Transient Natural Convection Heat Transfer Research Articles

New correlation for transient laminar natural convection heat transfer in a differentially heated square cavity between air and a PCM layer

New correlation for transient laminar natural convection heat transfer in a differentially heated square cavity between air and a PCM layer

Transient natural convection flows and heat transfer in a thermally stratified air-filled trapezoidal cavity

This paper focuses on studying the transient behavior of natural convective heat and fluid flow in a two-dimensional trapezoidal cavity subjected to a heated bottom surface, cooling from the top, and thermally stratified inclined surfaces. The Finite Volume (FV) method is employed to numerically simulate the transient flow. The study considers a thermally stratified environment with a Prandtl number of Pr set to 0.71 (for stratified air), an aspect ratio (A) of 0.5, and a large array of Rayleigh numbers (Ra) ranging from 100 to 108. The research examines how the Rayleigh numbers affect the flow structures, transient phenomena, and heat transfer (HT) characteristics within the cavity. The transitional flow reveals several supercritical bifurcations. These include a changeover from symmetric to asymmetric states known as a Pitchfork bifurcation, as well as a shift from a steady-state to a periodic state referred to as a Hopf bifurcation. The Pitchfork bifurcation happens between Ra values of 105 and 2 × 105, while the Hopf bifurcation happens within the range of the Ra values from 4.7 × 105 to 4.8 × 105. Moreover, another bifurcation from a periodic to a chaotic state is observed between Ra of 3 × 107 and 4 × 107. To examine the transient flows during the changeover to chaos, various techniques such as power spectral density (PSD), limit points, limit cycles, trajectory in phase space, and the largest Lyapunov exponent (LLE) are used. Furthermore, convective heat transfer is computed, and its corresponding impact on the Ra values is explained. The flow phenomena within the cavity are measured and verified.

Collaborative optimization of intersectional angle and installation height of branched fin for ameliorating melting characteristics of lowly thermal conductive phase change materials (PCMs)

Energy storage systems based on phase change materials (PCMs) have become reliable methods to alleviate energy shortages and adjust energy structure. Optimizing fin structure parameters has a vital impact on improving the equivalent thermal conductivity of PCMs and enhancing thermal charging performance. In this numerical investigation, collaborative optimization of intersectional angle and installation height of branched fin on melting of organic PCMs have been systematically studied to coordinate transient thermal conduction and natural convective heat transfer thus ameliorating melting characteristics. Results clarify that optimizing intersectional angle between adjustable fin and horizontal direction can shorten total melting time by 9.39% and ameliorate the average heat transfer rate during melting by 11.07% compared to the case of 0o intersectional angle. These improvements are dependent of installation height of adjustable fin. Meanwhile, average heat transfer rate during melting induced by optimizing intersectional angle is enhanced by 2.77% compared with that caused by optimal orthogonal fins. Moreover, optimum intersectional angle is significantly depended on installation height. A linear correlation between optimum intersectional angle and installation height is obtained. The reliability and rationality of the correlation is confirmed. Effective guidelines for designing optimum branched fin to improve melting performance of organic PCMs are consequently acquired.

Experimental Study of Natural Convection Heat Transfer in Confined Porous Media Heated From Side

Transient three-dimensional natural convection heat transfer due to the influences of heating from one side of an enclosure filled with a saturated porous media, whereas the opposite side is maintained at a constant cold temperature, and the other four sides are adiabatic, were investigated in the present work experimentally. Silica sand was used as a porous media saturated with distilled water filled in a cubic enclosure heated from the side,using six electrical controlled heaters, at constant temperatures of (60, 70, 80, 90, and 100oC). The inverse side cooled at a constant temperature of (24oC) using an aluminum heat exchanger, consisted of 15 channels feeded with constant temperature water. Eighty thermocouples were used to control the heated and cooled sides, and to measure the temperature in the entire enclosure. Experimental results showed that the heat transfer regime was mainly conduction for all Rayleigh numbers with small influence of convection for Ra=42 and greater for Ra=55. This effect increased with the angle of inclination of the enclosure. Numerical and experimental results showed a good agreement. There was a rapid increase in the temperature at the entire media at the early time, reduced gradually until the steady state condition reached. This temperature and heat transfer to and from the porous media, were increased as the Rayleigh number and/or inclination angle increased. The Nusselt number increased directly with the angle of inclination up to o θ = 45 and then decreased. Correlation equations are obtained from the experimental investigation, showed the change of the average and local Nusselt number with time, distance, Rayleigh number, and the inclination angle.

Transient natural convective heat transfer and fluid flow in an undulated cavity: Effects of localized heat sources

AbstractThe purpose of this research work is to investigate two‐dimensional transient natural convective heat transfer and fluid flows in an undulated cavity by placing solid objects with isolated heated surfaces on the bottom wall. We discretize the coupled nonlinear transport equations using a higher‐order compact finite‐difference scheme. First, we test our scheme using existing experimental and numerical data. Then, we analyze the transient and steady‐state natural convective flow phenomena for distributed heat sources on corrugations on the lower wall for a range of the Rayleigh number and Prandtl number . These simulated outcomes are presented in the form of central‐line velocity , local and averaged Nusselt numbers, streamlines , dispersion of isotherms , and so forth. It is found that the transient fluid flow behavior is more magnificent than the steady‐state solutions and shows the dominant behavior of the prominent primary cells over secondary cells, where it influences the heat transfer rates inside the entire enclosure. In steady states, at high Rayleigh numbers; convection dominates, formation of thermal boundary layers, compression of isotherms, and stratification of isotherms are significantly observed. Our results show many interesting flow phenomena that have not been analyzed previously.

Heat Transfer by Natural Convection in a Square Enclosure Containing PCM Suspensions

Research on using phase change material (PCM) suspension to improve the heat transfer and energy storage capabilities of thermal systems is booming; however, there are limited studies on the application of PCM suspension in transient natural convection. In this paper, the implicit finite difference method was used to numerically investigate the transient and steady-state natural convection heat transfer in a square enclosure containing a PCM suspension. The following parameters were included in the simulation: aspect ratio of the physical model = 1, ratio of the buoyancies caused by temperature and concentration gradients = 1, Raleigh number (RaT) = 103–105, Stefan number (Ste) = 0.005–0.1, subcooling factor (Sb) = 0–1.0, and initial mass fraction (or concentration) of PCM particles (ci) = 0–0.1. The results showed that the use of a PCM suspension can effectively enhance heat transfer by natural convection. For example, when RaT = 103, Ste = 0.01, ci = 0.1, and Sb = 1, the steady-state natural convection heat transfer rate inside the square enclosure can be improved by 70% compared with that of pure water. With increasing Sb, the Nusselt number can change nonlinearly, resulting in a local optimal value.

Transient conjugate natural convection heat transfer in a differentially-heated square cavity with a partition of finite thickness and thermal conductivity

The transient conjugate natural convection heat transfer in a differentially-heated cavity with a partition of finite thickness and thermal conductivity are investigated numerically over the range of the Rayleigh number from 103 to 108, the thermal conductivity ratio of partition to that of fluid from 0.1 to 1000, and the dimensionless partition thickness from 0.05 to 0.2. An analysis of the obtained temperature contours and profiles, the time for the onset of stratification and the Nusselt number shows that the thermal conductivity ratio effect is significant only over the range of 0.1–10, when the role played by the partition changes, whereas the effect becomes negligible as the thermal conductivity ratio is very large (100 or beyond). It is also found that the scaling relations developed for the non-partitioned cavity are found to be applicable for the partitioned cavity. The results further show that the effect of the partition thickness on heat transfer is significant mainly when the thermal conductivity ratio is small.

Enhancement of solar chimney performance by passive vortex generator

According to the global consensus on mitigation of greenhouse gas and human footprint as well as improvement of industrial sustainability by the exploitation of renewable energy, the mission of this study dedicated to the performance enhancement of planar solar chimneys in converting much more solar radiation into air enthalpy by vortex generation technique. For this purpose, a passive vortex generator (VG) as an inexpensive but effective approach is employed for the enhancement of heat transfer. The well-developed commercial software of COMSOL Multiphysics was used for two-way modeling and simulation of sophisticated fluid-solid interaction in transient turbulent natural convection heat transfer phenomena. An extensive comparison has been made between two configurations of solar chimney namely with and without VG. According to the numerical results, the natural vibration of elastic VG induces moving vortices into the flow field which is also responsible for the enhancement of natural convection heat transfer by mixing and reducing the thermal boundary layer. Moreover, the VG significantly improves ΔToutlet up to 300% and also decreases the temperature of the absorber surface more than 50% which is under constant heat flux. Both of these factors lead to higher performance for natural air heater.

Effects of porous material on transient natural convection heat transfer of nano-fluids inside a triangular chamber

This study numerically investigates the impact of porous materials, nano-particle types, and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular section. The governing equations of the two-phase mixture model are separated on the computational domain and solved using the Finite Volume Method, taking into account the Darcy–Brinkman model for porous medium. It was observed that convection heat transfer inside the triangular chamber consists of three stages named initial, transient, and semi-steady. The features of each step are provided in detail. The results suggested that the use of a hybrid nano-fluid (water/aluminum oxide-cooper) inside a porous glass material and an increase in volume fraction of nano-particles have adverse effects on heat transfer rate. In contrast, as the nano-particle volume fraction of the single nano-fluid (water/aluminum oxide) inside the chamber increased, convection heat transfer rate improved. At the same time, it was observed that the use of both nano-fluids (single and hybrid) in the porous environment of the aluminum foam could improve convection.

Transient natural convention heat and mass transfer flow in a vertical channel in the presence of Soret and Dufour effects: An analytical approach

This paper presents an analytical solution for transient natural convection heat and mass transfer flow in a vertical channel with Soret and Dufour effects. Due to the presence of these two effects, energy and concentration equations are coupled. The dimensionless governing equations for momentum, energy and concentration are first decoupled using perturbation method and then solved using Laplace Transform Technique (LTT) under relevant initial and boundary conditions. The expressions for temperature, concentration, velocity, rate of heat transfer, rate of mass transfer and skin-friction are obtained. Numerical solutions are also obtained using pdepe in MATLAB so as to validate the accuracy of the proposed analytical method. The effects of Soret parameter, Dufour parameter, Grashof number, modified Grashof number, Prandtl number, Schmidt number and dimensionless time are presented graphically and discussed. It is observed that the temperature and velocity increase with increase in Dufour number, while concentration decreases with increase of Dufour number. The Dufour effect is more significant on the temperature and velocity in comparison to concentration. Moreover, it is observed that the concentration and velocity increase with increase in Soret number while the impact of Soret number is just contrast on temperature variation.

Transient natural convection heat transfer analyses from a horizontal cylinder

Experiments are conducted to analyze the power-on transient natural convection heat transfer around a horizontal cylinder heated in air. The heat flux ranges from 177 W/m2 to 2426 W/m2 and Rayleigh number from 4.13 × 104 to 4.35 × 104. The effects of transient heat transfer data on different angular position of the thermocouple (0°, 90°, 180°) are reported. The results indicate that the transient heat transfer around the cylinder is strongly affected by the position of thermocouples. The test rig working condition is verified by comparing the steady-state natural convection heat transfer data with those obtained from the literature. It is observed that the transient heat transfer data obtained at 90° and 180° are higher than that of stagnation point (0°). Finally, based on the transient data, correlations are presented to predict the heat transfer behavior around the heated cylinder.

Numerical Investigation of Transient Natural Convection Heat Transfer of non-Newtonian Nanofluids Between Eccentric Annulus

The two-dimensional time-dependent natural convection heat transfer of non-Newtonian nanofluids is studied numerically between the gap of two horizontal cylinders. The inner and outer cylinders were kept at $$T_{\mathrm{i}}$$ and $$T_{\mathrm{o}}$$ ( $$T_{\mathrm{i}} > T_{\mathrm{o}}$$ ), respectively. The finite volume technique was used in the study. The effects of Ra number ( $$10^{3} \le Ra \le 10^{6}$$ ), aspect ratio ( $$0.4 \le \hbox {AR} \le 1.2$$ ), power law index of the nanofluid ( $$0.6 \le n \le 1.4$$ ), horizontal eccentricity ( $$0.2 \le {\varepsilon }_{\mathrm{H}} \le 0.8$$ ), vertical eccentricity ( $$-0.8 \le {\varepsilon }_{\mathrm{v}} \le +0.8$$ ) and rotation of the inner cylinder ( $$0 \le {\omega } \le 500$$ ) on the flow field and heat transfer were investigated. It was found that a very good agreement exists with the present numerical results and the results of the open literature. The results indicate that with increasing the Ra number from $$10^{3}$$ to $$10^{6}$$ the heat transfer increases by about 80%. The increase in aspect ratio also increases the heat transfer. The results showed that with increasing the power law index from 0.6 to 1.4, the heat transfer decreases by a rate of about 78%. In addition, the time to reach steady-state conditions increases with increasing power law index. Simulations were performed for a power law index of 0.8 to investigate the effect of eccentricity of the inner cylinder, and it was observed that the heat transfer is higher for negative vertical eccentricities, and the time to reach steady conditions shortens with the effect of negative vertical eccentricity and power law index.

Transient Natural Convection Heat Transfer to CO2 in the Supercritical Region

Present research paper investigates the transient laminar free convective supercritical carbon dioxide flow past a semi-infinite vertical cylinder using numerical methods. Two new thermodynamic models for the supercritical fluid (SCF) flow are considered. Based on these models, for supercritical carbon dioxide, two new equations for thermal expansion coefficient are obtained on the basis of Redlich–Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). Based on the calculated values of thermal expansion coefficient, it is shown that not only RK-EOS is closer to experimental values but also gives greater accuracy when compared to VW-EOS validating RK-EOS as suitable model for predicting natural convective properties of carbon dioxide under supercritical condition. The governing equations of SCF flow are solved numerically using Crank–Nicolson implicit finite difference scheme. Numerical simulations are performed for carbon dioxide in the region of its critical point. Results in subcritical, supercritical, and near-critical regions are shown graphically and discussed for different physical parameters. From the obtained numerical results, it is clear that the steady-state time increases for the increasing values of reduced temperature and reduced pressure for carbon dioxide in supercritical region.

A numerical investigation of transient natural convective heat transfer to isobutane in the supercritical region

Current research article investigates numerically the time-dependent laminar free convective supercritical fluid (SCF) flow past a vertical cylinder. Two new thermodynamic models for the SCF have been considered. Based on these proposed models, in SCF two new equations for thermal expansion coefficient is obtained on the basis of Redlich-Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). It is shown that the thermal expansion coefficient is a function of temperature, pressure and compressibility factor. The evaluated analytical values of volumetric thermal expansion coefficient using RK-EOS are closer to the experimental values which confirm the greater accuracy of proposed RK-EOS as compared to that of VW-EOS. The set of non-dimensional partial differential equations for the SCF flow over a vertical cylinder are obtained and they are time-dependent, highly non-linear and coupled. Therefore, these complex equations are solved using the computational techniques such as Crank-Nicolson implicit finite difference scheme. Numerical simulations are performed for a well-known chemical compound like isobutane in the region of its critical point. The results concerning the velocity, temperature, and average momentum and heat transport coefficient profiles across the boundary layer are shown graphically and discussed for various values of control parameters. From the obtained graphical data, it is clear that temperature plays a prominent role than the pressure under supercritical condition.

Effect of spatial side-wall temperature variation on transient natural convection of a nanofluid in a trapezoidal cavity

PurposeThis paper aims to study analytically and numerically the problem of transient natural convection heat transfer in a trapezoidal cavity with spatial side-wall temperature variation.Design/methodology/approachThe governing equations subject to the initial and boundary conditions are solved numerically by the finite difference scheme consisting of the alternating direction implicit method and the tri-diagonal matrix algorithm. The left sloping wall of the cavity is heated to non-uniform temperature, and the right sloping wall is maintained at a constant cold temperature, while the horizontal walls are kept adiabatic.FindingsIt is shown that the heat transfer rate increases in non-uniform heating increments, whereby low wave number values are more affected by the convection. The best heat transfer enhancement results from larger side wall inclination angle; however, trapezoidal cavities require longer time compared to that of square to reach steady state.Originality/valueThe study of natural convection heat transfer in a trapezoidal cavity filled with nanofluid and heated by spatial side-wall temperature has not yet been undertaken. Thus, the authors of the present study believe that this work is valuable.

Transient natural convective heat transfer in a trapezoidal cavity filled with non-Newtonian nanofluid with sinusoidal boundary conditions on both sidewalls

Transient, laminar natural convection in a trapezoidal cavity filled with a non-Newtonian nanofluid with sinusoidal boundary conditions on both sidewalls is studied numerically by using the finite element method. The sloping walls of the cavity are heated by sinusoidal temperature distributions, while the horizontal walls allow no heat transfer to the surrounding. Water-based nanofluids with Ag or Cu or Al2O3 or TiO2 nanoparticles are chosen for investigation. The governing parameters of this study are the Rayleigh number (104 ≤Ra ≤ 106), phase deviation (0 ≤ γ ≤ π), amplitude ratio (0 ≤ ε ≤ 1), power-law index (0.6 ≤ n ≤ 1.4), sidewall inclination angle (0°≤ φ ≤ 21.8°), nanoparticle volume fraction (0 ≤ ϕ ≤ 0.2), and dimensionless time (0 ≤ τ ≤ 0.2). The results show that the heat transfer rate increases significantly by the addition of phase deviation. Strong heat transfer enhancements are obtained by higher sidewall inclination angles. However, for a square cavity, the heat transfer approaches the steady-state condition with the increment of the dimensionless time.

Transient natural convection heat transfer of liquid D-mannitol on a horizontal cylinder

Transient and steady state natural convection heat transfer for D-mannitol on a horizontal cylinder was investigated experimentally at various liquid temperatures and heat input conditions. To clarify the natural convection phenomena of D-mannitol, transient and steady heat transfer coefficients were measured under various liquid temperatures of D-mannitol and periods of heat generation rates from a horizontal platinum cylinder. The platinum cylinder with a diameter of 1 mm and a length of 43.5 mm was used as the test heater in this experiment. Experimental results indicated that the steady heat transfer coefficient of D-mannitol was affected by the liquid temperature. As the liquid temperature increased, it was understood that the effect of liquid temperature weakened. When the period of the heat generation rate was changed, the heat transfer process was divided into natural convection heat transfer and conductive heat transfer. It was considered that the conductive heat transfer was more dominant as the period of the heat generation rate decreased. The empirical correlations of steady and transient heat transfer coefficients for D-mannitol were obtained.

Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity

In this study, a transient heat transfer process of freezing water inside a two-dimensional square cavity has been investigated numerically. Water was used as a phase-change medium, and the numerical model has been created with control volume approach by using C++ programming language. To be able to accelerate the numerical calculations, CUT (Consistent-Update-Technique) algorithm has been implemented in the numerical code. Span-wise variations of the vertical component of the velocity have been represented in comparison with the experimental measurements from the literature at various vertical positions to examine the accuracy of the numerical scheme. The influence of natural convection has been considered by comparing the conduction and convection dominated solidification under same boundary conditions. Comparative results have been obtained regarding time-wise variations of the cold wall temperature and the dimensionless effectiveness. Moreover, the streamlines and isotherms have been represented to understand the differences between the conduction and convection driven phase change processes.Results indicate that natural convection becomes remarkable and has different forms at the initial periods of the phase change process. Increasing the effect of natural convection in the cavity increases the cooling rate of water. Near the density inversion temperature of water (4°C), temperature variations fluctuate and counter currents observed in the domain.

Transient natural convection heat transfer in nanoliquid-saturated porous oblique cavity using thermal non-equilibrium model

The problem of transient natural convection heat transfer in a nanoliquid-saturated porous oblique cavity is studied numerically using the finite difference method. The hot left wall of the cavity is maintained at a constant temperature and so is the cold right wall. The horizontal walls allow no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The heat transfer equations are those of a two-phase medium, one for the nanoliquid and another for the porous medium. Water-based nanoliquids with Ag or Cu or Al2O3 or TiO2 nanoparticles are chosen for investigation. The governing parameters of this study are the Rayleigh number (102≤Ra⩽104), modified conductivity ratio (0.1≤γ⩽1000), inter-phase heat transfer (0.1≤H⩽1000), inclination angle of the sloping walls (−π3≤ω≤π3), volume fraction of nanoparticles (0≤φ≤0.2) and dimensionless time (0≤τ⩽0.1). The assumption of local thermal non-equilibrium leads to an enhanced heat transfer situation in nanoliquids saturating a porous medium compared to that in a porous medium with local thermal equilibrium. Explanation for the observed influences of various parameters on streamlines, isotherms and weighted average Nusselt number is given in terms of thermophysical properties of four nanoparticles, water and porous medium. It is shown that the strength of the flow circulation increases for the relative concentration of nanoliquid with the increment of the inclination angle to the positive direction.

Numerical models for heat conduction and natural convection with symmetry boundary condition based on particle method

Numerical models of heat conduction and natural convection are developed based on Meshless Moving particle semi-implicit (MPS) method to study the unsteady complex flow coupling with heat transfer. Fundamental heat exchange process is systematically investigated in one dimension and extended to two dimensions without internal heat source. The energy conservation equation is discretized on particles and coupled with flow by momentum change that caused by temperature difference. Both Dirichlet and Neumann boundary conditions are proposed with mirror image technique and the numerical results are verified to have high accuracy against benchmark solutions (theoretical or experimental, and or other numerical solutions) for several representative examples. To improve the calculation efficiency, symmetry boundary models are established and applied in transient heat conduction and natural convection heat transfer. The results using the symmetry boundary are comparable and reliable to the full-domain results, both of which agree well with the experimental and other numerical solutions.