Free Convection Heat Transfer Research Articles

Influence of porosity properties on natural convection heat transfer in porous square cavity

A numerical investigation was conducted to examine free convection heat transfer within a square cavity containing a fluid-saturated porous layer at the bottom under laminar flow conditions. The enclosure's left and right walls experienced heating and cooling, while the top and bottom walls remained adiabatic. The study explored the influence of the Darcy number, porosity number, and dimensionless thickness of the porous layer on heat transmission. This investigation utilized a FORTRAN computation program alongside the finite volume method, effectively solving the equations governing flow and heat exchange within porous materials through natural convection. The flow pattern is determined by the Navier–Stokes equations in the fluid region and the Darcy–Brinkman–Forchheimer formula in the porous region. The energy equation was employed to compute the thermal field. The increase in the Darcy number results in both an increase in heat transfer rate due to enhanced fluid flow through pores and an intensification of fluid flow patterns. Higher porosity leads to higher heat transfer rates due to greater fluid penetration and an increased surface area for heat exchange. The thicker porous layer reduces heat transfer rate due to increased resistance to fluid flow and decreased contact area.

Soret Effect on Magneto Hydrodynamic Free Convective Heat and Mass Transfer Effects Flow over an Inclined Plate Embedded in a Porous Medium

Soret Effect on Magneto Hydrodynamic Free Convective Heat and Mass Transfer Effects Flow over an Inclined Plate Embedded in a Porous Medium

Revolutionizing energy flow: Unleashing the influence of MHD in the presence of free convective heat transfer with radiation

This study investigates the complex interplay between radiation and magneto-flow on a porous, perpendicular plate immersed in a viscoelastic Maxwell fluid. The significance lies in understanding how the Lorentz force shapes dynamics and energy transfer in such systems, which is crucial for various industrial applications. Utilizing a comprehensive model that accounts for heat generation and absorption, we transform partial differential equations into ordinary ones through flow similarity analysis, providing valuable insights into the system's behavior. Employing the bvp4c solver in MATLAB, we evaluate velocity and energy profiles in Maxwell fluid flow. Graphical representations allow for a thorough examination of the influence of thermophysical parameters. Our findings reveal an intensified velocity profile attributed to prolonged material relaxation times.Furthermore, temperature profiles progressively increase with higher radiation and porous parameters. These results hold significant implications for industrial applications, particularly in Maxwell fluids' heat transport studies. Insights from this research can inform the design and optimization of systems such as ovens, boilers, cross-flow heat exchangers, and solar panels, enhancing efficiency and performance. Overall, this study contributes novel insights that advance understanding beyond previous efforts in the literature, paving the way for further exploration in this field. The primary finding of this study indicates that as the Rayleigh number increases, the velocity profile experiences an increase, whereas the temperature profile shows a decrease.

Natural convective heat transfer of Al2O3-Cu/water hybrid nanofluid in a rectotrapezoidal enclosure under the influence of periodic magnetic field

This study seeks to examine quantitatively the two-dimensional unsteady free convective heat transfer enhancement of Al2O3-Cu/H2O hybrid nanofluid within a rectotrapezoidal-shaped structure. The lower wall is both uniformly and non-uniformly heated with different thermal boundary conditions, the top horizontal wall is adiabatic, and the vertical and inclined walls are assumed chilly. The enclosure is penetrated by a periodic magnetic field. A set of variable transformations is used to render the governing equations dimensionless, which makes it possible to identify the model parameters that control it. The finite element method is then used to numerically solve these equations. To verify the code's numerical precision, comparisons with formerly available works are performed and, a high level of agreement is obtained among the results. The generated outcomes are shown for the principal parameters that control the flow in the context of streamlines, heat lines, isotherms, average Nusselt number, friction factor, and thermal efficiency index. The findings demonstrated that the efficiency index, friction factor, and heat transmission are all considerably influenced by the Rayleigh number (Ra). The lowest Ra yields the maximum thermal efficiency. The results also revealed that the hybrid nanoparticle volume fraction and period of the magnetic field amplified the heat transfer rate and efficiency index due to the increased pumping force. It is observed that when the percentage of the mixing ratios for Cu nanoparticles rises from 0% to 100%, the heat transport in Al2O3-Cu/H2O hybrid nanofluid increases for a fixed volume fraction of hybrid nanoparticles. As compared to parabolic and sinusoidal boundary conditions, the uniform temperature boundary setting for Ra = 105 exhibits the highest average rate of heat transport of 10.04. The average Nusselt number increases by 25.12% at Ra = 103 with a 3% volume fraction of hybrid nanofluid as compared to pure water and the mixing ratios of Al2O3:Cu = 0:300 gives the highest increased rate of 16.30%. The results further illustrate that Al2O3-Cu/H2O hybrid nanofluid has the highest heat transfer rate compared to the pure water and Al2O3– H2O nanofluid.

LBM Simulation of Free Convection Heat Transfer of Cu/Water Nanofluid in Inclined Cavity with Non-Uniform Heating Temperature Distribution

In the present study, natural convection of Cu/water nanofluid in an inclined square cavity has been investigated numerically using lattice Boltzmann method (LBM). The left wall of the cavity is maintained at a constant hot temperature, while the right wall is subjected to non-uniform temperature distribution. The upper and lower walls are insulated. The fluid flow and heat transfer characteristics are investigated over a wide range of parameters, including Rayleigh numbers (Ra = 103, 104 and 105), solid volume fractions (Φ = 0%, 2%, 4% and 6%), amplitude ratio (A = 0, 0.5 and 1) and phase deviations of sinusoidal temperature distribution (Φ = 0, π/4, π/2, 3π/4 and π). The results are presented graphically in the form of streamlines, isotherms and Nusselt numbers for the different combinations of the considered parameters. The heat transfer rate inside the nanofluid increases as the Rayleigh number and the volume fraction of nanoparticles increase. Further, an increase in the amplitude ratio results in a decrease in the heat transfer rate, with a reduction of up to 8.67% at A = 1. On the other hand, changes in the phase deviation of the sinusoidal temperature distribution lead to an increase in the heat transfer rate, with a surge of up to 32.04% observed at Φ = π.

Optimization and sensitivity analysis of hydromagnetic convective heat transfer in a square cavity filled with a porous medium saturated by Ag-MgO/water hybrid nanofluid using response surface methodology

A computational exploration is presented to emphasis on optimization and sensitivity inspection of the unsteady free convective heat transfer flow of hybrid nanofluid in a square cavity under multidirectional periodic magnetic field with aluminum foam porous medium. The vertical walls of the cavity are maintained at constant low temperature whereas the constant as well as the variable thermal conditions on the bottom wall is considered and the top wall is considered as adiabatic. The finite element technique has been applied to solve the governing equations after changing them into dimensionless form. In the numerical simulations, the Ag-MgO/water hybrid nanofluid has been engaged to gain insight into the flow and thermal arenas. The obtained outcomes are exhibited in terms of streamlines, isotherms and average Nusselt number as well as plotting the response surface and contours. The average Nu is displayed in line graphs, response surface and contours graphs as well as tabular form for different flow parameters. Response surface methodology is applied to achieve an optimization procedure to search for the best situation in which the highest heat transfer rate occurs when the distinct model parameters namely Darcy number, porosity and hybrid nanoparticles volume fraction are treated as the sensitivity of the parameters. A correlation equation between the output response and input variables has been derived with the help of response surface methodology. The magnetic field and its path regime the flow decoration of hybrid nanofluid suggestively. The Ag and Ag-MgO nanomaterial with water flow arenas are compared. While considering Ag-H2O nanofluid, the average Nu increases 23.97 % at Ra = 107 with ϕhnp = 0.02 whereas the corresponding increases is 25.68 % if the Ag-MgO/H2O hybrid nanofluid is taken into account. The average Nu upsurges suggestively, as hybrid nanoparticles volume fraction, period number, magnetic field leaning angle, Darcy number and Rayleigh number rises but porosity and Hartmann number have inverse effect. The outcomes showed that the average Nu is more sensitive to the hybrid nanoparticles volume fraction rather than the porosity or Darcy number. Also, it is discovered that the optimum condition arises at Da = 0.001, ε = 0.2 and ϕhnp = 0.02 with the final Nuave = 2358.21.

EFFECT OF INNER BOUNDARIES GEOMETRY ON NATURALCONVECTION HEAT TRANSFER IN HORIZONTAL ANNULI

 An analytical modeling of natural convection in physically-based analysis is developed for investigate free convective heat transfer in horizontal eccentric annulus between a circular outer cylinder and heated different shape inner envelope with used four models of the shapes of the inner cross section of (circular, triangular, square and hexagon inner boundary). The main objective of this paper was taking a composite model based on asymptotic solutions for three limiting cases: pure conduction, laminar boundary layer convection and transition flow convection. Laminar conditions up to Rayleigh number RaPi of 5×104 were investigated. By using data from MATLAB simulations for a wide range of two cylinder temperature difference in order to study the effects of annulus diameter ratio, Rayleigh number, and the cross section geometries of inner cylinder on the Nusslte number and the ratio of thermal conductivity. The numerical result illustrated for the circular the increasing the Rayleigh number leading to slightly increasing the non-dimensional Nusslte number with various value of annulus diameter ratio and when used the high annulus perimeter ratio (Po/Pi( about (4.5,2.6,1.6 and 1.175). There is rapid increasing in the non-dimensional ratio of thermal conductivity with increasing the Rayleigh number at the high values of (Po/Pi(, and the result showed that the non-dimensional ratio of thermal conductivity and the Nusslte number values of the (triangular, square and hexagon) less than in the case of circular inner boundary, but the hexagon model showed the Nusslte number more that than in the (triangular and square). the mathematical results compared with model developed by pervious numerical the model and data are in good agreement, with an average RMS difference of 10.6% for the circular annulus of dimensional Nusselt number (NuPi) and less than 4.9 % and 9.8% for the square inner geometry non-dimensional ratio thermal conductivity. 

A transient free convection heat transfer study in an oil tank with vertical and horizontal arrangements of heating coils

A transient free convection heat transfer study in an oil tank with vertical and horizontal arrangements of heating coils

Magnetohydrodynamic free convection of nano-encapsulated phase change materials between two square cylinders: Mapping the thermal behavior using neural networks

The study focused on investigating the convective heat transfer of nano-encapsulated phase change suspensions in the presence of a non-uniform magnetic field within an annuli space between two square cylinders. The principal equations for the fluid flow and phase change heat transfer were formulated as partial differential equations and then represented into dimensionless format. The finite element method was used to solve these equations and simulate the free convection heat transfer. The effect of various factors, including Hartmann, Rayleigh, Eckert and Stefan numbers, geometry aspect ratio, nanoparticles’ concentration, and fusion temperature, on the heat transfer rate was examined. A neural network was also introduced and trained to establish the connection between the control parameters (inputs) and the heat transfer rate (output). The outcomes were presented in the form of the modified Nusselt number, along with isotherms, heat capacity ratio (phase change) contours, and streamlines. The results demonstrated that the neural network could accurately predict the heat transfer rate and provide a comprehensive map of heat transfer with respect to the control parameters. Nano-Encapsulated Phase Change Materials (NEPCMs) can be considered as a new type of nanofluids, in which the nanoparticle consists of a core and a shell. The core part is made of a Phase Change Material (PCM) which can undergo solid-liquid phase change at a certain fusion temperature, and absorb/release a significant amount of energy due to latent heat of the phase change.

Correction: Investigation of free convection heat transfer and entropy generation of nanofluid flow inside a cavity affected by magnetic field and thermal radiation

Correction: Investigation of free convection heat transfer and entropy generation of nanofluid flow inside a cavity affected by magnetic field and thermal radiation

Heat and Mass Transfer on Unsteady MHD Chemically Reacting Rotating Flow of Jeffrey Fluid Past an Inclined Plates under the Impact of Hall Current, Diffusion Thermo and Radiation Absorption

An analytical solution for two dimensional unsteady MHD free convective double diffusive heat and mass transfer rotating flow of viscous incompressible optically thin non Newtonian fluid (jeffrey fluid) past a semi-infinite porous plate in the presence of generation of heat absorption with hall current, radiation absorption and Dufour effects are presented in this paper. Lorentz force is applied perpendicular direction to the plate with a first-order chemical reaction. The governing PDEs transformed into ODEs by applying the perturbation technique. The effects of various physical parameters like Hall current, heat absorption, radiation parameter, radiation absorption parameter, Grashof number, modified Grashof number, Dufour effect, magnetic field parameter, inclined angle, chemical reaction parameter, etc., are studied with graphically. Temperature profile is increased by raising the values of Dufour effect, radiation absorption parameter and reverse effect of the heat absorption parameter and also concentration profile distribution is downfall by raising the values of Schmited number, chemical reaction parameter. Another significant finding of the current study is that the numerical data are displayed with the use of Matlab programmes to investigate the outcomes of the skin friction solution. the rate of heat and mass transfer at the wall rising under the influence of Dufour effect. Tables, graphs, and reports can be used to display the impact of all pertinent parameters.

Natural nanofluid convection in rectangular porous domains

In this paper, the free convective flow and heat transfer in a porous rectangular enclosures filled with Cu-water nanofluid is studied and analyzed. The cavity side-walls are exposed to a constant heat flux and the horizontal walls are assumed to be adiabatic. The governing equations describing the problem are solved using a finite difference method. The main parameters of our problem are: aspect ratio, volume fraction of nanoparticles, types of media, porosity of the medium, and Rayleigh number. The results indicate that an increase in aspect ratio from 0.1 to 0.7 leads to a significant increase of Nusselt number, which then reaches a maximum value. However, the heat transfer rate progressively decreases for aspect ratios greater than 0.7. Moreover, the addition of Cu-nanoparticles weakens the heat transfer. As a result, when the porous medium has low thermal conductivity, the solid matrix porosity becomes particularly more effective in improving heat transfer. Also, a correlation was established between the average Nusselt number and the influencing parameters. Results show that the governing parameters impact the flow regime.

Free convection heat transfer and buoyancy-assisted flow over a heated plate inserted horizontally in a vertical channel with time-varying conditions

Free convection heat transfer and buoyancy-assisted flow over a heated plate inserted horizontally in a vertical channel with time-varying conditions

Analytical, numerical and scale analysis study of thermal diffusion effect on free convection boundary layer flows in a slender porous layer

This paper reports an analytical, numerical and scale analysis study of free convective heat and mass transfer flows coupled with thermal diffusion effect in a slender vertical porous cavity subjected to cooperating lateral temperature and concentration gradients. The top and bottom walls of the cavity are assumed to be adiabatic and impermeable to mass transfer. This study aims to analyze the different hydrodynamic, thermal and solutal behaviors developed in laminar boundary layer flow regime reached at high Rayleigh numbers. Based on the parallel flow approximation, an analytical solution of the problem is derived in the extreme case of heat-driven (N≪1) free convection. The obtained analytical results are validated numerically by generating the solutions of the full governing differential equations by means of finite-difference method (FDM). To estimate the order of magnitudes involved in the boundary layer regime, a scale analysis of the conservation equations is performed. The order of magnitudes of boundary layer thickness, Nusselt and Sherwood numbers are derived in this study. For all these quantities, the trends predicted by the scaling law theory are found to be in good agreement with those of the parallel flow approach. The combined effects of Rayleigh and Soret numbers on the boundary layer thickness, flow intensity and heat and mass transfers are illustrated graphically for representative values of N, Le and A_r, and the main results are highlighted and discussed.

Thermal interaction between water and liquid paraffin wax inside an intertwined enclosure: The role of natural convection in design of latent heat storage units

This work numerically investigated free convective heat transfer between water in a tank and melted paraffin-wax in an enclosure mounted inside the tank. The mediums were separated by thermally conductive walls. Three aspect ratios (AR = 0.3, 0.5, and 0.7) and three Rayleigh numbers (Ra = 104, 105, and 106) were examined for side- and bottom-heating orientations. The computations were conducted separately for the convection and conduction cases to observe the effects of natural convective heat transfer between the enclosures of the storage tank. The results showed that the heating orientation had a remarkable impact on the heat transfer between two fluids inside the intertwined enclosures. In the side-heating orientation, the variation of the average Nusselt number (Nu) with respect to Ra did not exhibit a consistent trend. It increased by 23.1 % when Ra increased from Ra = 104 to 105, but it decreased by 52.8 % when Ra was further increased from Ra = 105 to 106, at AR = 0.5. The Nu along the bottom wall of the inner enclosure was up to 24-folds of that along its side walls for the side-heating orientation and was 2.45-folds in the bottom-heating orientation. Furthermore, accumulation of hot fluid around the inner cavity walls, which occurred in side-heating cases, reduced convective heat transfer because of the low temperature gradient in these regions. Considering the outcomes of the present work, the bottom-heating orientation with AR = 0.5 can be recommended for future applications involving phase change processes as it ensured an effective thermal interaction between the two fluids.

Free Convection Heat Transfer in Composite Enclosures with Porous and Nanofluid Layers

This work conducts a numerical investigation of convection heat transfer within two composite enclosures. These enclosures consist of porous and nanofluidic layers, where the porous layers are saturated with the same nanofluid. The first enclosure has two porous layers of different sizes and permeabilities, while the second is separated by a single porous layer. As the porous layer thickness approaches zero, both enclosures transition to clear nanofluid enclosures. The study uses the Navier–Stokes equations to govern fluid flow in the nanofluid domain and the Brinkman–Forchheimer extended Darcy model to describe flow within the saturated porous layer. Numerical solutions are obtained using an iterative finite difference method. Key parameters studied include the porous thickness ( 0.0 ≤ S ≤ 1.0 ), the nanoparticle volume fraction ( 0.0 ≤ ϕ ≤ 0.05 ), the thermal conductivity ratio ( 0.5 ≤ R k ≤ 10 ), and the Darcy number ( 10 − 5 ≤ D a ≤ 10 − 2 ). Key findings include the observation that the highest heat transfer is achieved at the highest concentration, regardless of the porous layer configuration, permeability value, or thermal conductivity ratio. Specifically, an augmentation in values of N u ― I up to 22% is obtained as concentration is adjusted from 1% to 5%. Similarly, an augmentation in values of N u ― II up to 25% is obtained as concentration is adjusted from 1% to 5%.

MHD Free Convection Heat Transfer in Nano-Fluid Flow in Square Porous Cavity of TiO2 Nanoparticles with Base Fluid Engine Oil

MHD Free Convection Heat Transfer in Nano-Fluid Flow in Square Porous Cavity of TiO2 Nanoparticles with Base Fluid Engine Oil

MHD nonlinear natural convection from a uniformly moving porous vertical plate with constant heat and mass flux in the presence of thermal radiation, diffusion‐thermo, heat sink, and chemical reaction

AbstractAn attempt has been made to investigate the problem of nonlinear free convection heat and mass transfer flow past an infinite vertical porous plate embedded in a porous medium by taking into account thermal radiation and heat sink with constant heat and mass flux. Transversely oriented and of uniform strength , a magnetic field has been introduced to the fluid area. The nonlinear density variation with temperature as well as concentration are the basis for the current physical situation, which is explained by this mathematical model. Exact solutions are derived for momentum equation, energy equation, and species continuity equation under the relevant boundary conditions. The dimensionless governing equations are analytically solved. The influence of various physical parameters, such as Dufour number, Schmidt number, thermal Grashof number, magnetic parameter, mass Grashof number, heat sink, thermal radiation, Prandtl number, chemical reaction parameter on the flow, and transport characteristic, has been presented graphically and in tabular form. The novelty of the present investigation is that here both constant heat and mass flux at the plate are taken into account in addition to thermal radiation and heat sink. The findings of the mathematical study demonstrate that velocity, temperature, and skin friction intensify with a rise in the Dufour number this is due to the fact that the convection current becomes stronger as the Dufour number rises. Fluid's concentration declines as the Schmidt number grows, or the concentration rises as the mass diffusivity rises. Fluid temperature is enhanced with high thermal diffusivity. Frictional resistance on the plate hikes due to thermal buoyancy force.

Exploring the Limits of Empirical Correlations for the Design of Energy Systems With Complex Fluids: Liquid Sulfur Thermal Energy Storage as a Case Study

Abstract Sustainable energy technologies often use fluids with complex properties. As an example, sulfur is a promising fluid for use in thermal energy storage (TES) systems, with highly nonlinear thermophysical properties. The viscosity of liquid-phase sulfur varies by four orders of magnitude due to polymerization of sulfur rings between 400 K and 500 K, followed by depolymerization of long rigid chains, and a decrease in viscosity, as temperature increases. These properties may compromise the accuracy of long-established empirical correlations in the design of TES systems. This work uses computational fluid dynamics to compute steady-state free convection heat transfer coefficients of sulfur in concentric cylinders at temperatures between 400 K and 600 K. The results show that uneven distributions of high and low-viscosity sulfur in the system cause variations in flow patterns and highly nonlinear heat transfer coefficients as temperature gradients increase. As a result, existing empirical correlations for describing system performance become inaccurate. Comparisons of simulation results to predictions from well-established literature correlations show that deviations may surpass 50%. Nusselt versus Rayleigh number correlations for heat transfer are significantly affected by the loss of self-similarity. The analysis proves that existing correlations are not able to capture the complex properties of sulfur in this temperature range, suggesting that alternative modeling techniques are needed for the design and optimization of sulfur TES systems. These challenges are unlikely to be limited to sulfur as a working fluid or TES but will appear in a range of energy systems.

Experimental Investigation and Comparison of Natural and Forced Convective Heat Transfer Enhancement Using Water -Cuo Nano Fluid

Free and forced convective heat transfer along a vertical cylinder immersed in water– CuO nanofluid for numerous concentrations (0, 0.05, 0.1, 0.15, 0.2vol %) below consistent heat flux circumstance turned into investigated experimentally with and without vibrations and compared the effects. The vibrational movement is acquired by way of placing vibratory motor beneath the experimental setup. The accelerometer is used to measure the vibration frequencies 100HZ-220HZ. Thermal stratification become discovered out of doors the boundary layer in the ambient fluid after steady-state condition is done as the fluid temperature is going on growing alongside the axial course. It is found that the temperatures of the cylinder and the fluid increases alongside the axial route and the fluid temperature decreases inside the radial route. Experiments had been conducted for various heat inputs (30 W, 40 W, 45 W and 50 W) and quantity concentrations and determined that the addition of Copper oxide nanoparticles as much as 0.15 vol. % complements the thermal overall performance and then the further addition of nanoparticles ends in deterioration. The most enhancement in the free convection (without vibration) i.e., the heat transfer coefficient is 478.4214 w/m2 k at 0.15 vol. % and in forced convection (with vibration) i.e., the heat transfer coefficient is 489.4614 w/m2 k at 0.15 vol. %. Thus it is observed that for the same heat input, the heat transfer enhancement is greater for forced convection in comparison to free convection due to vibratory impact.