Natural convection heat transfer by heated partitions within enclosure

In this study, natural convection heat transfer and fluid flow of two heated partitions. within an enclosure have been analysed numerically. The right side wall and the bottom wall of the enclosure were insulated perfectly while the left side wall and top wall were maintained at the same uniform temperature. The partitions were placed on the bottom of the enclosure and their temperatures were kept higher than the non-isolated walls. The effects of position and heights of the partitions on heat transfer and flow field have been investigated. Computations for Rayleigh number in the range of 10⁴ and 10⁶ have been conducted. Using the control volume approach, finite difference equations are obtained with non-staggered grid arrangement, a computer program based on the SIMPLEM algorithm was developed. The finite difference equations were solved iteratively with a line-by-line Thomas algorithm.     

Entropy generation analysis in a uniformly heated microchannel heat sink

Present investigation analyzes the issue of entropy generation in a uniformly heated microchannel heat sink (MCHS). Analytical approach used to solve forced convection problem across MCHS, is a porous medium model based on extended Darcy equation for fluid flow and two-equation model for heat transfer. Simultaneously, closed form velocity solution in a rectangular channel is employed to capture z-directional viscous effect diffusion and its pronounced effect on entropy generation through fluid flow. Subsequently, governing equations are cast into dimensionless form and solved analytically. Second law analysis of problem is then conducted on the basis of obtained velocity and temperature fields and expressions for local and average entropy generation rate are derived in dimensionless form. Average entropy generation rate is then utilized as a criterion for assessing the system performance. Finally, the effect of influential parameters such as, channel aspect ratio (α_S), group parameter (Br/Ω), thermal conductivity ratio (C) and porosity (ε) on thermal and total entropy generation is investigated. In order to examine the accuracy of the analysis, the results of thermal evaluation are compared to one of the previous investigations conducted for thermal optimization of MCHS.     

Temperature distribution in a rectangular plate heated by a moving heat source

In this paper, a solution to the problem of heat conduction in a rectangular plate subjected to the activity of a moving heat source is presented. The temperature of the plate changes because a limited area on the plate surface is heated by a heat source. The heat source moves along an elliptical trajectory which always remains within the plate area. An exact solution to the problem in an analytical form is obtained by applying the Green’s function method. Exemplary results of numerical calculations to determine the temperature distribution in the plate are presented.     

Resonance of natural convection in a side heated enclosure with a mechanically oscillating bottom wall

An experimental study has been implemented to elucidate a resonance of natural convection in a side-heated enclosure with a mechanically oscillating bottom wall. The impetus of the present study is to provide an experimental verification of the resonant frequency of natural convection that has been numerically predicted so far. The experimental results show that the amplitude of fluctuating air temperature inside the enclosure peaks at a particular frequency of the bottom wall oscillation, which is indicative of resonance. The resonant frequency increases with the increase of the system Rayleigh number and it is little affected by the increase of forcing amplitude. The resonant frequency measured in the present experiment is in good accordance with the previous numerical predictions in which the models are based on the degree of thermal stratification in the interior.     

Natural convective heat transfer in uniformly heated vertical pipe annuli

Natural convective heat transfer in vertical concentric pipe annuli is investigated both numerically and experimentally for a fluid having a Prandtl number of 0.7. Numerical calculations for three cases of different heating conditions for pipes (heated inner pipe, heated outer pipe, both pipes heated) are made of laminar flows for different inner‐to‐outer‐pipe diameter ratios d_i/d_o from 0.2 to 0.8. For each case, the thermal entrance length x/b at the modified Grashof numbers Gr^*=10² to 5 × 10⁵ is well correlated with Grashof number Gr^* and annulus length to clearance ratio L/b. Local Nusselt numbers Nu_i and Nu_o in the thermally fully developed region have certain constant values dependent on the diameter ratio d_i/d_o, regardless of Gr^* and L/b. Average Nusselt numbers Nu_i and Nu_o in the thermal entrance region are also independent of Gr^* and L/b. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 676–688, 2001     

Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 10⁵ to 10⁸ with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed except for the density where Boussinesq’s approximation has been considered. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh number with corrugation amplitude and frequency.     

Experimental study on melting in a rectangular enclosure heated below with discrete heat sources

lntroductionSolid-liquid phase change hed transfer involvingmelhng and solidification has received considerableattenhon for many years because of its wide-rangingaPplicationsI']. Generall speaking, there are tWo kindsof melting phenomena: fixed melting"l and contactmelhng[',]. In the case of fixed mehng, the solid phasechange material is forced to rehan stahonary and themelted liquid takes up the space betWeen the solid-liquldinteiface and the hea source schce. In the case ofcontaCt melhng,…     

A numerical simulation of heat transfer in an enclosure with a nonlinear heat source

Two-dimensional simulations of natural convection driven by the absorption of nonuniform concentrated solar radiation in a molten binary salt-filled enclosure inclined at 0?≤???≤?60 are presented. The enclosure is volumetrically heated from the top boundary and accommodates a black rigid, heat-conducting plate of finite thickness at the lower boundary, which aids in the generation of natural convective mixing at the lower boundary. The governing equations that account for the depth-dependent absorption of radiation are solved using the finite-element method. Numerical results reveal that increasing the inclination angles decreases the natural convection and higher Rayleigh promotes natural convection.     

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.     

Experimental study of conjugate heat transfer within a bottom heated vertical concentric cylindrical enclosure

In this research work an experimental study of conjugate heat transfer within an air filled bottom-heated vertical enclosure is conducted. The enclosure consists of two concentric cylinders with inner cylinder being shorter and open at the top. The study is important with respect to the centrifuge machine used in the process industry. Eighteen different experiments are performed by varying the bottom disc central temperature between 353 and 433 K, using three different materials (aluminum, mild steel and stainless steel) of the inner cylinder and two different diameter outer cylinders of mild steel. This study unfolds the temperature, material and geometric effects of bottom disc, inner cylinder and outer cylinder respectively on thermal convection in the enclosure. Generally, a uniform temperature is required in such enclosures. A more uniform axial and radial temperature is observed in the enclosure by using aluminum inner cylinder within a temperature range of 353–433 K of the bottom disc and using two different diameter outer cylinders. It is observed that the maximum temperature in the enclosure is lowest for aluminum inner cylinder and higher for mild steel and highest for stainless steel. The heat balance and non-dimensional analysis of the enclosure are carried out and discussed critically.     

Flow structure and heat transfer in a lower half heated and upper half cooled rectangular enclosure

This paper presents an experimental and numerical investigation on the natural convection in a rectangular enclosure with lower-half-heated, upper-half-cooled sidewalls. The flow structure contains thin wall-layers and large central vortical circulating zones. The mixing process and the fluid paths caused by the wall-layer head-on collisions and stream–stream interaction are fundamental to the development of the heat and fluid transport mechanisms. The understanding of the flow structures and their mutual interaction provides a guide leading to the optimization of the autoclave internal architecture and to practical suggestions for the design strategy of crystal growth vessels.     

Natural convection of water-based nanofluids in an inclined enclosure with a heat source

This study investigates natural convection heat transfer of water-based nanofluids in an inclined square enclosure where the left vertical side is heated with a constant heat flux, the right side is cooled, and the other sides are kept adiabatic. The governing equations are solved using polynomial differential quadrature (PDQ) method. Calculations were performed for inclination angles from 0° to 90°, solid volume fractions ranging from 0% to 20%, constant heat flux heaters of lengths 0.25, 0.50 and 1.0, and a Rayleigh number varying from 10⁴ to 10⁶. The ratio of the nanolayer thickness to the original particle radius is kept at a constant value of 0.1. The heat source is placed at the center of the left wall. Five types of nanoparticles are taken into consideration: Cu, Ag, CuO, Al₂O₃, and TiO₂. The results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. The results also show that the length of the heater is also an important parameter affecting the flow and temperature fields. The average heat transfer decreases with an increase in the length of the heater. As the heater length is increased, the average heat transfer rate starts to decrease for a smaller inclination angle (it starts to decrease with inclination at 90° for ? = 0.25, 60° for ? = 0.50, 45° for ? = 1.0, respectively).     

Melting of a semi-infinite solid with a volume distributed substrate heat source

The analysis of the melting of a semi-infinite slab initially at its melting temperature with a heat source, volume distributed within a supporting substrate layer, is performed by the heat balance integral method.     

辐射侧加热腔内自然对流传热特性研究

为了明确辐射侧加热封闭方腔内半透明流体的自然对流传热现象及规律,采用有限体积法进行数值模拟研究,分析了瑞利数和光学厚度对流场、温度场以及传热特性的影响。结果表明：与传统侧壁加热腔内自然对流相比,辐射侧加热腔内等温线和流场分布规律不一致;随着瑞利数和光学厚度增加,涡心由中心位置沿直线向辐射入射侧斜上方偏移;随着瑞利数增加,等温线变得更均匀;随着光学厚度增加,等温线变密,努塞尔数Nu与瑞利数RaT的标度律指数减小,当光学厚度增加到一定时标度律不再变化,此时传热标度律与传统恒壁温侧加热腔内自然对流相当,满足Nu~Ra0.29T。     

Combined forced and natural convection heat transfer for upward flow in a uniformly heated,vertical pipe

For predicting the fully developed upward flow in a uniformly heated, vertical pipe by taking account of the buoyancy force, the k-ε models of turbulence for low Reynolds number flows were adopted. The regime map for forced, mixed and natural convections as well as for laminar and turbulent flows was plotted from the numerical predictions. At the same time, experiments were carried out at Reynolds numbers of 3000 and 5000, with the Grashof number varying over a wide range, by using pressurized nitrogen gas as a test fluid. In agreement with the prediction, buoyancy-induced impairment of heat transfer was correctly measured in the mixed convection regime. Furthermore, from hot-wire measurements, complete laminarization was demonstrated in the mixed-convection region at a Reynolds number of 3000.     

Transient natural convective heat transfer from a heated triangular cylinder to its air-filled coaxial cylindrical enclosure

A numerical study of transient natural convection inside an air-filled horizontal cylinder with a coaxial inner triangular cylinder is performed with the Prandtl number and aspect ratio being fixed at 0.72 and 2.0, respectively. The effects of two different positions of the inner triangular cylinder and Grashof number are examined. The predicted development of the convective flow and heat transfer is presented by means of snapshots of streamlines and isotherms. It is shown that the flow development can be representatively classified into several stages based on time histories of the average Nusselt number over the outer circular cylinder. The time-averaged Nusselt number is scaled with Grashof number of power 0.21–0.24 and time duration for attaining a steady/quasi-steady state is also correlated to Grashof number.     

Natural convection in uniformly heated vertical annuli

A numerical study of natural convection through vertical annuli with one wall uniformly heated and the other wall adiabatic was made. In this study the boundary layer simplifications of the NavierStokes equations for developing laminar flow with constant properties were solved by means of a finite difference method. Three radius ratios (0.26, 0.5 and 0.9) were investigated. The different variables (velocity, pressure defect, temperature, etc.) were determined. An apparatus was built to check the obtained numerical results for one of the conditions employed. Agreement between the theoretical and experimental values was good.     

Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations

In this model, a numerical study of two dimensional steady natural convection is performed for a uniform heat source applied on the inner circular cylinder in a square air (Pr = 0.7) filled enclosure in which all boundaries are assumed to be isothermal (at a constant low temperature). The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of vertical cylinder locations and Rayleigh numbers on fluid flow and heat transfer performance are investigated. Rayleigh number is varied from 10³ to 10⁶ and the location of the inner cylinder is changed vertically along the centerline of the enclosure from − 0.25 L to 0.25 L upward and downward, respectively. It is found that at small Rayleigh numbers does not have much influence on the flow field while at high Rayleigh numbers have considerable effect on the flow pattern. In addition, the numerical solutions yield a two cellular flow field between the inner cylinder and the enclosure. Also, the total average Nusselt number behaves nonlinearly as a function of locations. Results are presented in terms of the streamlines, isotherms, local and average Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.     

The structure of a double-diffusive interface in a laterally heated enclosure

Experiments are carried out to investigate the structure of a double diffusive interface separating two layers in a laterally heated enclosure. Due to the differential heating of the enclosure sidewalls, a circulating flow is induced in each layer such that the interface is simultaneously exposed to a velocity shear and double diffusive convection. The main goal of this work is to study the structure of the interface and some of its instability characteristics. The experiments are carried out in a box with inner length, width and height dimensions of 100 × 100 × 92 mm. The velocity field at the vicinity of the interface is measured by a PIV system. Vertical concentration and temperature profiles are measured using a micro-scale conductivity/temperature instrument and the flow is visualized using the schlieren technique. Analysis of mean horizontal velocity profiles, obtained at different times during the experiment, illustrates the increasing tilt of the interface with time. Spectral analyses of velocity perturbations under unstable and stable conditions confirm the existence of the coherent vortices observed by the schlieren technique. The vortices above and below the interface are associated with different dominant frequencies due to the asymmetric character of the flow. Measurements show that the vortices are generated outside the region of the stabilizing concentration profile by a mechanism, which is essentially thermal and similar to Rayleigh–Bénard instability with weak shear.