Conjugate natural convection in an enclosure with a heat source of constant heat transfer rate

A numerical study of two-dimensional transient natural convection in a rectangular enclosure having finite thickness heat-conducting walls with a heat source of constant heat transfer rate located on the inner side of the left wall in conditions of convection–radiation heat exchange with an environment on one of the external boundaries has been performed. Mathematical simulation has been carried out in terms of the dimensionless variables such as stream function – vorticity – temperature. Stream function, vorticity and energy equations have been solved by finite difference numerical method. The relevant governing parameters were: the Grashof number from 10⁶ to 10⁸, the Prandtl number, Pr = 0.7 and the conductivity ratio. Detailed results including streamlines and temperature profiles have been obtained.     

Magnetoconvection in an enclosure with partially active vertical walls

Magnetoconvection of an electrically conducting fluid in a square cavity with partially thermally active vertical walls is investigated numerically. The active part of the left side wall is at a higher temperature than the active part of the right side wall. The top, bottom and the inactive parts of the side walls are thermally inactive. Nine different combinations of the relative positions of the active zones are considered. The governing equations are discretized by the control volume method with QUICK scheme and solved numerically by SIMPLE algorithm for the pressure–velocity coupling together with underrelaxation technique. The results are obtained for Grashof numbers between 10⁴ and 10⁶, Hartmann numbers between 0 and 100 and Prandtl numbers 0.054–2.05. The heat transfer characteristics are presented in the form of streamlines and isotherms. The heat transfer rate is maximum for the middle–middle thermally active locations while it is poor for the top–bottom thermally active locations. The average Nusselt number decreases with an increase of Hartmann number and increases with an increase of Grashof number. For sufficiently large magnetic field Ha = 100 the convective mode of heat transfer is converted into conductive mode in the low region of Grashof number than in the high region.     

MIXED CONVECTION HEAT TRANSFER IN A TEE BRANCH

The heat transfer characteristics of a Newtonian fluid in a two-dimensional, planar, right-angled tee branch are studied over a range of inlet Reynolds numbers and Grashof numbers. The flow and heat transfer equations, subject to the Boussinesq approximation, are solved using a finite-element discretization. The effects of the branch length and the grid size on the interior flow field are examined to assess the accuracy of the solutions. Results are presented for two types of experimentally realizable boundary conditions—equal exit pressure at the outlet of each branch and specified flow split between the branches. The thermal boundary condition of uniform wall temperature is examined. The effect of increasing Reynolds number is to increase the size and strength of the recirculation zones in both the main and side branches, while that of increasing Grashof number is to decrease such an effect. For the case of equal exit pressures there is a significant flow reversal in the side branch and the exit flow rate from the main branch increases linearly with increasing Gr/Re². For the case of specified flow split, an increasing back pressure is required to be maintained at the exit of the main branch to regulate the flow split at the desired level.     

Transient study of buoyancy-assisted mixed convection in laminar plane wall jet flow

A numerical investigation of two-dimensional transient buoyancy-assisted laminar plane wall jet flow has been conducted. The governing equations in the stream function-vorticity formulation have been solved by alternating direction implicit (ADI) method. The parameters used are Grashof number 10⁴ − 10⁷, Prandtl number 0.01, 0.71, 7.1, 10.0 and 15.0 with a constant Reynolds number 400. The plate is considered at a higher temperature and the fluid is assumed to be initially at a uniform cold temperature. The streamline, u-velocity and the isotherm contours are presented at different time levels. The time required for the average Nusselt number to attain a steady-state value decreases with increase in Grashof number.     

SIMULATION OF MIXED CONVECTION HEAT TRANSFER AT THE WALL OF A PACKED BED

Numerical investigations of the effect of mixed convection on the fluid flow pattern and heat transfer at the boundary layer of a packed bed are reported. A volume-averaged Navier-Stolces equation incorporating the Boussinesq approximation is used to predict the fluid flow, and a volume-averaged heat balance equation, the heat transfer. An exponential variation in the porosity of the packing is assumed in the region near the wall. Simulations are performed using a modified penalty Galerkin finite-element method. The Nusselt number is found to depend on the Grashof to Reynolds number ratio, Graetz number, and ratio of thermal conductivity of the solid and fluid phases. The heat transfer rate is enhanced by a positive Grashof number and hindered by a negative value. The velocity and temperature profiles in the bed are also found to be strong functions of the Gr/Re² ratio. At higher values of this ratio the flow becomes unsteady     

A numerical study of three-dimensional laminar mixed convection past an open cavity

A numerical study has been carried out to analyze the effects of mixed convective flow over a three-dimensional cavity that lies at the bottom of a horizontal channel. The vertical walls of the cavity are isothermal and all other walls are adiabatic. The cavity is assumed to be cubic in geometry and the flow is laminar and incompressible. A direct numerical simulation is undertaken to investigate the flow structure, the heat transfer characteristics and the complex interaction between the induced stream flow at ambient temperature and the buoyancy-induced flow from the heated wall over a wide range of the Grashof number (10³–10⁶) and two Reynolds numbers Re = 100 and 1000. The computed thermal and flow fields are displayed and discussed in terms of the velocity fields, streamlines, the temperature distribution and the averaged Nusselt number at the heated and cooled walls. It is found that the flow becomes stable at moderate Grashof number and exhibit a three-dimensional structure, while for both high Reynolds and Grashof numbers the mixed convection effects come into play, push the recirculating zone further upstream and the flow becomes unsteady with Kelvin–Helmholtz instabilities at the shear layer.     

A numerical study of turbulent flow and conjugate heat transfer in concentric annuli with moving inner rod

A numerical study is conducted to investigate turbulent flow and conjugate heat transfer in a concentric annulus with a heated inner cylinder moving in the streamwise direction. A modified two-equation k-ε model with low Reynolds number treatment near wall is employed to model the Reynolds stress and turbulent thermal field which are based on Boussinesq’s approximation. The governing equations are numerically resolved by means of a hybrid finite analysis method. A uniform inlet flow and thermal conditions are specified to consider the effects of entrance of both solid and fluid regions. For a constant Prandtl number of 6.99 of water flow, calculating results of the time-averaged streamwise velocity, turbulent viscosity and temperature field are obtained for the Reynolds numbers from 1.0 × 10⁴ to 5.0 × 10⁵, rod velocity ratio between 0 and 1.0, and the radius ratio ranging from 0.286 to 0.750. The parametric studies show that the bigger rod speed ratio or the radius ratio is, the temperature is higher within solid rod. For a certain absolute rod speed, temperature profile diminishes at both sides of solid rod and fluid as Reynolds number grows. Numerical results also show that compared with the case of β=0 where solid rod is stationary, for large rod speed ratio the averaged axial velocity and turbulent viscosity profiles have substantial deformations, that is, the gradient of averaged axial velocity and turbulent viscosity near rod surface greatly reduced by the axial movement of solid rod.     

Natural-Convection Heat Transfer in Channels With Isoflux Convex Surfaces

Numerical solutions are presented for laminar natural convection heat transfer in channels with convex surfaces that are subjected to a uniform heat flux. Simulations are conducted for several values of Grashof number (10 to 10⁴) and radius of curvature (1 to ∞). The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a collocated control-volume-based numerical procedure. The results are presented in terms of streamline and isotherm plots, inlet mass flow rates, curved wall temperature profiles, maximum hot wall temperature estimates, and average Nusselt number values. At the lowest radius of curvature, computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. For a radius of curvature equal to or greater than 2, recirculation does not occur at any Grashof number. For values of radius of curvature between 1 and 2, the value of Grashof number at which recirculation occurs decreases with increasing values of the former. The variation in the buoyancy-induced volume flow rate is highly nonlinear with respect to the radius of curvature, and the value of the radius of curvature at which the volume flow rate is maximum increases with increasing Grashof number. The value of radius of curvature at which the maximum hot wall temperature is minimized increases with Grashof number. For all configurations studied, the average Nusselt number increases with increasing Grashof number values. Correlations for maximum wall temperature and average Nusselt number are provided.     

Investigation on the characteristics and mechanisms of unusual heat transfer of supercritical pressure water in vertically-upward tubes

The heat transfer characteristics of supercritical pressure water in a vertically-upward optimized internally-ribbed tube was investigated experimentally to study the mechanisms of unusual heat transfer of supercritical pressure water in the so-called large specific heat region. The experimental parameters were as follows. The pressure at the inlet of the test section ranged from 22.5 to 29.0 MPa, and the mass flux of the fluid was from 650 to 1200 kg/m² s, and the heat flux on the inside wall of the tube varied from 200 to 660 kW/m². According to experimental data, the characteristics of heat transfer enhancement and also the heat transfer deterioration of supercritical pressure water in the large specific heat region was analyzed and based on the comparison and analysis of the current major theories that were used to explain the reasons for unusual heat transfer to occur, the mechanisms of heat transfer enhancement and deterioration were discussed, respectively. The enhanced heat transfer was characterized by the gently changing wall temperature, the small temperature difference between the inside-tube-wall and the bulk fluid and the high heat transfer coefficient in comparison to the normal heat transfer. The deteriorated heat transfer could be characterized by the sharply increasing wall temperature, the large temperature difference and a sudden decrease in heat transfer coefficient in comparison to the normal heat transfer. The heat transfer enhancement of the supercritical pressure water in the large specific heat region was suggested to be a result of combined effect caused by the rapid variations of thermophysical properties of the supercritical pressure water in the large specific heat region, and the same was true of the heat transfer deterioration. The drastic changes in thermophysical properties near the pseudocritical points, especially the sudden rise in the specific heat of water at supercritical pressures, might result in the occurrence of the heat transfer enhancement, while the covering of the heat transfer surface by fluids lighter and hotter than the bulk fluid made the heat transfer deteriorated eventually and explained how this lighter fluid layer formed.     

Laminar conjugate mixed convection in a vertical channel with heat generating components

Conjugate mixed convection arising from protruding heat generating ribs attached to substrates (printed circuit boards) forming channel walls is numerically studied. The substrates with ribs form a series of vertical parallel plate channels. Assuming identical disposition and heat generation of the ribs on each board, a channel with periodic boundary conditions in the transverse direction is considered for analysis. The governing equations are discretised using a control volume approach on a staggered mesh and a pressure correction method is employed for the pressure–velocity coupling. The solid regions are considered as fluid regions with infinite viscosity and the thermal coupling between the solid and fluid regions is taken into account by the harmonic thermal conductivity method. Parametric studies are performed by varying the heat generation based Grashof number in the range 10⁴–10⁷ and the fan velocity based Reynolds number in the range 0–1500, with air as the working medium. Results are obtained for the velocity and temperature distributions, natural convection induced mass flow rate through the channel, the maximum temperatures in the heat sources and the local Nusselt numbers. The natural convection induced mass flow rate in mixed convection is correlated in terms of the Grashof and Reynolds numbers. In pure natural convection the induced mass flow rate varies as 0.44 power of Grashof number. The maximum dimensionless temperature is correlated in terms of pure natural convection and forced convection inlet velocity asymptotes. For the parameter values considered, the heat transferred to the working fluid via substrate heat conduction is found to account for 41–47% of the heat removal from the ribs.     

Magnetoconvection in a square cavity with partially active vertical walls: Time periodic boundary condition

Magnetoconvection of an electrically conducting fluid in a square cavity with partially thermally active sidewalls is investigated numerically. Temperature of one of the thermally active regions of the side walls is periodic in time while the opposite wall is isothermal. The horizontal walls and the remaining parts of the side walls are thermally inactive. Nine different combinations of the relative positions of the active zones are considered. The governing equations are discretized by the control volume method with QUICK scheme and solved numerically by SIMPLE algorithm for the pressure–velocity coupling together with under relaxation technique. The tests were carried out for various values of amplitude, period, Grashof number, Hartmann number and Prandtl number. The heat transfer characteristics are presented in the form of streamlines, isotherms and velocity profiles both for transient and steady state. It is observed that the flow and the heat transfer rate in the cavity are affected by the sinusoidal temperature profile and by the magnetic field at lower values of Grashof number. The rate of heat transfer oscillates for increasing periods but it is maximum for Ω = 3 and it is found to be an increasing function of amplitude but decreases for higher values of Hartmann number. The heat transfer rate is maximum for the middle–middle thermally active locations while it is poor for the top heating and bottom cooling active locations. The average Nusselt number decreases with an increase of Hartmann number and increases with increase of Prandtl number and Grashof number.     

Investigation effect of nanoparticle mean diameter on mixed convection Al2O3-water nanofluid flow in an annulus by two phase mixture model

In this paper, laminar mixed convection of nanofluid (Al₂O₃–water) in horizontal concentric annulus with constant heat flux boundary condition has been studied. Two thermal boundary conditions were investigated, one in which a uniform heat flux at the inner wall and an adiabatic at the other wall, and the other inner and outer walls were heated in a same heat flux. Two phase mixture model employed to investigate effect of mean diameter of nanoparticle on the hydrodynamics and thermal characteristic. The fluid flow properties are assumed constant except for the density in the body force, which varies linearly with the temperature (Boussinesq's hypothesis), thus the fluid flow characteristics are affected by the buoyancy force. Three dimensional elliptical governing equations have been discretized using the finite volume approach (FVM) using SIMPELC algorithm to investigate fluid flow throughout of an annulus duct. Numerical simulations have been carried out for the nanoparticle volume fraction (ϕ = 0.02) and various mean diameters of nanoparticles (d_p) between 13 and 72 nm and different values of the Grashof and Reynolds numbers. The calculated results demonstrate that Nusselt number decreases with increasing nanoparticle mean diameter while it does not influence significantly the hydrodynamic parameters. Also this results show that nanoparticle distribution at the annuluses cross section is non-uniformity.     

Three-dimensional laminar flow and heat transfer in a parallel array of microchannels etched on a substrate

Heat transfer and laminar fluid flow in an array of parallel microchannels etched on a silicon substrate with water as the circulating fluid was studied numerically. The fluid region consisted of a microchannel with a hydraulic diameter of 85.6 μm and aspect ratios ranging from 0.10 to 1.0. A constant heat flux of 90 W/cm² was applied to the y = H face of the computational domain, which simulates thermal energy generation from an integrated circuit. Generalized transport equations were discretized and solved in three dimensions for velocities, pressure, and temperature. The SIMPLE algorithm [S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980] was used to link pressure and velocity fields, and a thermally repeated boundary condition was applied in the lateral direction to model the repeating nature of the geometry. The numerical results for apparent friction coefficient and convective thermal resistance at the channel inlet and exit closely matched the experimental data in the literature for the case of 0.32 aspect ratio. Apparent friction coefficients were found to increase linearly with Reynolds number. Inlet and outlet thermal resistance values monotonically decreased with increasing Reynolds number and increased with aspect ratio.     

Investigation of mixed convection heat transfer in a horizontal channel with discrete heat sources at the top and at the bottom

Mixed convection heat transfer from arrays of discrete heat sources inside a horizontal channel has been investigated experimentally. Each of the lower and upper surfaces of the channel was equipped with 8 × 4 flush mounted heat sources subjected to uniform heat flux. Sidewalls, lower and upper walls are insulated and adiabatic. The experimental parametric study was made for aspect ratios of AR = 2, 4 and 10, at various Reynolds and Grashof numbers. From the experimental measurements, row-average surface temperature and Nusselt number distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these numbers were investigated. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that top and bottom heater surface temperatures increase with increasing Grashof number. The top heater average-surface temperatures for AR = 2 are greater than those of bottom ones. For high values of Grashof numbers where natural convection is the dominant heat transfer regime (Gr¹/Re² ≫ 1), temperatures of top heaters can have much greater values. The variation of the row-average Nusselt numbers for the aspect ratio of AR = 4, show that with the increase in the buoyancy affected secondary flow and the onset of instability, values of Nusselt number level off and even rise as a result of heat transfer enhancement especially for low Reynolds numbers.     

Numerical analysis of Grashof number,Reynolds number and inclination effects on mixed convection heat transfer in rectangular channels

Mixed convection heat transfer in rectangular channels has been investigated computationally 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. Solutions were obtained for Pr=0.7, inclination angles 0° ≤ θ ≤ 90°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr = 7.0×10⁵ to 4.0×10⁶. The three-dimensional elliptic governing equations were solved using a finite volume based computational fluid dynamics (CFD) code. From a 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 obtained from the simulations are compared with the literature and a parallel conducted experimental study, from which a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle.     

Free Convective Flow in an Open‐Ended Vertical Porous Wavy Channel with a Perfectly Conductive Thin Baffle

The problem of steady two‐dimensional free convective flow of a Walters fluid (model B ′) in a porous medium between a long vertical wavy wall and parallel flat wall in the presence of a heat source is discussed. The channel is divided into two passages by means of a thin, perfectly conductive plane baffle and each stream will have its own pressure gradient and hence the velocity will be individual in each stream. The governing equations of the fluid and the heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and disturbance or perturbed part. Exact solutions are obtained for the mean part and the perturbed part is solved using long wave approximation. Results are presented graphically for the distribution of velocity and temperature fields for varying physical parameters such as Grashof number, wall temperature ratio, porous parameter, heat source/sink parameter, product of non‐dimensional wave number, and space‐coordinate and viscoelastic parameter at different positions of the baffle. The relevant flow and heat transfer characteristics, namely, skin friction and the rate of heat transfer at both walls, has been discussed in detail. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21118     

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.     

Numerical study of hydrodynamic and heat transfer of nanofluid flow in microchannels containing micromixer

In this study heat transfer and fluid flow of Al₂O₃/water nanofluid in two dimensional parallel plate microchannel without and with micromixers have been investigated for nanoparticle volume fractions of ϕ = 0, ϕ = 4%  and base fluid Reynolds numbers of Re_f = 5, 20, 50. One baffle on the bottom wall and another on the top wall work as a micromixer and heat transfer enhancement device. A single-phase finite difference FORTRAN code using Projection method has been written to solve governing equations with constant wall temperature boundary condition. The effect of various parameters such as nanoparticle volume fraction, base fluid Reynolds number, baffle distance, height and order of arrangement have been studied. Results showed that the presence of baffles and also increasing the Re number and nanoparticle volume fraction increase the local and averaged heat transfer and friction coefficients. Also, the effect of nanoparticle volume fraction on heat transfer coefficient is more than the friction coefficient in most of the cases. It was found that the main mechanism of enhancing heat transfer or mixing is the recirculation zones that are created behind the baffles. The size of these zones increases with Reynolds number and baffle height. The fluid pushing toward the wall by the opposed wall baffle and reattaching of separated flow are the locations of local maximum heat transfer and friction coefficients.     

Effect of surfactant addition on boiling heat transfer in a liquid film flowing in a diverging open channel

An experimental study was conducted to investigate how the addition of small amounts of a surfactant influences the heat transfer characteristics in a thin boiling liquid film flowing in a diverging open channel. Heat transfer experiments were conducted with fluid inlet temperatures from 40 °C to 92 °C. The flow field on the plate included thin film supercritical flow upstream of a hydraulic jump and thick film subcritical flow downstream of a hydraulic jump. Nusselt numbers for the non-boiling heat transfer without surfactant addition scaled linearly with the film Reynolds number. The boiling heat transfer produced higher Nusselt numbers with a weaker dependence on the Reynolds number. Experimental results showed that a boiling surfactant solution created a thick foam layer with high heat transfer rates and Nusselt numbers that are very weakly dependent on the inlet flow rate or the inlet Reynolds number.     

Constructal design and thermal analysis of microchannel heat sinks with multistage bifurcations in single-phase liquid flow

Based on constructal theory, five different cases with multistage bifurcations are designed as well as one case without bifurcations, and the corresponding laminar fluid flow and thermal performance have been investigated numerically. All laminar fluid flow and heat transfer results are obtained using computation fluid dynamics, and a uniform wall heat flux thermal boundary condition is applied all heated surfaces. The inlet velocity ranges from 0.66 m/s to 1.6 m/s with the corresponding Reynolds number ranging from 230 to 560. The pressure, velocity, temperature distributions and averaged Nusselt number are presented. The overall thermal resistances versus inlet Reynolds number or pumping power are evaluated and compared for the six microchannel heat sinks. Numerical results show that the thermal performance of the microchannel heat sink with multistage bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sink with a long bifurcation length in the first stage (Case 1A) is superior. The usage of multistage bifurcated plates in microchannel heat sink can reduce the overall thermal resistance and make the temperature of the heated surface more uniform (Case 3). It is suggested that proper design of the multistage bifurcations could be employed to improve the overall thermal performance of microchannel heat sinks and the maximum number of stages of bifurcations is recommended to be two. The study complements and extends previous works.