A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries

This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - c_m mass concentration of microcapsules - c_p specific heat, kJ kg^–1 K^–1 - h_fs phase change material heat of fusion, kJ kg^–1 - h_m* modified convective heat transfer coefficient, W m^–2 K^–1 - k thermal conductivity, W m^–1 K^–1 - k_e effective thermal conductivity of slurry, W m^–1 K^–1 - k_b slurry bulk thermal conductivity, W m^–1 K^–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - q_wⁿ wall heat flux, Wm^–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r₀ duct radius, m - r₁ dimensionless radial coordinate - Ste Stefan number - T temperature, K - T₁ lower phase change temperature limit, K - T₂ upper phase change temperature limit, K - T_i slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x₁ dimensionless axial coordinate - thermal diffusivity, m²/s - dimensionless temperature - dynamic viscosity, N·s/m² - kinematic viscosity, m²/s - _t width of thermal boundary, m - degree of heat transfer enhancement, = h_m*/(h_m*)_single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid     

Droplets splashing upon films of the same fluid of various depths

We explore the effects of fluid films of variable depths on droplets impacting into them. Corresponding to a range of fluid “film” depths, a non-dimensional parameter—H*, defined as the ratio of the film thickness to the droplet diameter—is varied in the range 0.1≤H*≤10. In general, the effect of the fluid film imposes a dramatic difference on the dynamics of the droplet–surface interaction when compared to a similar impact on a dry surface. This is illustrated by the size distribution and number of the splash products. While thin fluid films (H*≈0.1) promote splashing, thicker films (1≤H*≤10) act to inhibit it. The relative roles of surface tension and viscosity are investigated by comparison of a matrix of fluids with low and high values of these properties. Impingement conditions, as characterized by Reynolds and Weber numbers, are varied by velocity over a range from 1.34 to 4.22 m/s, maintaining a constant droplet diameter of 2.0 mm. The dependence of splashing dynamics, characterized by splash product size and number, on the fluid surface tension and viscosity and film thickness are discussed.     

Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 Re_Dh 980, and modified Grashof numbers Gr^* = 9.53 × 10⁵ to 1.53 × 10⁷ . 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, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. 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, especially for low Reynolds numbers.     

Transient combined natural convection-conduction in open-ended vertical concentric annuli

Transient conjugate natural convection heat transfer in open-ended vertical concentric annuli is investigated numerically. The governing equations of an induced laminar flow for a fluid of Pr=0.7 are solved using a finite-difference technique. The heating is achieved by a step change in the temperature of the outer surface of the outer tube while the inner surface of the inner tube is kept adiabatic. The range of Grashof number considered is 500≤Gr^*≤10⁵. The effects of solid-fluid conductivity ratio and diffusivity ratio on the transient induced flow characteristics are presented. Received on 25 March 1998     

Non-Darcian and Anisotropic Effects on Free Convection in a Porous Enclosure

The free convective flow and heat transfer, within the framework of Boussinesq approximation, in an anisotropic fluid filled porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Brinkman extended non-Darcy flow model. The studies involve simultaneous consideration of hydrodynamic and thermal anisotropy. The flow and temperature fields in general are governed by, Ra, the Rayleigh number, AR, the aspect ratio of the slab, K*, the permeability ratio and k*, the thermal conductivity ratio, and Da, Darcy number. Numerical solutions employing the successive accelerated replacement (SAR) scheme have been obtained for 100 ≤ Ra ≤ 1000, 0.5 ≤ AR ≤ 5, 0.5 ≤ K* ≤ 5, 0.5 ≤ k* ≤ 5, and 0 ≤ Da ≤ 0.1. It has been found that [`(Nu)]{\overline {Nu}}, average Nusselt number increases with increase in K* and decreases as k* increases. However, the magnitude of the change in [`(Nu)]{\overline {Nu}} depends on the parameter Da, characterizing the Brinkman extended non-Darcy flow.     

Investigation of the different base fluid effects on the nanofluids heat transfer and pressure drop

A numerical study of laminar forced convective flows of three different nanofluids through a horizontal circular tube with a constant heat flux condition has been performed. The effect of Al₂O₃ volume concentration 0 ≤ φ ≤ 0.09 in the pure water, water-ethylene glycol mixture and pure ethylene glycol as base fluids, and Reynolds number of 100 ≤ Re ≤ 2,000 for different power inputs in the range of 10 ≤ Q(W) ≤ 400 have been investigated. In this study, all of the nanofluid properties are temperature and nanoparticle volume concentration dependent. The governing equations have been solved using finite volume approach with the SIMPLER algorithm. The results indicate an increase in the averaged heat transfer coefficient with increasing the mass of ethylene glycol in the water base fluid, solid concentration and Reynolds number. From the investigations it can be inferred that, the pressure drop and pumping power in the nanofluids at low solid volumetric concentration (φ < 3%) is approximately the same as in the pure base fluid in the various Reynolds numbers, but the higher solid nanoparticle volume concentration causes a penalty drop in the pressure. Moreover, this study shows it is possible to achieve a higher heat transfer rate with lower wall shear stress with the use of proper nanofluids.     

Experimental investigation of mixed convection heat transfer in a horizontal and inclined rectangular channel

 Mixed convection heat transfer in rectangular channels has been investigated experimentally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Experiments were conducted for Pr=0.7, aspect ratios AR=5 and 10, inclination angles 0° ≤ θ ≤ 30°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr*=7.0 × 10⁵ to 4.0 × 10⁷. From the parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results related to the buoyancy affected secondary flow and the onset of instability have been discussed. Some of the results obtained from the experimental measurements are also compared with the literature, and a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number and increasing aspect ratio. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle. Received on 19 March 2001 / Published online: 29 November 2001     

Mixed convection heat transfer in open ended channels with protruding heaters

Mixed convection heat transfer has been studied in vertical channels, open at the bottom and top, with protruding discrete heaters installed on one side. The flow is assumed to be steady, laminar and two-dimensional. The Boussinesq approximation is used to account for the density variation. Non-dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation are solved using the SIMPLER method. Heat transfer through the top and the right are calculated as functions of the Rayleigh number (0≤Ra≤10⁷), the Reynolds number (0≤Re≤200), various aspect ratios (1≤A≤6). The effect of the entrance and exit lengths and that of the position of the electronic components in the channel are also examined. Flow and temperature fields for various cases are produced, and the temperature variations in the electronic components are calculated. Received on 2 March 1998     

Mixed convection around a liquid sphere in an air stream

 A linearized finite-difference scheme has been used to investigate the mixed convection boundary-layer flow about a liquid sphere subjected to an air stream. For Prandtl number = 0.7, velocity and temperature profiles are obtained for a wide range of the other controlling parameters: Reynolds number, interior-to-exterior (liquid- to-air) viscosity ratio and Grashof number. Both aiding and opposing natural convections are considered in this study. The effect of the controlling parameters on engineering quantities such as the shear stress and the Nusselt number is also presented. Received on 27 September 2000 / Published online: 29 November 2001     

Drag of a strongly heated sphere at small Reynolds numbers

Using an asymptotic small-perturbation method, the flow around a strongly heated sphere at small Reynolds numbers Re ≪ 1 is considered with account for thermal stresses in the gas in the higher-order approximations, beyond the Stokes one. It is assumed that the value of the Prandtl number Pr is arbitrary and the temperature dependence of the viscosity is described by a power law with an arbitrary exponent. In the O(Re²) and O(Re³ ln(Re)) approximations, the drag force of a heated sphere is found over a wide range of the ratios of sphere’s temperature to the gas free-stream temperature T _W /T _∞. The limits of applicability of the first (in Re) approximation are investigated, including the negative-drag effect, attributable to the action of the thermal stresses. The results are compared with numerical calculations of the flow around a hot sphere. The limits of applicability of the approximations found are examined. Similar results are obtained for the standard Navier-Stokes equations in which the thermal stresses are neglected.     

Experimental and numerical study on laminar natural convection in a cavity heated from bottom due to an inclined fin

Natural convection heat transfer in an inclined fin attached square enclosure is studied both experimentally and numerically. Bottom wall of enclosure has higher temperature than that of top wall while vertical walls are adiabatic. Inclined fin has also adiabatic boundary conditions. Numerical solutions have been done by writing a computer code in Fortran platform and results are compared with Fluent commercial code and experimental method. Governing parameters are Rayleigh numbers (8.10⁵ ≤ Ra ≤ 4 × 10⁶) and inclination angle (30° ≤ and ≤ 120°). The temperature measurements are done by using thermocouples distributed uniformly at the wall of the enclosure. Remarkably good agreement is obtained between the predicted results and experimental data. A correlation is also developed including all effective parameters on heat transfer and fluid flow. It was observed that heat transfer can be controlled by attaching an inclined fin onto wall.     

Conjugate heat transfer in the unbounded flow of a viscoelastic fluid past a sphere

This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime (Re = 0.01). The problem is numerically solved with the finite-volume method assuming axisymmetry, absence of natural convection and constant physical properties. The sphere generates heat at a constant and uniform rate, and the analysis is conducted for a range of Deborah (0 ≤ De ≤ 100), Prandtl (10⁰ ≤ Pr ≤ 10⁵) and Brinkman (0 ≤ Br ≤ 100) numbers, in the presence or absence of thermal contact resistance at the solid–fluid interface and for different conductivity ratios (0.1 ≤ κ ≤ 10). The drag coefficient shows a monotonic decrease with De, whereas the normalized stresses on the sphere surface and in the wake first increase and then decrease with De. A negative wake was observed for the two solvent viscosity ratios tested (β = 0.1 and 0.5), being more intense for the more elastic fluid. In the absence of viscous dissipation, the average Nusselt number starts to decrease with De after an initial increase. Heat transfer enhancement relative to an equivalent Newtonian fluid was observed for the whole range of conditions tested. The dimensionless temperature of the sphere decreases and becomes more homogeneous when its thermal conductivity increases in relation to the conductivity of the fluid, although small changes are observed in the Nusselt number. The thermal contact resistance at the interface increases the average temperature of the sphere, without affecting significantly the shape of the temperature profiles inside the sphere. When viscous dissipation is considered, significant changes are observed in the heat transfer process as Br increases. Overall, a simplified PTT fluid can moderately enhance heat transfer compared to a Newtonian fluid, but increasing De does not necessarily improve heat exchange.     

Forced convection from a straight elliptical tube

The paper deals with the problem of two-dimensional laminar forced convection heat transfer from a straight isothermal tube of elliptic cross-section placed in a uniform stream. The study is based on numerical solutions of the conservation equations of mass, momentum, and energy which covers the entire flow domain including the wake region. The parameters influencing the heat transfer process are essentially the Reynolds number, Re, the tube geometry represented by its minor to major axis ratio, Ar, and the angle of inclination, λ. The study focuses on the effect of Re, Ar, and λ on the heat transfer process in the range of Re from 20 to 500. The study reveals that the rate of heat transfer reaches its maximum when λ=0^∘ while the minimum occurs when λ=90^∘. The results also show that smaller axis ratio gives higher heat transfer rate when λ=0^∘. The local Nusselt number and surface vorticity distributions are plotted for a number of cases and the effect of vortex shedding on the overall rate of heat transfer is briefly discussed. Received on 20 September, 1997     

Heat transfer characteristics from in-line arrays of free impinging jets

An experimental investigation of the convective heat transfer on a flat surface in a multiple-jet system is described. A thin metal sheet was heated electrically and cooled from one side. On the other black coated side the temperature field was measured using an IR camera. Varied parameters were the jet Reynolds number in the range from 1,400 to 41,400, the normalized distance nozzle to sheet H/d from 1 to 10, and the normalized nozzle spacing S/d from 2 to 10. A geometrical arrangement of nine nozzle in-line arrays was tested. The results show that the multiple-jet system enhances the local and average heat transfer in comparison with that of a single nozzle. A maximum of the heat transfer was found for the normalized spacing S/d = 6.0. The normalized distance H/d has nearly no effect on the heat transfer in the range 2 ≤ H/d ≤ 4. The maximum average Nusselt number was correlated as a function of the jet Reynolds number      

Lattice Boltzmann simulation of heat transfer and fluid flow in a microchannel with nanofluids

Mathematical modeling is performed to simulate forced convection flow of 47 nm- Al₂O₃/water nanofluids in a microchannel using the lattice Boltzmann method (LBM). Single channel flow and conjugate heat transfer problem are taken into consideration and the heat transfer rate using a nanofluid is examined. Simulations are conducted at low Reynolds numbers (2 ≤ Re ≤ 16). The computed average Nusselt number, which is associated with the thermal conductivity of nanofluid, is in the range of 0.6 ￡ [`(Nu)] ￡ 13 0.6 \le \overline{Nu} \le 13 . Results indicate that the average Nusselt number increases with the increase of Reynolds number and particle volume concentration. The fluid temperature distribution is more uniform with the use of nanofluid than that of pure water. Furthermore, great deviations of computed Nusselt numbers using different models associated with the physical properties of a nanofluid are revealed. The results of LBM agree well with the classical CFD method for predictions of flow and heat transfer in a single channel and a microchannel heat sink concerning the conjugate heat transfer problem, and consequently LBM is robust and promising for practical applications.     

Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (Re = 2,000–5,500), angles of V corrugated plates (θ = 20°, 40°, 60°), and constant heat fluxs (q″ = 580, 830, 1,090 W/m²). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (θ) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.     

Behaviors of flow mechanisms and heat transfer of non-Newtonian fluids through a spinneret

This investigation examines non-Newtonian flow mechanisms and heat transfer characteristics for a micro spinneret. The working fluid, Polyethylene terephthalate (PET), is the raw material of micro fiber, and a large-scale experimental test model was designed to visualize the complex viscous flow system in the micro spinneret. To visualize the complex convective flow system, an experimental test model was constructed, using glycerin instead of PET. The related parameters of PET were compared with those of glycerin. The power law correlates the shear strain with PET viscosity at various temperatures. The pressure distribution along the flow direction was measured and the flow pattern was visualized using polyethylene (PE) powder of 20–40 m. Similar configurations were calculated for micro spinneret physical parameters to determine the thermal flow characteristics. The Reynolds number in the test model is not less than 10^–2. In the non-Newtonian PET working fluid of practical micro spinneret, flows with Re = 10⁴ to 10^–2 are in the same low Reynolds number flow regime. Therefore, the working fluid is expected to have the same flow characteristic. A numerical solution covering the range of approximately Re = 10^–4 at PET confirms that the flow characteristics of glycerin are constant for Re = 1.228 × 10^–2. The Peclet number in the test model can be adjusted to a value similar to that in the micro spinneret. The flow visualization was compared with that of the numerical solution, and the friction factor and Nusselt number in the micro spinneret were analyzed. Finally, numerical results and friction factor with various exit angles of micro spinneret in a triangular zone flow system were also summarized.     

Non-Darcy buoyancy driven flows in a fluid saturated porous medium: the use of asymptotic computational fluid dynamics (ACFD) approach

Natural convection in a fluid saturated porous medium has been numerically investigated using a generalized non-Darcy approach. The governing equations are solved by using Finite Volume approach. First order upwind scheme is employed for convective formulation and SIMPLE algorithm for pressure velocity coupling. Numerical results are presented to study the influence of parameters such as Rayleigh number (10⁶ ≤Ra ≤10⁸), Darcy number (10⁻⁵ ≤ Da ≤ 10⁻²), porosity (0.4 ≤ ɛ ≤ 0.9) and Prandtl number (0.01 ≤ Pr ≤ 10) on the flow behavior and heat transfer. By combining the method of matched asymptotic expansions with computational fluid dynamics (CFD), so called asymptotic computational fluid dynamics (ACFD) technique has been employed to generate correlation for average Nusselt number. The technique is found to be an attractive option for generating correlation and also in the analysis of natural convection in porous medium over a fairly wide range of parameters with fewer simulations for numerical solutions.     

An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid

We present detailed experimental results examining “negative wakes” behind spheres settling along the centerline of a tube containing a viscoelastic aqueous polyacrylamide solution. Negative wakes are found for all Deborah numbers (2.43≤De(˙γ)≤8.75) and sphere-to-tube aspect ratios (0.060≤a/R≤0.396) examined. The wake structures are investigated using laser-Doppler velocimetry (LDV) to examine the centerline fluid velocity around the sphere and digital particle image velocimetry (DPIV) for full-field velocity profiles. For a fixed aspect ratio, the magnitude of the most negative velocity, U _min , in the wake is seen to increase with increasing De. Additionally, as the Deborah number becomes larger, the location of this minimum velocity shifts farther downstream. When normalized with the sphere radius and the steady state velocity of the sphere, the axial velocity profiles become self-similar to the point of the minimum velocity. Beyond this point, the wake structure varies weakly with aspect ratio and De, and it extends more than 20 radii downstream. Inertial effects at high Reynolds numbers are observed to shift the entire negative wake farther downstream. Using DPIV to investigate the transient kinematic response of the fluid to the initial acceleration of the sphere from rest, it is seen that the wake develops from the nonlinear fluid response at large strains. Measurements of the transient uniaxial extensional viscosity of this weakly strain-hardening fluid using a filament stretching rheometer show that the existence of a negative wake is consistent with theoretical arguments based on the opposing roles of extensional stresses and shearing stresses in the wake of the sphere. Received: 10 November 1997 Accepted: 1 May 1998