Visualization of Heat Transport during Natural Convection Within Porous Triangular Cavities via Heatline Approach

In this article, natural convection in a porous triangular cavity has been analyzed. Bejan's heatlines concept has been used for visualization of heat transfer. Penalty finite-element method with biquadratic elements is used to solve the nondimensional governing equations for the triangular cavity involving hot inclined walls and cold top wall. The numerical solutions are studied in terms of isotherms, streamlines, heatlines, and local and average Nusselt numbers for a wide range of parameters Da (10^?5–10^?3), Pr (0.015–1000), and Ra (Ra = 10³–5 × 10⁵). For low Darcy number (Da = 10^?5), the heat transfer occurs due to conduction as the heatlines are smooth and orthogonal to the isotherms. As the Rayleigh number increases, conduction dominant mode changes into convection dominant mode for Da = 10^?3, and the critical Rayleigh number corresponding to the on-set of convection is obtained. Distribution of heatlines illustrate that most of the heat transport for a low Darcy number (Da = 10^?5) occurs from the top region of hot inclined walls to the cold top wall, whereas heat transfer is more from the bottom region of hot inclined walls to the cold top wall for a high Darcy number (Da = 10^?3). Interesting features of streamlines and heatlines are discussed for lower and higher Prandtl numbers. Heat transfer analysis is obtained in terms of local and average Nusselt numbers (Nu _l , Nu _t ) and the local and average Nusselt numbers are found to be correlated with heatline patterns within the cavity.     

Numerical modeling of heat and mass transfer characteristics during the forced convection drying of a square cylinder under strong blockage

Two-dimensional analysis of heat and mass transfer during drying of a square cylinder (SC) for confined flow with a strong blockage ratio (β?=?0.8) was performed using the alternating direction implicit (ADI)-based software. The influence of Reynolds number (Re?=?10–50) and moisture diffusivity number (D?=?1?×?10^?5???1?×?10^?8?m²/s) on the heat and mass transfer mechanisms was investigated. The convective heat transfer coefficients on SC surfaces were obtained using a commercial software package. The moisture content distributions inside a SC under transient conditions were calculated using the ADI method. The calculations showed that a higher Reynolds number enhances the overall mean Nusselt number and heat transfer coefficient value. The largest mean Nusselt number and heat transfer coefficient values were obtained at the front face of the SC, which makes the greatest contribution to the overall mean Nusselt number and heat transfer coefficient values for all surfaces of the SC. The effect of Reynolds number on the overall drying time was also investigated. Low Reynolds number and moisture diffusivity values lead to an increase in the overall drying time (Δt_od). For Re?=?10, the Δt_od values are 502.19?→?220288?s and for Re?=?50, the Δt_od values are 126.14?→?70353.21?s for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-Re?=?10/Δt_od-Re?=?50 ratios are 3.98–3.89 and 3.13 for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-D2/Δt_od-D1 is 7.47 for Re?=?10, and Δt_od-D3/Δt_od-D2 is 7.63 for Re?=?50, whereas Δt_od-D3/Δt_od-D1 is 438.66 for Re?=?10, and Δt_od-D3/Δt_od-D1 is 557.74 for Re?=?50. Additionally, iso-moisture contours of SC were presented and relations for Nusselt number and mass transfer coefficient values were derived.     

Effect of Darcy,Reynolds, and Prandtl Numbers on the Performance of Two‐Phase Flow Heat Exchanger Filled with Porous Media

Experimental investigation of two‐phase laminar forced convection in a single porous tube heat exchanger is presented. The effect of Darcy, Reynolds, and Prandtl numbers on the performance of this heat exchanger during the condensation process of carbon dioxide at different test conditions were investigated. Gravel sand with different porosities is used as a porous medium. The flow in the porous medium is modeled using the Brinkman–Forchheimer‐extended Darcy model. Parametric studies are also conducted to evaluate the effects of porosity and Reynolds and Prandtl numbers on the heat transfer coefficient and the friction factor. A dimensionless performance parameter is developed in order to be used in evaluating the porous tube heat exchanger based on both the heat transfer enhancement and the associated pressure drop. The study covers a wide range of inlet pressure (P_in), mass flow rate (), porosity of gravel sand (ε), and Darcy number (Da) which ranged: 34.5 ≤ P_in ≤ 43 bars, 8 * 10^{? 5} ≤ ≤ 16 * 10^{? 5} kg/s, 34.9% ≤ ε ≤ 44.5%, 1.6 * 10^{? 6} ≤ Da ≤ 5 * 10^{? 6}, respectively. The study predicted the combined effect of the Reynolds number, Darcy number, porosity, and Prandtl number on the heat transfer and pressure drop of carbon dioxide during the condensation process in a porous medium. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21117     

Numerical investigation of unsteady natural convection heat transfer and entropy generation from a pair of cylinders in a porous enclosure

Abstract

The present study analyses numerically the unsteady heat transfer and entropy generation characteristics in a two-dimensional porous enclosure embedded with two heated circular cylinders at different positions at the vertical mid-plane. The heat transfer is primarily due to conduction for lower values of Darcy number (10^?4), while heat transfer by convection becomes significant for higher values of Darcy number (10^?3, 10^?2). Contrasting features are observed in the variation of time-average Nusselt number with interspacing distance. The major contributor of irreversibility is the entropy generation due to heat transfer for lower values of Darcy number, while for larger values of Darcy number, it varies with Rayleigh number.     

Mixed Convection in an Obstructed Open-Ended Cavity

Mixed convection in an obstructed cavity with heated horizontal walls is investigated in this work. Brinkman-Forchheimer-extended Darcy model is utilized to describe the flow characteristics within a porous medium for different angles of attack with respect to the forced convection. Numerical results are obtained for a wide range of Grashof numbers (10²–10⁹), Reynolds numbers (10²–10⁵), Darcy numbers (10^?6–10^?1), and aspect ratios (0.25–2). Effects of the pertinent physical parameters are investigated in terms of the flow and temperature fields, as well as Nusselt number distributions. The presented results show that the Darcy number plays a significant role on the flow and thermal fields and the Nusselt number distributions for different flow configurations. For an inclined flow, the vertical velocity component is substantially diminished within a narrow entrance section near the inlet boundary. It is shown that as the aspect ratio increases the thickness of the thermal boundary layer increases, resulting in a decrease in the heat transfer rate though the horizontal walls.     

Heat transfer enhancement in self-sustained oscillatory flow in a staggered baffled vertical channel under the buoyancy effect

Unsteady laminar heat transfer enhancement in asymmetrically heated vertical baffled channel under buoyancy effect is investigated numerically. The baffles are installed on the two walls in an offset manner with constant spacing. The governing equations are solved by the finite volume formulation using openFoam© open-source code. Air (Pr?=?0.71) is used as working fluid. The effects of Reynolds number (100–1400) and Grashof number (2.5?×?10⁴ to 2?×?10⁵) in addition to the baffle height (0.1–0.5) on heat transfer and friction factor are studied. The results are given in the form of dimensionless isotherm contours and streamlines in addition to the Nusselt number and friction factor. The results obtained revealed that the flow bifurcates to self-sustained oscillatory flow at moderate Reynolds number (below 600 for a blockage ratio of 0.25). The unsteady self-sustained flow leads to heat transfer enhancement up to 2.8 times for baffle height h_b?=?0.25 and up to 3.7 when compared to the smooth channel. Unfortunately, this heat transfer is accompanied by an important increase in pumping power.     

Elucidating the Effects of Cu‐Nanoparticles in a Porous Medium vis‐à‐vis Heat Transfer Phenomena

In this paper, a numerical simulation technique is developed to investigate the qualitative and quantitative behaviour of Cu‐nanoparticles in a porous medium vis‐a‐vis the heat transfer enhancements—buoyancy driven flow in a two‐dimensional square cavity, with moving walls is presented. The model utilizes the finite volume approach to solve the Brinkman–Darcy equations for Cu‐nanoparticles in a porous media. Discretization is carried out for convective and diffusive fluxes using Quadratic Upwind Interpolation for Convective Kinematics (QUICK) and central difference schemes, respectively. Tri‐Diagonal Matrix Algorithm is invoked to solve the set of algebraic equations. The Darcy number (Da), Prandtl number (Pr), and volume fraction (χ) are varied from 10^?3 to 10^?1, 3 to 7, and 0% to 20%, respectively. Insight into the cause of variations in isotherms, streamlines, Nusselt number (Nu), and mid‐plane velocities is explicated. The present numerical results are compared with the existing literature and found to be in good agreement. Even though nanoparticles slightly hinder the activity of the fluid, they can augment the average Nu by 90% for Pr = 7, Da = 0.1, and χ = 20% as compared to the absence of nanoparticles. Their efficacy is more prominent for flows with higher Da and Pr. Quantitative values for Nu were obtained for various combinations of Pr, Da, and χ.     

Numerical Analysis of the Effects of Selected Geometrical Parameters and Fluid Properties on MHD Natural Convection Flow in an Inclined Elliptic Porous Enclosure with Localized Heating

Magnetohydrodynamic (MHD) natural convection flow and associated heat convection in an oriented elliptic enclosure has been investigated with numerical simulations. A magnetic field was applied to the cylindrical wall of the configuration, the top and bottom walls of the enclosure were circumferentially cooled and heated, respectively, while the extreme ends along the cross‐section of the elliptic duct were considered adiabatic. The full governing equations in terms of continuity, momentum, and energy transport were transformed into nondimensional form and solved numerically using finite difference method adopting Gauss–Seidel iteration technique. The selected geometrical parameters and flow properties considered for the study were eccentricity (0, 0.2, 0.4, 0.6, and 0.8), angle of inclination (0°, 30°, 60°, and 90°), Hartmann number (0, 25, and 50), Grashof number (10⁴, 10⁵, and 10⁶), and Darcy number (10^?3, 10^?4, and 10^?5). The Prandtl number was held constant at 0.7. Numerical results were presented by velocity distributions as well as heat transfer characteristics in terms of local and average Nusselt numbers (i.e., rate of heat transfer). The optimum heat transfer rate was attained at e value of 0.8. Also, the heat transfer rate increased significantly between the angles of inclination 58° and 90°. In addition, Hartmann number increased with decreased heat transfer rate and flow circulation. A strong flow circulation (in terms of velocity distribution) was observed with increased Grashof and Darcy numbers. The combination of the geometric and fluid properties therefore can be used to regulate the circulation and heat transfer characteristics of the flow in the enclosure.     

Effect of Undulations on the Natural Convection Heat Transfer and Entropy Generation Inside a Porous Right-Angled Triangular Enclosure

In the present study, natural convection in a two-dimensional porous right-angled triangular enclosure with one wavy wall is studied numerically. Three cases with one, two, and three undulations on the left wall are studied in this analysis. The stream function-vorticity equations are solved using finite-difference technique and a structured nonorthogonal body-fitted mesh is used for computations. The effect of Rayleigh number (Ra = 10³–10⁶), Darcy number (Da = 10^?4–10^?2) and undulations on the heat transfer, fluid flow, and entropy generation is investigated. It is found that average Nusselt number increases with Darcy number and number of undulations present on the left wall at fixed Darcy number.     

Role of various moving walls on entropy generation during mixed convection within entrapped porous triangular cavities

The aim of the present investigation is to analyze the effect of the motion of horizontal walls on the entropy generation and heat transfer rates in an entrapped triangular porous cavity during mixed convection. Two different thermal boundary conditions are considered as follows: (i) hot inclined walls and cold horizontal walls and (ii) cold inclined walls and hot horizontal walls. Overall, Re?=?100 may be recommended at Pr_m?=?0.026, 7.2, Gr?=?10⁵, and Da_m?=?10^?4 to 10^?2 within the upper and lower cavities for cases 1 and 2.     

Heatlines for Visualization of Heat Transport for Natural Convection within Porous Trapezoidal Enclosures with Various Wall Heating

A detailed study on natural convection heat transfer within porous trapezoidal enclosures has been carried out for two different cases. The effect of linearly heated side walls on flow pattern is investigated in case 1; whereas, the effect of linearly heated left wall and cold right wall is studied in case 2. In both cases, the bottom wall of the cavity is uniformly heated and the upper wall is adiabatic. The results are analyzed for a wide range of parameters such as Rayleigh number, Ra(10³ ≤ Ra ≤ 10⁶), Prandtl number, Pr(0.015 ≤Pr ≤ 988.24), and Darcy number, Da(10^?5 ≤ Da ≤ 10^?3).     

Double-Diffusive Natural Convection in a Mixture-Filled Cavity with Walls' Opposite Temperatures and Concentrations

ABSTRACT

This paper deals with natural convection flows evolving inside an ended and differentially heated cavity, which is filled either with an air or an air–CO₂ mixture. The investigation was conducted through the laminar regime to analyze buoyancy ratio changes' effect on heat and mass transfers both in aiding and opposing flows. The thermal Rayleigh number was varied from 10³ to 10⁷. Streamlines, isotherms, iso-concentrations, and local and average Nusselt and Sherwood numbers are provided to demonstrate the convective flow induced. The governing equations are solved by finite volume method using SIMPLEC algorithm to handle the pressure–velocity coupling. The buoyancy ratio effect on dynamic, thermal, and mass fields is noteworthy, exhibiting both the competition between thermosolutal forces and fields' stratification. From the results, it turned out that, in general, when the buoyancy ratio is: (1) positive, thermosolutal buoyancy forces are cooperative, (2) nil, solutal buoyancy forces are weak and the flow is merely thermoconvective, (3) negative and greater than ?1, buoyancy effects are competing and thermal convection dominates, (4) ?1, buoyancy effects are canceled and heat and mass transfers are driven only by diffusion, and (5) less than ?1, buoyancy forces compete with a dominant solutal convection.     

Experimental study on the effect of porous medium on performance of a single tube heat exchanger: A CO2 case study

An experimental study on single‐phase laminar forced convection in a single porous tube heat exchanger is presented. Parametric studies are conducted for different inlet pressures, different mass flow rates, and different porosities to evaluate the effects of particle diameter and Reynolds number on the heat transfer and friction factor. The Nusselt number and friction factor are developed for efficient design of a porous heat exchanger based on the present configuration. Heat is transferred to the walls of the heat exchanger by natural convection mode. Gravel sand with different porosities is used as a porous medium during the tests. The flow of carbon dioxide as a working fluid in the porous medium is modeled using the Brinkman–Forchheimer‐extended Darcy model. A dimensionless performance parameter is developed in order to be used in evaluating the porous tube heat exchanger based on both the heat transfer enhancement and the associated pressure drop. The study covers a wide range of inlet pressures (P_i), mass flow rates ( ), porosity of gravel sand (ε), and particle diameters (d_m) which ranged 34.5 ≤ P_i ≤ 43 bars, 8 ?? 10^?5 ≤ ≤ 16 ?? 10^?5 kg/s, 34.9% ≤ ε ≤ 44.5%, 1.25 ≤ d_m ≤ 5.15 mm, respectively. This study revealed that a smaller particle diameter can be used to achieve higher heat transfer enhancement, but a larger particle diameter leads to a more efficient performance based on heat transfer enhancement. The average heat transfer coefficient of carbon dioxide decreases when the porosity increases. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21059     

Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media

Numerical simulations have been carried out to investigate the turbulent heat transfer enhancement in the pipe filled with porous media. Two-dimensional axisymmetric numerical simulations using the k–? turbulent model is used to calculate the fluid flow and heat transfer characteristics in a pipe filled with porous media. The parameters studied include the Reynolds number (Re = 5000–15,000), the Darcy number (Da = 10^?1–10^?6), and the porous radius ratio (e = 0.0–1.0). The numerical results show that the flow field can be adjusted and the thickness of boundary layer can be decreased by the inserted porous medium so that the heat transfer can be enhanced in the pipe. The local distributions of the Nusselt number along the flow direction increase with the increase of the Reynolds number and thickness of the porous layer, but increase with the decreasing Darcy number. For a porous radius ratio less than about 0.6, the effect of the Darcy number on the pressure drop is not that significant. The optimum porous radius ratio is around 0.8 for the range of the parameters investigated, which can be used to enhance heat transfer in heat exchangers.     

Natural convection in a triangular cavity filled with air under the effect of external air stream cooling

Natural convection in a triangular cavity filled with air is investigated numerically. In this paper, the cavity is exposed to air stream cooling exerted on its sides and it is heated by a fixed heat flux from the base. The air inside the cavity is assumed to be laminar and obeying Boussinesq approximation. The governing equations are solved numerically using the finite volume technique with SIMPLE algorithm. The results are achieved with a range of Rayleigh number (10⁴ < Ra < 10⁷), free stream Reynolds number (10³ < Re_∞ < 1.5 × 10⁴), four aspect ratios (AR = 0.25, 0.5, 0.866, and 1) and five inclination angles (? = 0°, 30°, 45°, 60°, 90°). The influence of these parameters is displayed on the stream function, isotherms lines, local and average Nusselt numbers. The results reveal that the heat transfer rate increases as Rayleigh number, free stream Reynolds number and AR increase. The highest heat transfer rate is obtained at ? = 0° while the lowest one is obtained at ? = 90°. Furthermore, as the AR augments, the local and average Nusselt numbers are enhanced and the stream function is formed of two symmetric counter‐rotating vortices.     

Mixed Convection in a Vertical Channel with Discrete Heat Sources Using a Porous Matrix

In this work, we present the mixed convection air-cooling of two identical heat sources mounted in a vertical channel by using a porous matrix. The flow field is governed by the Navier–Stokes equation in the fluid region, the Darcy–Brinkman–Forchheimer equation in the porous region, and the thermal field by the energy equation. The effects of the Richardson number, Darcy number, thermal conductivity, and thickness of the porous matrix on the flow and heat transfer were studied. Results show that a better cooling is obtained for the channel completely filled with a porous material, except the components, with the Richardson number (Ri = Gr/Re² = 0.25), where Gr = 10⁴ is the Grashof number and Re = 200 is the Reynolds number, and for all Darcy numbers (10^?5 ≤ Da ≤ 10^?3). It was also seen that for Gr/Re² = 20, where the buoyancy effect is stronger, the average Nusselt number with porous matrix is higher than without porous matrix for all Richardson numbers (Ri = 0.25, 1, 10, and 20). As a result, we can economize the energy of the fan. Finally, the insertion of the porous matrix with high thermal conductivity ameliorates the cooling of the heat sources.     

Simulation of natural convection and entropy generation of MHD non-Newtonian nanofluid in a cavity using Buongiorno's mathematical model

In this paper, natural convection and entropy generation of non-Newtonian nanofluid, using the Buongiorno's mathematical model in a cavity in the presence of a uniform magnetic field has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10⁴ and 10⁵), Hartmann number (Ha = 0, 15, 30), buoyancy ratio number (N_r = 0.1, 1, and 4), power-law index (n = 0.4–1), Lewis number (Le = 1, 5, and 10), Thermophoresis parameter (N_t = 0.1, 0.5, 1), and Brownian motion parameter (N_b = 0.1, 1, 5). The Prandtl number is fixed at Pr = 1. The Results indicate that the augmentation of Hartmann number causes heat and mass transfer to drop. The increase in Rayleigh number enhances heat and mass transfer for various power-law indexes. The alteration of the power-law index changes heat and mass transfer. In addition, the rise of Hartmann number declines the shear-thinning behavior. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorate mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. The augmentation of the power-law index declines various entropy generations in different Rayleigh numbers and Hartmann numbers. The increase in Hartmann number declines total entropy generation in different Rayleigh numbers. In addition, the rise of Rayleigh number and Hartmann number causes Bejan number to drop in various power-law indexes. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters enhance the total irreversibility.     

Non‐Darcy assisted flow along a channel with an open cavity filled with water–TiO2 nanofluid

Numerical investigation on forced (assisted) convection heat transfer in a two‐dimensional horizontal porous channel with an open cavity is studied in this article. A non‐uniform heat flux is considered to be located on the bottom surface of the cavity. The rest of the surfaces are taken to be perfectly insulated. The physical domain is filled with a water‐based nanofluid containing TiO₂ nanoparticles. The fluid enters from the left and exits from the right with initial velocity U_i and temperature T_i. Governing equations are discretized using the penalty finite element method. The simulation is carried out for a wide range of Reynolds number Re (= 10–500) and Darcy number Da (= 10^?5–∞). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt numbers, average temperatures of the fluid, horizontal and vertical velocities at mid‐height of the channel and mean velocity fields for various Re and Da. The enhancement of heat transfer rate is caused by the increasing Re and falling Da. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21046     

Numerical investigation of heat transfer enhancement on a porous vortex-generator applied to a block-heated channel

The numerical simulation is used to obtain the unsteady laminar flow and convective heat transfer in the block-heated channel with the porous vortex-generator. The general Darcy–Brinkman–Forchheimer model is adopted for the porous vortex-generator. The parameters studies including porosity, Darcy number, width-to-height ratio of porous vortex-generator and Reynolds number have been explored on heat transfer enhancement and vortex-induced vibration in detail. The results indicate that heat transfer enhancement and vortex-induced vibration increase with increasing Reynolds number and width-to-height ratio. However, the porosity has slight influence on heat transfer enhancement and vortex-induced vibration. When Darcy number is 10^?3 or 10^?4, installing a porous vortex-generator with B/h = 1.0 improves overall heat transfer the best along heated blocks, and has a strong reduction of vortex-induced vibration.     

Enhanced thermal performance and entropy generation analysis in a novel cavity design with circular cylinder

Analyzing fluid dynamics and heat transfer holds significant importance in the design and enhancement of engineering systems. The current investigation utilizes the finite element method to explore natural convection and heat transfer intricacies within a novel cavity containing an inner circular cylinder under steady and laminar flow conditions. The principal aim of this study is to assess the impact of Rayleigh number (Ra), Bejan number (Be), and the presence of adiabatic, hot, and cold cylinders on heat transfer, entropy generation, and fluid flow. The range of Ra considered in this investigation spans from 10³ to 10⁶, while the Prandtl number for the air is fixed at 0.71. The findings illustrate that the presence of a cylinder leads to higher Be as Ra increase, compared to scenarios where no cylinder is present. This observation suggests that buoyancy forces dominate in the absence of a cylinder, resulting in significantly enhanced convective heat transfer efficiency. However, the presence of a heated cylinder within the tooth-shaped cavity exerts a substantial influence on the overall thermal performance of the system. Notably, the average Nusselt Number (Nu) experiences a remarkable increase of 41.97% under the influence of a heated cylinder, when compared to situations where a cold cylinder is present. This elevated average Nu signifies improved heat transfer characteristics, ultimately resulting in an overall improvement in the thermal system's efficiency.