity vortices and recirculation zones. It was noticed that the formation and generation of vortices and recirculation have important effects on the convective heat transfer rate at the impingement surface. Local Nusselt number, formation of complex vortices, and airflow recirculation in the cooling channel decreased with the increase in the distance between the jet hole and the targeted surface. It was found that with the increase in the Reynolds number of the jet, heat transfer between cold airflow and the targeted surface increased. Moreover, it was observed that the cooling performance of the round and square jet holes was better than the rectangular holes.     

An experimental study on convection heat transfer from an array of discrete heat sources

Convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally for air. The lower surface of the channel was equipped with 8×4 flush-mounted heat sources subjected to uniform heat flux; the sidewalls and the upper wall were insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR=2, Reynolds numbers 864≤Re_Dh≤7955, and modified Grashof numbers Gr*=1.72×10⁸ to 2.76×10⁹. From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit.     

Correlations for solar air heater duct with V-shaped perforated baffles as roughness elements on absorber plate

An experimental investigation has been carried out to study the effect of heat transfer and friction characteristics of air passing through a rectangular duct which is roughened by V-down perforated baffles. The experiment encompassed Reynolds number (Re) from 3800 to 19,000, relative roughness height (e/H) values of 0.285–0.6, relative roughness pitch (P/e) range of 1–4 and open area ratio values from 12% to 44%. The effect of roughness parameters on Nusselt number (Nu) and friction factor (f) has been determined and increase in heat transfer and friction loss has been observed for ducts having a roughened test plate. Maximum Nusselt number is observed for the relative roughness pitch ranging from 1.5 to 3 for flow and geometrical parameters under consideration. The experimental data have been used to develop Nusselt number and friction factor correlations as a function of roughness and flow parameters.     

Laminar heat transfer in a porous channel simulated with a two-energy equation model

Laminar heat transfer in a porous channel is numerically simulated with a two-energy equation model for conduction and convection. Macroscopic equations for continuity, momentum and energy transport for the fluid and solid phases are presented. The numerical methodology employed is based on the control volume approach with a boundary-fitted non-orthogonal coordinate system. Fully developed forced convection in a porous channel bounded by parallel plates is considered. Solutions for Nusselt numbers along the channel are presented for laminar flows. Results simulate the effects Reynolds number Re, porosity, particle size and solid-to-fluid thermal conductivity ratio on Nusselt sumber, Nu, which is defined for both the solid and fluid phases. High Re, low porosities, low particle diameters and low thermal conductivity ratios promote thermal equilibrium between phases leading to higher values of Nu.     

Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in unconfined flowing Newtonian fluids have been investigated numerically. The governing equations, namely, continuity, Navier–Stokes and energy, have been solved in the steady flow regime over wide ranges of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr ? 100). Prior to the investigation of drag and heat transfer phenomena, the critical values of the Reynolds number for wake formation (0.55 < Re^c < 0.6) and for the onset of vortex shedding (39.5 < Re_c < 40) have been identified. The corresponding values of the lift coefficient, drag coefficient, and Strouhal number are also presented. After establishing the limit of the steady flow regime, the influence of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr = 0.72, 1, 10, 50 and 100) on the global flow and heat transfer characteristics have been elucidated. Detailed kinematics of the flow is investigated in terms of the streamline and vorticity profiles and the variation of pressure coefficient in the vicinity of the cylinder. The functional dependence of the individual and total drag coefficients on the Reynolds number is explored. The Nusselt number shows an additional dependence on the Prandtl number. In addition, the isotherm profiles, local Nusselt number (Nu_L) and average Nusselt number (Nu) are also presented to analyze the heat transfer characteristic of a semi-circular cylinder in Newtonian media.     

Influence of channel aspect ratio on heat transfer in rotating rectangular ducts with skewed ribs at high rotation numbers

Centerline heat transfer measurements along two opposite ribbed walls in three rotating rectangular ducts roughened by 45° staggered ribs with channel aspect ratios (AR) of 1:1, 2:1 and 4:1 are performed at Reynolds (Re), rotation (Ro) and buoyancy (Bu) numbers in the ranges of 5000–30,000, 0–2, and 0.005–8.879, respectively. These channel geometries are in common use as the internal cooling passages of a gas turbine rotor blade and the tested Ro and Bu ranges are considerably extended from the previous experiences. This study focuses on the heat transfer characteristics in response to the change of AR under the parameter ranges examined. With zero-rotation (Ro = 0), the local Nusselt numbers (Nu₀) along the centerlines of two opposite ribbed walls increase as AR increases due to the increased rib-height to channel-height ratio. The Bu impact on heat transfer appears to be AR dependent, i.e. the increase of Bu elevates Nusselt number ratios Nu/Nu₀ in the square channel but impairs heat transfer in the rectangular channels of AR = 2 and 4. Acting by the Coriolis effect alone, all the leading edge Nu values in the present Ro range are lower than the zero-rotation references but started to recover as Ro increases from 0.1 in the channels of AR = 1, 2 and from 0.3 in the channel of AR = 4. The trailing edge Nu/Nu₀ ratios increase consistently from unity as Ro increases but their responses toward the increase of AR are less systematic than those found along the leading edge. The above findings, with the aids of extended Ro and Bu ranges achieved by this study, serve as the original contributions for this technical community. The Nu/Nu₀ ratios in the rotating channels of AR = 1, 2, and 4 fall in the ranges of 0.6–2.2, 0.5–2.7, and 0.5–2.1, respectively. A set of heat transfer correlations is derived to represent all the heat transfer data in the periodically developed flow regions of three rotating ducts.     

Drag forces and heat transfer coefficients for spherical,cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers

This work is devoted to the numerical calculation of heat and fluid flow past spherical particles and non-spherical particles of various shapes. Although numerous works have investigated drag forces (c_d) for spherical and non-spherical particles, works about the Nusselt number (Nu) relations for non-spherical particles are rare. Motivated by this fact, as a first step we consider cuboid, spherical and ellipsoidal particles in steady-state regimes corresponding to Reynolds numbers (Re) from 10 up to 250. Due to the asymmetric flow existing when Re approaches the value of 250, all simulations are made using a three-dimensional domain. Good agreement was observed when our numerical results gained for the sphere were compared with published values for drag coefficients and Nusselt numbers. Based on the analysis of numerical results obtained for non-spherical particles we found out that in addition to the Reynolds number three geometry parameters influence particle-fluid interaction: the drag coefficient depends primarily on the normalized longitudinal length, while both the sphericity and the crosswise sphericity influence the Nusselt number. For that reason new correlations are developed for both the drag coefficient and the Nusselt number. The accuracy of the closures developed for c_d and Nu is discussed in a comparison with published models.     

Heat transfer and pressure drop in furrowed channels with transverse and skewed sinusoidal wavy walls

This comparative study examines the detailed Nusselt number (Nu) distributions, pressure drop coefficients (f) and thermal performance factors (η) for two furrowed rectangular channels with transverse and skewed sinusoidal wavy walls. Detailed heat transfer measurements over these transverse and skewed sinusoidal wavy walls at the Reynolds numbers (Re) = 1000, 1500, 2000, 5000, 10,000, 15,000, 20,000, 25,000 and 30,000 are performed using the steady-state infrared thermo-graphic method. Impacts of Re on Nu and f for two tested furrowed channels with transverse and skewed waviness are individually examined. In addition to the macroscopic mixing between the near-wall recirculations and core flows due to the shear layer instabilities in each wavy channel, the secondary flows tripped by the skewed wall-waves further elevate heat transfer performances and distinguish their Nu distributions from those over the transverse wavy wall. The area-averaged Nusselt numbers ($\overline{\mathit{Nu}}$) for two tested furrowed channels with transverse and skewed waviness with 5000 < Re < 30000 fall, respectively, in the ranges of 3.45–3.71 and 3.98–4.2 times of the Dittus–Boelter levels. A set of $\overline{\mathit{Nu}}$ and f correlations for each tested furrowed channel is individually derived using Re as the controlling parameter. By way of comparing the thermal performance factors (η) with a selection of rib-roughened channels, the η factors for the present skewed wavy channel are compatible with those in the channel roughened by the compound V-ribs and deepened scales due to the relative low pressure drop penalties with the equivalent heat transfer augmentations to those offered by V-ribs.     

Heat transfer and friction factor correlations for a duct having dimple-shape artificial roughness for solar air heaters

The heat transfer coefficient between the absorber plate and air can be considerably increased by using artificial roughness on the underside of the absorber plate of a solar air heater duct. Under the present work, an experimental study has been carried out to investigate the effect of roughness and operating parameters on heat transfer and friction factor in a roughened duct provided with dimple-shape roughness geometry. The investigation has covered the range of Reynolds number (Re) from 2000 to 12,000, relative roughness height (e/D) from 0.018 to 0.037 and relative pitch (p/e) from 8 to 12. Based on the experimental data, values of Nusselt number (Nu) and friction factor (f_r) have been determined for different values of roughness and operating parameters. In order to determine the enhancement in heat transfer and increment in friction factor values of Nusselt number and friction factor have been compared with those of smooth duct under similar flow conditions. Correlations for Nusselt number and friction factor have been developed for solar air heater duct provided such artificial roughness geometry.     

Development of correlations for Nusselt number and friction factor for solar air heater with roughened duct having arc-shaped wire as artificial roughness

An experimental study has been carried out for enhancement of heat transfer coefficient of a solar air heater having roughened air duct provided with artificial roughness in the form of arc-shape parallel wire as roughness element. Increment in friction factor by provided with such artificial roughness elements has also been studied. The effect of system parameters such as relative roughness height (e/d) and arc angle (α/90) have been studied on Nusselt number (Nu) and friction factor (f) with Reynolds number (Re) varied from 2000 to 17000. Considerable enhancement in heat transfer coefficient has been achieved with such roughness element. Using experimental data correlations for Nusselt number and friction factor have also been developed for such solar air heaters, which gives a good agreement between predicted values and experimental values of Nusselt number and friction factor.     

Pressure drop and heat transfer of arrays of in-line circular blocks on the wall of parallel channel

Pressure drop and heat transfer of arrays of in-line circular blocks on the wall of a parallel channel are measured. Diameter and height of the blocks are 40 and 18 mm, respectively, while pitches of the blocks are varied. The effects of the number of lines and rows and other factors on pressure drop and heat transfer are investigated. The pressure loss coefficient ζ is the sum of the pressure drop across three regions, the inlet, intermediate and outlet regions, and is formulated as an empirical equation that agrees with experimental data to within ±10%. Average heat transfer coefficient of the first row of blocks is 10% lower than that of the second row. Coefficients of the first 5 rows Nu_mi, are approximated to within ±10% by Nu_mi=0.118(Re/β)^0.75, where β is the opening ratio. The average Nusselt number of the second to fifth rows is also correlated to fan power, P_w, to within 5% by Nu_ave=190P_w^0.25, where P_w=ΔPU_mA₀,ΔP is the pressure difference, U_m is the mean velocity and A₀ is the cross-sectional area of the duct. Finally, the Nusselt number is represented by a non-dimensional expression as Nu_ave=0.134(ζ^1/3Re)^0.75.     

Variation of Nusselt number with flow regimes behind a circular cylinder for Reynolds numbers from 70 to 30 000

The dependence of the Nusselt number in the separated flow behind a circular cylinder to the cross-flow varies greatly with Reynolds number according to the flow regimes, i.e., laminar shedding, wake transition, and shear-layer transition regimes. The Nusselt number at the rear stagnation point, Nu_r/Re^0.5, increases with Reynolds number in the laminar shedding regime (Re < 150) and the shear-layer transition regime (3000 < Re < 15 000), corresponding to the shortening of the vortex formation region. On the contrary, the Nusselt number, Nu_r/Re^0.5, decreases with Reynolds number in the regime in which the wake develops to a complex three-dimensional flow (300 < Re < 1500), corresponding to the lengthening of the vortex formation region. This distinctive change affects the correlation of the overall Nusselt number with Reynolds number, i.e., the exponent of the Reynolds number has a lower value for 200 < Re < 2000 than that for 70 < Re < 200 and Re > 2000.     

A numerical study of mixed convection in a vertical channel flow impinging on a horizontal surface

In this study, mixed convection in a vertical channel flow discharging over a horizontal isotherm surface is investigated numerically using a finite difference method based on projection algorithm. The governing equations are discretized by a second order central difference in space and first order in time. The average Nusselt number is calculated on the horizontal surface in various vertical channels of varying areas considering non-dimensional parameters consisting of Reynolds and Richardson (or Grashof) numbers. Analysis of the results shows that there is an optimum gap to have a maximum heat transfer rate over the surface. The optimum gap value varies with Grashof and Reynolds numbers and inlet length of the channel but for high Richardson numbers, Nu has an increasing trend with reduction of gap size. By increasing the Re, Gr and Ri numbers, Nu number increases but in Ri of 0.1 and 0.01 the variations are approximately similar to each other. In addition, a divergent channel is usually more efficient than convergent one concerning heat transfer over the horizontal surface. Effects of Prandtl number and asymmetricity in channel are investigated in detail too.     

Hydromagnetic effect on mixed convection in a lid-driven cavity with sinusoidal corrugated bottom surface

The present numerical simulation is conducted to analyze the mixed convection flow and heat transfer in a lid-driven cavity with sinusoidal wavy bottom surface in presence of transverse magnetic field. The enclosure is saturated with electrically conducting fluid. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. In addition, the transport equations are solved by using the finite element formulation based on the Galerkin method of weighted residuals. The implications of Reynolds number (Re), Hartmann number (Ha) and number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail while, Prandtl number (Pr) and Rayleigh number (Ra) are considered fixed. The trend of the local heat transfer is found to follow a wavy pattern. The results of this investigation illustrate that the average Nusselt number (Nu) at the heated surface increases with an increase of the number of waves as well as the Reynolds number, while decreases with increasing Hartmann number.