Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Analysis of entropy generation during natural convection in tilted triangular enclosures with various base angles

ABSTRACT

This paper presents a study of entropy generation during natural convection in a triangular enclosure with various configurations (cases 1 and 2 symmetric about Y-axis, and case 3 symmetric about X-axis) for the linearly heated inclined walls. The detailed analysis and comparison for the various base angles (φ = 45° and 60°) of the triangular enclosures have been carried out for Pr = 0.015 ? 1,000 and Ra = 10³ ? 10⁵. The results show that, case 3 configuration with the tilt angle φ = 60° may be the optimal shape based on the minimum total entropy generation (S_total) with the high heat transfer rate at Ra = 10⁵, irrespective of Pr.     

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.     

Lattice Boltzmann Simulation of Natural Convection in an Inclined Square Cavity with Spatial Temperature Variation

In this paper, natural convection heat transfer in an inclined square cavity filled with pure air (Pr = 0.71) was numerically analyzed with the lattice Boltzmann method. The heat source element is symmetrically embedded over the center of the bottom wall, and its temperature varies sinusoidally along the length. The top and the rest part of the bottom wall are adiabatic while the sidewalls are fixed at a low temperature. The influences of heat source length, inclination angle, and Rayleigh number (Ra) on flow and heat transfer were investigated. The Nusselt number (Nu) distributions on the heat source surface, the streamlines, and the isotherms were presented. The results show that the inclination angle and heat source length have a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In addition, the average Nu firstly increases with γ and reaches a local maximum at around γ = 45°, then decreases with increasing γ and reaches minimum at γ = 180° in the cavity with ? = 0.4. Similar behaviors are observed for ? = 0.2 at Ra = 10⁴. Moreover, nonuniform heating produces a significant different type of average Nu and two local minimum average Nu values are observed at around γ = 45° and γ = 180° for Ra = 10⁵ in the cavity with ? = 0.2.     

Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions

Entropy generation plays a significant role in the overall efficiency of a given system, and a judicious choice of optimal boundary conditions can be made based on a knowledge of entropy generation. Five different boundary conditions are considered and their effect of the permeability of the porous medium, heat transfer regime (conduction and convection) on entropy generation due to heat transfer, and fluid friction irreversibilities are investigated in detail for molten metals (Pr = 0.026) and aqueous solutions (Pr = 10), with Darcy numbers (Da) between 10^?5–10^?3 and at a representative high Rayleigh number, Ra = 5 × 10⁵. It is observed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating (case 1), with a penalty on thermal mixing. Finally, the analysis of total entropy generation due to variation in Da and thermal mixing and temperature uniformity indicates that, there exists an intermediate Da for optimal values of entropy generation, thermal mixing, and temperature uniformity.     

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 Entropy Generation On Thermal Management During Natural Convection in a Tilted Square Cavity with Isothermal and Non-Isothermal Hot Walls

Entropy generation during natural convection within tilted square cavity inclined with different angles (? = 30°and 75°) for various thermal boundary conditions (case 1: isothermal heating and case 2: non-isothermal heating) has been studied. Simulations are carried out over a range of parameters: Rayleigh number (10³ ≤ Ra ≤ 10⁵) and Prandtl numbers (Pr = 0.025 and 998.24). The numerical results are presented in terms of isotherms (θ), streamlines (ψ), entropy generation due to heat transfer (S _θ ) and fluid friction (S _ψ ). Heating strategy is energy efficient for case 2 (non-isothermal heating) due to its less total entropy generation with reasonable heat transfer rate, irrespective of Pr.     

Natural Convection Heat Transfer Enhancement in a Square Cavity Periodically Cooled from Above

The present article reports numerical results of natural convection within an air filled square cavity with its horizontal walls submitted to different heating models. The temperature of the bottom horizontal surface (hot temperature) is maintained constant, while that of the opposite surface (cold temperature) is varied sinusoidally with time. The remaining vertical walls are considered adiabatic. The parameters governing the problem are the amplitude (0 ≤ a ≤ 0.8) and the period (τ ≥ 0.001) of the variable temperature, the Rayleigh number (10³ ≤ Ra ≤ 7 × 10⁶), and the Prandtl number (Pr = 0.71). In constant cooling conditions (a = 0), up to three different solutions (monocellular flow MF, bicellular vertical flow BVF, and bicellular horizontal flow BHF) are obtained. Their existence ranges are delineated and, in the limits of the existence range of each solution, the transitions observed are identified and described. In the variable cooling conditions, the effect of the amplitude and the period of the exciting temperature on fluid flow and heat transfer is examined in the case of the MF, and BHF for specific values of Ra. Results are presented in terms of Ψ _max (t), Ψ _min (t), Nu(t) and streamlines, heatlines, and isotherms during the evolutions of selected flow cycles. In comparison with the constant heating conditions, it is found that the variable cooling temperature could lead to a drastic change in the flow structure and the corresponding heat transfer, especially at specific low periods of the cold variable temperature. This leads to a resonance phenomenon characterized by an important increase in heat transfer by about 46.1% compared to the case of a constant cold temperature boundary condition.     

Coupled Natural Convection and Radiation in a Horizontal Rectangular Enclosure Discretely Heated from Below

A numerical study is carried out to investigate the interaction between natural convection and thermal radiation in a horizontal enclosure filled with air and heated discretely from below. The results are presented for a cavity having an aspect ratio A _r  = L′/H′ = 10, while the Rayleigh number and the emissivity of the walls are varied in the ranges 10³ ≤ Ra ≤ 10⁶ and 0 ≤ ε ≤ 1, respectively. The results of the study, presented in terms of flow and temperature patterns, average convective, radiative and total Nusselt numbers, evaluated on the cold wall, show that the problem has multiple solutions. Each of these solutions is characterized by a specific flow structure, and its appearance and range of existence depend strongly on the parameters Ra and ε. The amount of heat evacuated through the cold surface is dependent on the type of solution.     

Natural Convection Heat Transfer in an Enclosure Filled with an Ethylene Glycol—Copper Nanofluid Under Magnetic Fields

This article presents the results of a numerical study on natural convection in a square enclosure filled with ethylene glycol–copper nanofluid in the presence of magnetic fields. Two opposite horizontal walls of the enclosure are insulated and the two vertical walls are kept constant at different temperatures. A uniform horizontal magnetic field is externally imposed. The governing equations (mass, momentum, and energy) are formulated and solved numerically with a finite element using COMSOL Multiphysics. The effects of pertinent parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁷), Hartmann number (0 ≤ Ha ≤ 120), and solid volume fraction (0 ≤ φ ≤ 0.06) on the flow and the heat transfer performance of the enclosure are examined when the Prandtl number is assumed to be Pr = 151.     

NATURAL-CONVECTIVE HEAT TRANSFER IN A SQUARE CAVITY WITH TIME-VARYING SIDE-WALL TEMPERATURE

ABSTRACT

The natural-convective heat transfer in an inclined square enclosure is studied numerically. The top and bottom horizontal walls are adiabatic, and the right side wall is maintained at a constant temperature T ₀. The temperature of the opposing vertical wall varies by sine law with time about a mean value T ₀. The system of Navier–Stokes Equations in Boussinesq approximation is solved numerically by the control-volume method with SIMPLER algorithm. The enclosure is filled with air (Pr = 1) and results are obtained in the range of inclination angle 0° ≤ α ≤ 90° for two values of Grashof number (2 × 10⁵ and 3 × 10⁵). It can be noted that there is a nonzero time-averaged heat flux through the enclosure at α ≠ 0°. The dependencies of time-averaged heat flux on oscillation frequency and inclination angle are depicted. It is found that the maximal heat transfer corresponds to the values of inclination angle α = 54^○ and dimensionless frequency f = 20π for both Grashof numbers studied (2 × 10⁵ and 3 × 10⁵).     

Effect of Inclination on Heat Transfer and Fluid Flow in a Finned Enclosure Filled with a Dielectric Liquid

The problem of two-dimensional natural convection flow of a dielectric fluid in a square inclined enclosure with a fin placed on the hot wall is investigated numerically. The fin thickness and length are 1/10 and 1/2 of the enclosure side, respectively. The Rayleigh number is varied from 10³ to 5 × 10⁵ and the solid to fluid thermal conductivity ratio is fixed at 10³. The enclosure tilt or inclination angle is varied from 0° to 90°. The streamlines and isotherms within the enclosure are produced and the heat transfer is calculated. It is found that for 2.5 × 10⁴ ≤ Ra ≤ 2.5 × 10⁵, the average Nusselt number is maximum when γ = 0° and minimum when γ = 90°. For Ra = 5 × 10⁵, the values of enclosure tilt angle for which the average Nusselt number is maximum or minimum are completely different due to the transition to unsteady state. In this case, the maximum heat transfer is obtained for γ = 60°, while the minimum heat transfer is predicted for γ = 0°. Monomial correlations relating the average Nusselt number with the different values of the Rayleigh number from 10⁴ to 10⁵ are determined for two different angles, γ = 0° and γ = 90°.     

On the Validity of the Isothermal Model for Natural Convection Flow around Blocks Submitted to Volumetric Heat Generation in a Horizontal Channel

This work presents numerical results of natural convection in a horizontal channel provided with heating blocks periodically mounted on its lower adiabatic surface. The upper surface of the channel is maintained cold at a constant temperature. The parameters of the study are the ratio of solid blocks to fluid thermal conductivities (0.1 ≤ k* = k _s /k _a ≤ 200), the Rayleigh number (10⁴ ≤ Ra ≤ 10⁷), and the relative blocks height (1/8 ≤ B ≤ 1/2). Two models are considered in this study depending on whether the blocks are submitted to uniform heat generation (model 1), or maintained isothermal (model 2) at the average temperature calculated using model 1. The effect of the thermal conductivities ratio and the other controlling parameters on the validity of the isothermal model is examined. It is found that when multiple steady solutions are possible, some of the solutions obtained with the isothermal model may not reproduce the results of the model with blocks submitted to volumetric heat generation, even at very large conductivities ratio.     

Mixed Convection from a Heated Sphere in Bingham Plastic Fluids

In this work, the steady and laminar mixed-convection heat transfer from an isothermal sphere immersed in Bingham plastic fluids has been investigated in the aiding-buoyancy configuration. The pertinent coupled equations of motion and thermal energy have been solved numerically over the following ranges of conditions: Richardson number, 0 ≤ Ri ≤ 2, Bingham number, 0 ≤ Bn ≤ 10, Reynolds number, 0.1 ≤ Re ≤ 100 and Prandtl number, 10 ≤ Pr ≤ 100. Flow characteristics like streamlines, pressure coefficient, morphology of yielded/unyielded regions and drag coefficient are discussed extensively. Similarly, isotherms, local Nusselt number and average Nusselt number are thoroughly examined to develop an overall understanding of the corresponding heat transfer characteristics. All else being equal, in contrast to the positive role of the aiding-buoyancy free convection in Newtonian and power-law fluids, due to the fluid yield stress, heat transfer is impeded in viscoplastic fluids. While the average value of the Nusselt number is influenced by four dimensionless groups, namely, Reynolds number, Bingham number, Prandtl number and Richardson number, by using novel scaling, it has been possible to consolidate the present results via the use of the Colburn j-factor in a simple form. This is particularly suitable for predicting the value of the Nusselt number in a new application.     

Numerical Investigation on the Steady State Natural Convection in a Horizontal Open-Ended Cavity with a Heated Upper Wall

In this article, the investigation is focused on a configuration made of two horizontal parallel plates with the upper plate heated at uniform heat flux and the lower one adiabatic. Results are presented in terms of velocity and temperature fields, and both the temperature and the velocity profiles at different sections are shown. They are reported at two Rayleigh numbers, 10³ and 10⁵, and for two aspect ratio values, 1 and 10. Results are also shown in terms of the upper and lower wall temperature profiles. Correlations for average Nusselt numbers and maximum dimensionless wall temperature, in terms of Rayleigh number and aspect ratio, are given for 10³ ≤ Ra ≤ 10⁵ and 1 ≤ L/b ≤ 10.     

Kinetic parameter estimation and simulation of trickle-bed reactor for hydrodenitrogenation of whole-fraction low-temperature coal tar

A kinetic model of whole-fraction low-temperature coal tar (LTCT) hydrodenitrogenation (HDN) was established and applied to a bench-scale trickle-bed reactor (TBR). The gPROMS software was used for parameter estimation, and nonlinear regression method was used to get the kinetic parameters: Ea = 98,173; k₀ = 1.7 × 10⁶; n = 1.56; α = -0.16; m = 0.5; t_c = 12,196; β = 1.06. The concentration of nitrogen compounds in the liquid phase at different axial positions of TBR was obtained. At the same time, the order of influence of reaction conditions on HDN was temperature, LHSV, and pressure. The effectiveness factors at different positions of the catalyst bed were analyzed, and the influence of different reaction conditions on the effectiveness factor was studied.     

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.     

Effect of Radiative Heat Transfer on Three-Dimensional Double Diffusive Natural Convection

This work presents a numerical study of the effect of the radiative heat transfer on the three-dimensional double diffusive convection in a differentially heated cubic cavity for different optical parameters of the medium. This numerical study is conducted for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 10⁵, Le = 2, and buoyancy ratio N in the range [–2, 0]. The natural convection equations, using the Boussinesq approximation for the treatment of buoyancy term in the momentum equation, are expressed using the vorticity–stream function formulation. These equations and the radiative transfer equation are discretized, respectively, with the control volume finite difference method and the FTn finite volume method. The influences of the optical thickness and the conduction–radiation parameter of the semitransparent fluid on heat and mass transfer are depicted. Results show different transitions of the structure of the main flow when varying the conduction–radiation parameter and the optical thickness.