Dispersion of a buoyant plume in a turbulent pressure-driven channel flow

Direct numerical simulations of the turbulent dispersion of a buoyant line of hot fluid released at the inlet of a plane channel flow are reported (Re_τ = 180, Gr = 10⁷ and Pr = 0.7). Results of turbulent dispersion of a neutrally buoyant scalar and mixed convection flow are also included. The buoyancy force induces a vertical movement that, although small in mean, exhibits a significant fluctuation in the vertical velocity component and deflects the plume with the consequent loss of symmetry found in the neutrally buoyant results. The modification of the budgets for the time averaged momentum and heat transport equations reflects the rearranging of the different contributions induced by the buoyancy force.     

Oscillatory double-diffusive mixed convection in a two-dimensional ventilated enclosure

By starting from a steady flow configuration based on the work of Deng et al. [Qi-Hong Deng, Jiemin Zhou, Chi Mei, Yong-Ming Shen, Fluid, heat and contaminant transport structures of laminar double-diffusive mixed convection in a two-dimensional ventilated enclosure, Int. J. Heat Mass Transfer 47 (2004) 5257–5269], a numerical investigation was conducted to analyse the unsteady double-diffusive mixed convection in two-dimensional ventilated room due to heat and contaminant sources. Owing to the large number of parameters, the results are reported only for a constant buoyancy ratio N equal to 1. The flow is found to be oscillatory for a fixed Reynolds number (700 ⩽ Re ⩽ 1000) when the Grashof number is varied in a wide range (10³ ⩽ Gr ⩽ 10⁶). Results of the simulations show that the onset of the oscillatory indoor airflow occurs for couples (Re, Gr) values that can be correlated as Re = aGr^b.     

The temperature statistics of a surfactant-covered air/water interface during mixed convection heat transfer and evaporation

Surface temperature fields were measured of an air/water interface where heat was transferred from the water to the air under mixed convection conditions. The interfacial temperature field was measured using an infrared (IR) camera for mean wind speeds ranging from 0 to 4.0 m/s, in 1.0 m/s increments. Statistics of these surface temperature fields, specifically, the root mean square (rms) and the skewness were obtained. Plots of the rms versus the heat flux showed linear behavior for low wind speeds (U = 0–3 m/s), and the skewness was also found to increase with heat flux for U = 0–3 m/s, although these data exhibited significant scatter. The scaled root mean square temperature was revealed to be governed by the ratio Ra^1/3/(Re^14/5Pr^1/3) where Ra is the Rayleigh number, Re¹ the Reynolds number based on water side friction velocity and Pr is the Prandtl number.     

Coriolis and rotating buoyancy effect on detailed heat transfer distributions in a two-pass square channel roughened by 45° ribs at high rotation numbers

Heat transfer measurements from a rotating two-pass square channel with two opposite leading and trailing walls roughened by 45° parallel ribs arranged in the staggered manner are performed to examine the effects of Reynolds (Re), rotation (Ro) and buoyancy (Bu) numbers on local and area-averaged Nusselt numbers (Nu and $\overline{\mathit{Nu}}$). Full-field Nu distributions over the two rib-roughened leading and trailing walls are measured at the conditions of 4000 ? Re ? 16,000, 0 ? Ro ? 0.8 and 0.0015 ? Bu ? 0.93 (0.05 ? Δρ/ρ ? 0.1) using the infrared thermography which allows for the detailed examination of the Coriolis and rotating buoyancy effects on Nu distributions over the rotating ribbed surface. Selected heat transfer data in term of Nu ratio between rotating and stationary levels illustrates the influences of rotation on local and area-averaged heat transfer performances. Area-averaged $\overline{\mathit{Nu}}$ for the turn region and the inlet and outlet ribbed legs of the rotating two-pass channel are parametrically analyzed to devise a set of empirical heat transfer correlations that permits the evaluation of the interdependent and individual effects of Re, Ro and Bu on $\overline{\mathit{Nu}}$.     

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.     

Unsteady mixed convection flow from a moving vertical plate in a parallel free stream: Influence of heat generation or absorption

An unsteady mixed convection flow over a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of heat generation or absorption. The unsteadiness is introduced by the time dependent free stream velocity as well as by the moving plate velocity. The governing boundary layer equations are transformed into a non-dimensional form by a special group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Computations are performed and numerical results are displayed graphically to illustrate the influence of the buoyancy (mixed convection) parameter, Prandtl number, the ratio of free stream velocity to the composite reference velocity and heat generation or absorption parameter on the velocity and temperature profiles. The numerical results for the local skin-friction coefficient and local Nusselt number are also presented. Present results are compared with previously published work and are found to be in excellent agreement. It is found that in presence of buoyancy force (λ > 0), the velocity profile exhibits velocity overshoot 80% more for lower Prandtl number (Pr = 0.7) as compared to the magnitude of the velocity overshoot for higher Prandtl number (Pr = 7.0).     

Flow visualizations and heat transfer measurements for a rotating pin-fin heat sink with a circular impinging jet

This work experimentally investigated the fluid flow and heat transfer behaviors of jet impingement onto the rotating heat sink. Air was used as impinging coolant, while the square heat sinks with uniformly in-line arranged 5 × 5 and 9 × 9 pin-fins were employed. The side length (L) of the heat sink equaled 60 mm and was fixed. Variable parameters were the relative length of the heat sink (L/d = 2.222 and 4.615), the relative distance of nozzle-to-fin tip (C/d = 0–11), the jet Reynolds number (Re = 5019–25,096) and the rotational Reynolds number (Re_r = 0–8114). Both flow characteristics of stationary and rotating systems were illustrated by the smoke visualization. Besides, the results of heat transfer indicate that, for a stationary system with a given air flow rate, there was a larger average Nusselt number (Nu₀) for the 9 × 9 pin-fin heat sink with L/d = 4.615 and C/d = 11. For a rotating system, a bigger Re_r meant a more obvious heat transfer enhancement (Nu_Ω/Nu₀) in the case of smaller Re, but Nu_Ω/Nu₀ decreased with increasing Re. In this work, Nu_Ω/Nu₀ in L/d = 2.222 is higher than in L/d = 4.615; among the systems in L/d = 2.222, bigger Nu_Ω/Nu₀ exists in the case of C/d = 9–11, but among the systems in L/d = 4.615, bigger Nu_Ω/Nu₀ exists in the case of C/d = 1–3. Finally, according to the base of Nu_Ω/Nu₀ ? 1.1, the criterion of the substantial rotation was suggested to be Re_r/Re ? 1.154.     

Thermal management using the bi-disperse porous medium approach

Thermal management of distributed electronics similar to data centers is studied using a bi-disperse porous medium (BDPM) approach. The BDPM channel comprises heat generating micro-porous square blocks, separated by macro-pores. Laminar forced convection cooling fluid of Pr = 0.7 saturates both the micro- and macro-pores. Bi-dispersion effect is induced by varying the macro-pore volume fraction ?_E, and by changing the number of porous blocks N², both representing re-distribution of the electronics. When 0.2 ? ?_E ? 0.86, the heat transfer Nu is enhanced twice (from ～550 to ～ 1100) while the pressure drop Δp¹ reduces almost eightfold. For ?_E < 0.5, Nu reduces quickly to reach a minimum at the mono-disperse porous medium (MDPM) limit (?_E → 0). Compared to N² = 1 case, Nu for BDPM configuration is high when N² ? 1, i.e., the micro-porous blocks are many and well distributed. The Nu increase with Re changes from non-linear to linear as N² increases from 1 to 81, with corresponding insignificant pumping power increase.     

Numerical study of turbulent double-diffusive natural convection in a square cavity by LES-based lattice Boltzmann model

Turbulent double-diffusive natural convection in a square cavity represents numerous important problems in practice as well as in fundamental. However up to date the study on it is quite sparse and most previous studies just focus on laminar regime. To the best knowledge of the present authors, only several k–? models were developed to investigate turbulent double-diffusive convection and there is no attempt to use Large Eddy Simulation (LES). In order to deepen our knowledge on turbulent double-diffusive convection in a square cavity, we propose a novel LES-based lattice Boltzmann (LB) model to simulate such turbulent convectional flow. Previous LES-based LB models can be recovered from the present model. We find that the symmetry of the fluid circulation becomes broken since the Rayleigh number Ra = 10⁸, although the asymmetry is more clear when Ra ? 10¹⁰. More important, in the present study we find the power-law relationship among the Nusselt (Nu), the ratio of buoyancy forces (N) and the Rayleigh number (Ra) still exists in turbulent regime. The formula among them can be concluded as Nu = a × (Ra × ∣1 ? N∣)^b + c. The values of parameters a, b and c are given in this work.     

Heat transfer behavior in a rotating aluminum foam heat sink with a circular impinging jet

This work experimentally studied heat transfer associated with an impinging jet onto a rotating heat sink. Air was used as the impinging coolant, and a square Al-foam heat sink was adopted. The variable parameters were the jet Reynolds number (Re), the relative nozzle-to-foam tip distance (C/d), the rotational Reynolds number (Re_r) and the relative side length of the square heat sink (L/d). The effects of Re, C/d, Re_r and L/d on the dimensionless temperature distributions and the average Nusselt number were considered. For a stationary system, the results reveal that the average Nusselt number (Nu₀) with Al-foam was two to three times that without Al-foam. Nu₀ increased with Re. A larger L/d responded to a larger Nu₀ based on the same jet flow rate. The effect of C/d on Nu₀ was negligible herein. For a rotating system, when Re and L/d were small and C/d was large, the average Nusselt number (Nu_Ω) increased considerably with Re_r. Additionally, for Nu_Ω/Nu₀ ? 1.1, the results suggest that rotation was substantial at Re_r/Re ? 1.13 when L/d = 4.615 with C/d = 0–5 and at Re_r/Re ? 1.07 when L/d = 3.0 with C/d = 0–5. For L/d = 2.222, rotation was substantial at Re_r/Re ? 1.44 when C/d = 0 and was always substantial when C/d ? 1.     

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.     

Experimental study of natural convection in PV roof solar collector

The aim of this paper is to propose the PV roof solar collector (PV-RSC) to investigate the natural convection heat transfer and estimated the convective heat transfer coefficient in the channel. The experimental set-up was composed of a PV panel on the upper layer and the lower layer is aluminum plate of the channel. The inclination angle and air gap of channel were fixed at 30° and 15 cm, respectively. The channel width is 0.7 m, and length is 1.2 m. The data analysis were confirmed the effect of radiative exchange influent to natural convection within the channel. On the basis of the experimental results, an empirical formula is found; the Nu as a function of Ra_s sin30, that is Nu_s = 0.3282 (Ra_s sin30)^0.2249. The correlation obtained to range 3 × 10⁸ < Ra_s sin30 < 7 × 10⁸. A comparison between PV-RSC and normal PV panel, it was confirmed that the PV-RSC could be generated electric power than that normal PV panel by about 30 W; and also the percentage of power generation increase was rising about 25% throughout the day.     

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.     

Double-diffusive mixed convection in a vertical pipe: A thermal non-equilibrium approach

In this article, double-diffusive mixed convection in a vertical pipe under local thermal non-equilibrium state has been investigated. The non-Darcy Brinkman–Forchheimer-extended model has been used and solved numerically by spectral collocation method. Special attention is given to understand the effect of buoyancy ratio (N) and thermal non-equilibrium parameters: inter phase heat transfer coefficient (H) as well as porosity scaled thermal conductivity ratio (γ) on the flow profiles as well as on rates of heat and solute transfer. Judged from the influence of buoyancy ratio on velocity profile, when both the buoyancy forces: thermal as well as solutal are in favor of each other and for given any value of H considered in this study, it has been found that for N equal to 10 as well as 100, the basic velocity profile shows back flow for small subdomain of the domain of the flow. When two buoyancy forces are opposing to each other (Ra_T = ?1000), velocity profile possesses a kind of distortion, in which the number of zeroes increases on increasing N. Corresponding variation of heat transfer rate in the (N,  Nu_f)-plane shows a sinusoidal pattern. The flow separation on the flow profile dies out on increasing H for N = 0. It has been also found that for each N, when N < 0.7, there exists a minimum value of H such that the velocity profile becomes free from flow separation. Influence of H on the profiles of solid temperature as well as solute, in both situations are similar. Overall, the impact of LTNE parameters, specially γ, on heat transfer rate of double-diffusive convection is not straight forward.     

Effects of moving lid direction on MHD mixed convection in a linearly heated cavity

Effects of moving lid-direction on MHD mixed convection in a cavity with the bottom wall being linearly heated are analyzed using a numerical technique. Vertical walls of the enclosure are adiabatic and the sliding wall at the top has constant temperature. The lid moves in the negative and positive x-direction. Finite volume method has been used to solve the governing equations. Results are presented for different values of Hartmann number (0 ? Ha ? 30), Reynolds number (100 ? Re ? 1000) and Grashof number (10⁴ ? Gr ? 10⁶). It is found that direction of lid is more effective on heat transfer and fluid flow in the case of mixed convection than it is the case in forced convection. Heat transfer is also decreased with increasing of magnetic field for all studied parameters.     

A numerical study of the unsteady heat/mass transfer inside a circulating sphere

Numerical methods are used to investigate the transient, forced convection heat/mass transfer inside circulating spheres at low to moderate Reynolds numbers. The heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere interior Reynolds number are Re_int ? 1000. The computations were focused on the influence of the sphere Peclet number, Pe, and Re_int on heat/mass transfer rate for Pe/(1 + μ) ? 10⁴.     

Laminar forced convection in a heat generating bi-disperse porous medium channel

Thermal management of heat generating electronics using the Bi-Disperse Porous Medium (BDPM) approach is investigated. The BDPM channel comprises heat generating micro-porous square blocks separated by macro-pore gaps. Laminar forced convection cooling fluid of Pr = 0.7 saturates both the micro- and macro-pores. Bi-dispersion effect is induced by varying the porous block permeability Da_I and external permeability Da_E through variation in number of blocks N². For fixed Re, when 10^?5 ? Da_I ? 10^?2, the heat transfer Nu is enhanced four times (from ～200 to ～800) while the pressure drop Δp1 reduces almost eightfold. For Da_I < 10^?5, Nu decreases quickly to reach a minimum at the Mono-Disperse Porous Medium (MDPM) limit (Da_I → 0). Compared to N² = 1 case, Nu for BDPM configuration is high when N² ? 1, i.e., the micro-porous blocks are many and well distributed. The pumping power increase is very small for the entire range of N². Distributing heat generating electronics using the BDPM approach is shown to provide a viable method of thermo-hydraulic performance enhancement χ.     

Correlations for combined heat and mass transfer from an open cavity in a horizontal channel

Combined heat and mass transfer from a horizontal channel with an open cavity heated from below is numerically examined in this paper. Air is the fluid considered (Pr = 0.7). The main focus of the study is mass-transfer driven flows (|N| > 1). The governing parameters considered are the buoyancy ratio N, Lewis number Le, Reynolds number Re, and Grashof number Gr. Based on the scale analysis, correlations for the entire convection regime, from natural, mixed, to forced convection, were proposed.     

Research on the shell-side thermal performances of heat exchangers with helical tube coils

This paper presents the results of experimental research on shell-side heat transfer coefficient concerning 3 heat exchangers with helical coils. Measurements were carried in laboratory and the following correlation was found to be adequate Nu = 0.50 ? Re^0.55 ? Pr ^1/3 ? (η/η_w)^0.14 where Re and Nu are based on shell-side hydraulic diameter.     

Unsteady fluid mechanics and heat transfer study in a double-tube air–combustor heat exchanger with porous medium

Fluid mechanics and heat transfer are studied in a double-tube heat exchanger that uses the combustion gases from natural gas in a porous medium located in a cylindrical tube to warm up air that flows through a cylindrical annular space. The mathematical model is constructed based on the equations of continuity, linear momentum, energy and chemical species. Unsteady fluid mechanics and heat transfer by forced gas convection in the porous media, with combustion in the inner tube, coupled to the forced convection of air in the annular cylindrical space are predicted by use of finite volumes method. Numerical simulations are made for four values of the annular air flow Reynolds number in the range 100 ? Re ? 2000, keeping constant the excess air ψ = 4.88, the porosity ε = 0.4, and the air–fuel mixture inlet speed Uo = 0.43 m/s. The results obtained allow the characterization of the velocity and temperature distributions in the inner tube and in the annular space, and at the same time to describe the displacement of the moving combustion zone and the annular porous media heat exchanger thermal efficiency. It is concluded that the temperature increase is directly related to the outer Reynolds number.