Effects of inclination angle on conduction—natural convection in divided enclosures filled with different fluids

Laminar natural convection in inclined enclosures filled with different fluids was studied by a numerical method. The enclosure was divided by a solid impermeable divider. One side of partition of enclosure was filled with air and the other side had water. The enclosure was heated from one vertical wall and cooled from the other while horizontal walls were adiabatic. The governing equations which were written in stream function–vorticity form were solved using a finite difference technique. Results were presented by streamlines, isotherms, mean and local Nusselt numbers for different thermal conductivity ratios of solid impermeable material (plywood or concrete), inclination angle (0° ≤ ? ≤ 360°) and Grashof numbers (10³ ≤ Gr ≤ 10⁶). The code was validated by earlier studies, which are available in the literature on conjugate natural convection heat transfer. Analytical solutions were obtained for low Grashof numbers. Obtained results showed that both heat transfer and flow strength strongly depended on thermal conductivity ratio of the solid material of partition, inclination angle and Grashof numbers. The heat transfer was lower in the air side of the enclosure than that of the water side.     

Investigation of buoyancy-driven flow and heat transfer in a trapezoidal cavity filled with water–Cu nanofluid

A numerical study is conducted to investigate the transport mechanism of free convection in a trapezoidal enclosure filled with water–Cu nanofluid. The horizontal walls of the enclosure are insulated while the inclined walls are kept at constant but different temperatures. The numerical approach is based on the finite element technique with Galerkin's weighted residual simulation. Solutions are obtained for a wide range of the aspect ratio (AR) and Prandtl number (Pr) with Rayleigh number (Ra = 10⁵) and solid volume fraction (? = 0.05). The streamlines, isotherm plots and the variation of the average Nusselt number at the left hot wall are presented and discussed. It is found that both AR and Pr affect the fluid flow and heat transfer in the enclosure. A correlation is also developed graphically for the average Nusselt number as a function of the Prandtl number as well as the cavity aspect ratio.     

Coupled FHD–MHD free convection of a hybrid nanoliquid in an inversed T-shaped enclosure occupied by partitioned porous media

The article treats the study on free convection of a hybrid nanoliquid confined within contrariwise T-shaped enclosure saturated by two porous media with different material and structure. Nanocomposite particles of multiwall carbon nanotubes–Fe₃O₄ are dispersed into water. Variable magnetic source located to the bottom wall has been analyzed in terms of heat transport performance and nanofluid motion behavior in the enclosure. The governing equations with boundary conditions formulated using the primitive dimensionless variables have been numerically worked out by the finite element technique. Impacts of the Hartmann number, magnetic number, Rayleigh number, ratio of thermal conductivity, porosity ratio, the Darcy number, and convective heat transfer coefficient at solid–nanofluid interface have been investigated. It has been found that low values of dimensionless convection parameter ratio at the border between solid and nanoliquid phases characterize high values of the nanofluid dimensionless convective heat transfer parameter. The average Nusselt number for the solid state has maximum value for high quantities of ratio of Darcy number and low values of dimensionless convection parameter ratio at the border between solid and nanoliquid phases.     

Bounds on natural convective heat transfer in a porous layer with fixed heat flux

Using the background field variational method, bounds on natural convective heat transfer in a porous layer heated from below with fixed heat flux are derived from the primitive equations. The enhancement of heat transfer beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the non-dimensional forcing scale set by the ‘effective’ Rayleigh number (Rˆ) according to Nu ≤ 0.354Rˆ^1/2 and in terms of the conventional Rayleigh number (Ra) defined by the temperature drop across the layer according to Nu ≤ 0.125Ra. It is presented that fixing the heat flux at the boundaries does not change the linear dependence between Nusselt number and Rayleigh number at high Rayleigh number region.     

Experimental and numerical analysis of buoyancy-induced flow in inclined triangular enclosures

The buoyancy‐induced heat transfer and fluid flow in a triangular enclosure are investigated both numerically and experimentally. The enclosure is heated from one wall and the adjacent wall is insulated. Hypotenuse of the triangle is cooled isothermally. The numerical tests and experiments covered a range of Rayleigh number, Ra, from 1.5 × 10⁴ to 1.5 × 10⁵. The local and average Nusselt numbers are given for different orientation angles. A code was written based on finite difference method in Fortran platform to solve governing equations of natural convection. Experimental and numerical results show good agreement. It is observed that inclination angle can be used as a control parameter for heat transfer.     

Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid

Natural convection in enclosures using water/SiO₂ nanofluid is simulated with Lattice Boltzmann method (LBM). This investigation compared with other numerical methods and found to be in excellent agreement. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³-10⁵, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (A) of the enclosure between 0.5 and 2. The thermal conductivity of nanofluids is obtained on basis of experimental data. The comparisons show that the average Nusselt number increases with volume fraction for the whole range of Rayleigh numbers and aspect ratios. Also the effect of nanoparticles on heat transfer augments as the enclosure aspect ratio increases.     

A numerical comparison among different water-based hybrid nanofluids on their influences on natural convection heat transfer in a triangular solar collector for different tilt angles

Natural convection inside a triangular solar collector is investigated numerically for different nanofluids and hybrid nanofluids in this study. The individual effects of Al₂O₃–water, carbon nanotubes (CNT)–water, and Cu–water nanofluids are observed for different solid volume fractions of nanoparticles (0%–10%). Three types of hybrid nanofluids are prepared using different ratios of Al₂O₃, CNT, and Cu nanoparticles in water. A comparison is made varying the Rayleigh numbers within laminar range (10³–10⁶) for different tilt angles (0°, 30°, 60°, and 90°) of the solar collector. The inclined surface of the triangular solar collector is isothermally cold and the bottom wall (absorber plate) is isothermally hot, whereas the vertical wall with respect to the absorber plate is considered adiabatic. Average Nusselt numbers along the hot wall for different parameters are observed. Streamlines and isotherm contours are also plotted for different cases. Dimensionless governing Navier–Stokes and thermal energy conservation equations are solved by Galerkin weighted residual finite element method. Better convective heat transfer is found for higher Rayleigh number, solid volume fraction, and tilt angle. In the case of hybrid nanofluid, increasing the percentage of the nanoparticle that gives better heat transfer performance individually results in enhancing natural convection heat transfer inside the enclosure.     

Visualization of heat flow using Bejan’s heatline due to natural convection of water near 4 °C in thick walled porous cavity

A numerical study on natural convection heat transfer of cold water near 4 °C in a thick bottom walled cavity filled with a porous medium has been performed. It is assumed that the cavity is isothermally heated from the outside of the thick bottom wall and cooled from ceiling. The finite-difference method has been used to solve the governing partial differential equations of heat and fluid flow. Effects of thermal conductivity ratio, Rayleigh number and bottom wall thickness on heat transfer from the bottom to the ceiling have been studied. The heatline visualization technique has been used to demonstrate the path of heat transport through the enclosure. Moreover, streamlines and isotherms have been used to present fluid flow and temperature distributions. The obtained results show that multiple circulation cells are formed in the cavity and the local Nusselt numbers at the bottom wall and solid–fluid interface are highly affected by formed cells. The increase of Rayleigh number and thermal conductivity ratio increases heat transfer through the cavity. However, the increase of thickness of the bottom wall reduces the mean Nusselt number. Almost one-dimensional conduction heat transfer is observed in the solid bottom wall of the cavity.     

The Effect of Alumina–Water Nanofluid on Natural Convection Heat Transfer Inside Vertical Circular Enclosures Heated from Above

Experimental investigation on natural convection heat transfer is carried out inside vertical circular enclosures filled with Al₂O₃–water nanofluid with different concentrations; 0.0%, 0.85% (0.21%), 1.98 (0.51%), and 2.95% (0.75%) by mass (volume). Two enclosures are used with 0.20 m inside diameter and with two different aspect ratios. The top surface of the enclosure is heated using a constant-heat-flux flexible foil heater while the bottom surface is subject to cooling using an ambient air stream. Various heat fluxes are used to generate heat transfer through the nanofluid. The average Nusselt number is obtained for each enclosure and correlated with the modified Rayleigh number using the concentration ratio as a parameter. A general correlation for the average Nusselt number with the modified Rayleigh number is obtained using the volume fraction and the aspect ratio as parameters to cover both enclosures. The results show that the Nusselt number for the alumina–water nanofluid is less than that of the base fluid. This means that using the alumina–water nanofluids adversely affects the heat transfer coefficient compared to using pure water. It is also found that the degree of deterioration depends on the concentration ratio as well as the aspect ratio of the enclosure.     

Comparison between single-phase and two-phases CFD modeling of laminar forced convection flow of nanofluids in a circular tube under constant heat flux

In this article, forced convection heat transfer with laminar and developed flow for water-Al₂O₃ nanofluid inside a circular tube under constant heat flux from the wall was numerically investigated using computational fluid dynamics method. Both single and two-phase models are accomplished for either constant or temperature dependent properties. For this study nanofluids with size particles equal to 100 nm and particle concentrations of 1 and 4 wt% were used. It is observed that the nanoparticles when dispersed in base fluid such as water enhance the convective heat transfer coefficient. The Nusselt number and heat transfer coefficient of nanofluids were obtained for different nanoparticle concentrations and various Reynolds numbers. Heat transfer was enhanced by increasing the concentration of nanoparticles in nanofluid and Reynolds number. Also, a correlation based on the dimensionless numbers was obtained for the prediction the Nusselt number. The modeling results showed that the predicted values were in very good agreement with reference experimental data.     

Numerical study of mixed convective cooling in a square cavity ventilated and partially heated from the below utilizing nanofluid

A numerical investigation of mixed convection flows through a copper–water nanofluid in a square cavity with inlet and outlet ports has been executed. The natural convection effect is attained by heating from the constant flux heat source which is symmetrical located at the bottom wall and cooling from the injected flow. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Reynolds number in the range 50 ≤ Re ≤ 1000, with Richardson numbers 0 ≤ Ri ≤ 10 and for solid volume fraction 0 ≤ ? ≤ 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. Results are presented in the form of streamlines, isotherms, average Nusselt number and average bulk temperature. In addition, the effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated and discussed. The results indicate that increase in solid concentration leads to increase in the average Nusselt number at the heat source surface and decrease in the average bulk temperature.     

A heatline analysis of natural convection in a square inclined enclosure filled with a CuO nanofluid under non-uniform wall heating condition

Heatline visualization technique is used to understand heat transport path in an inclined non-uniformly heated enclosure filled with water based CuO nanofluid. The cavity has square cross-section and it is non-uniformly heated from a wall and cooled from opposite wall while other walls are adiabatic. The governing equations which are continuity, momentum and energy equations are solved using finite volume method. The dimensionless heatfunction for nanofluid heat flow is defined and solved to determine heatline patterns. Calculations were performed for Rayleigh numbers of 10³, 10⁴ and 10⁵, inclination angle of 0°, 30°, 60° and 90°, and nanoparticle fraction of 0, 0.02, 0.04, 0.06, 0.08 and 0.1. It is observed that heat transfer in the cavity increases by adding nanoparticles. The rate of increase is greater for the enclosures with low Rayleigh number. Visualization of heatline is successfully applied to nanoparticle convective flows. Based on the heatline patterns, three heat transfer regions are observed and discussed in details.     

Enhancement of heat transfer using CuO/water nanofluid and twisted tape with alternate axis

Heat transfer, friction and thermal performance characteristics of CuO/water nanofluid have been experimentally investigated. The nanofluid was employed in a circular tube equipped with modified twisted tape with alternate axis (TA). The concentration of nanofluid was varied from 0.3 to 0.7% by volume while the twisted ratio (y/W) of TA was kept constant at 3. The experiments were performed in laminar regime (Reynolds number spanned 830 ≤ Re ≤ 1990). The uses of nanofluid together with typical twisted tape (TT), TA alone and TT alone were also examined. To evaluate heat transfer enhancement and the increase of friction factor, the Nusselt number and friction factor of the base fluid in the plain tube were employed as reference data. The obtained results reveal that Nusselt number increases with increasing Reynolds number and nanofluid concentration. By the individual uses of TA and TT, Nusselt numbers increase up to 12.8 and 7.2 times of the plain tube, respectively. The simultaneous use of nanofluid and TA improves Nusselt number up to 13.8 times of the plain tube. Over the range investigated, the maximum thermal performance factor of 5.53 is found with the simultaneous employment of the CuO/water nanofluid at 0.7% volume and the TA at Reynolds number of 1990. In addition, the empirical correlations for heat transfer coefficient, friction factor and thermal performance factor are also developed and reported.     

Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid

Heat transfer enhancement has been investigated in a square cavity subject to different side wall temperatures using water/SiO₂ nanofluid. An experimental setup has been used to extract the conductivity value of nanofluid. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra_f = 10⁵–10⁷ and the volumetric fraction of nanoparticle between 0 and 4%. The comparisons show that the mean Nusselt number increases with volume fraction for the whole range of Rayleigh numbers. Although by using the theoretical formulations for conductivity no enhancement has been observed.     

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.     

NUMERICAL EXPERIMENTS WITH FLUID CONVECTION IN TILTED NONRECTANGULAR ENCLOSURES

Numerical experiments were performed on an incompressible fluid contained in a tilted nonrectangular enclosure. Rayleigh numbers of l0²-l0⁵ and Prandtl numbers of 0.001-100 are considered. The wall angles are 22.5°, 45°, and 77.5° with aspect ratios of 3 and 6. Results indicate that the heat transfer and fluid motion within the enclosure are strong functions of Rayleigh number, Prandtl number, and orientation angle of the enclosure. For Rayleigh numbers greater than 1& and Prandtl numbers greater than 0.1, a minimum and a maximum mean Nusselt number occurred as the angle of orientation was increased from 0° to 360°. A transition in the mode of circulation occurred at the angles corresponding to the minimum or maximum rate of heat transfer.     

Natural convective heat transfer in square enclosures heated from below

The paper deals with the results of an experimental and numerical study of free convective heat transfer in a square enclosure characterized by a discrete heater located on the lower wall and cooled from the lateral walls.The study analysed how the heat transfer develops inside the cavity at the increasing of the heat source length.The experimental data are obtained by measuring the temperature distribution in the air layer by real-time and double-exposure holographic interferometry while the commercial finite volumes code Fluent 6.0 is used for the numerical study. Convection has been studied for Rayleigh number from 10³ to 10⁶. Different convective forms are obtained depending on Ra and on the heat source length.The local Nusselt number is evaluated on the heat source surface and it shows a symmetrical form raising near the heat source borders. Graphs of the local Nusselt number on the heat source and of the average Nusselt number at several Ra are finally presented.     

Numerical investigation of heat transfer enhancement of nanofluids in an inclined lid-driven triangular enclosure

The behavior of nanofluids is investigated numerically in an inclined lid-driven triangular enclosure to gain insight into convective recirculation and flow processes induced by a nanofluid. The present model is developed to examine the behavior of nanofluids taking into account the solid volume fraction δ. Fluid mechanics and conjugate heat transfer, described in terms of continuity, linear momentum and energy equations, were predicted by using the Galerkin finite element method. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. Numerical results are obtained for a wide range of parameters such as the Richardson number, and solid volume fraction. Copper–water nanofluids are used with Prandtl number, Pr = 6.2 and solid volume fraction δ is varied as 0%, 4%, 8% and 10%. The streamlines, isotherm plots and the variation of the average Nusselt number at the hot surface as well as average fluid temperature in the enclosure are presented and discussed in detailed. It is observed that solid volume fraction strongly influenced the fluid flow and heat transfer in the enclosure at the three convective regimes. Moreover, the variation of the average Nusselt number and average fluid temperature in the cavity is linear with the solid volume fraction.     

Effects of Heating Location and Size on Natural Convection in Partially Heated Open-Ended Enclosure by Using Lattice Boltzmann Method

Natural convection heat transfer in an square enclosure, consisting of a partially heated west wall with east end open to ambient, is investigated numerically by using an in-house computational fluid dynamics solver based on thermal lattice Boltzmann method. In particular, the influences of Rayleigh number (10³–10⁶), heating location (bottom, middle, and top) on west wall, and dimensionless heating length (0.25–0.75) on momentum and heat transfer characteristics of air are presented and discussed. The streamline patterns show bifurcation at the lowest Rayleigh number for bottom and middle heating, whereas at the highest Rayleigh number, all heating positions yield bifurcation and elongation of flow patterns with a secondary vortex near the lower side of open end. The middle and bottom heating locations show a linear increase in Nusselt number with heater size, whereas inverse dependence is seen for top heating. The maximum heat transfer is observed in the case of middle heating. As expected, average Nusselt number increased with increasing Rayleigh number. Finally, the functional dependence of the average Nusselt number on flow governing parameters (Rayleigh number and heating length) for different heating locations is presented as a simple predictive empirical relationship.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.