Lattice Boltzmann investigation for enhancing the thermal conductivity of ice using Al2O3 porous matrix

An enthalpy-based Lattice Boltzmann method (LBM) with double-distribution function (DDF) model is used to investigate numerically the effects of inserting a porous matrix on the heat transfer performance of the phase change material (PCM). Simulations are carried out for melting of ice in saturated Al₂O₃ porous matrix encapsulated in a concentric annulus. The process is considered as a conduction/convection controlled phase change problem at a representative elementary volume (REV) scale. The present results are validated by previous published numerical simulations of melting with and without porous media. In this research paper, the effects of decreasing the porosity on the temperature contours, flow patterns within the melt zone, complete melting time of the PCM and average Nusselt number are discussed qualitatively and quantitatively.     

Thermal convective instability of a horizontal saturated porous layer with a segment of inhomogeneity

Convective stability is studied for an infinite horizontal porous layer containing a vertical porous segment of different properties. The critical Rayleigh number depends on the aspect ratio of the nonhomogeneous region and the ratios of permeability, thermal conductivity, and thermal diffusivity of the matrix. Incipient streamlines may be either symmetric or antisymmetric.     

Effects of the heat transfer fluid velocity on the storage characteristics of a cylindrical latent heat energy storage system: a numerical study

A numerical study of the effects of the thermal fluid velocity on the storage characteristics of a cylindrical latent heat energy storage system (LHESS) was conducted. Due to the low thermal conductivity of phase change materials (PCMs) used in LHESS, fins were added to the system to increase the rate of heat transfer and charging. Finite elements were used to implement the developed numerical method needed to study and solve for the phase change heat transfer (melting of PCM) encountered in a LHESS during charging. The effective heat capacity method was applied in order to account for the large amount of latent energy stored during melting of the PCM and the moving interface between the solid and liquid phases. The effects of the heat transfer fluid (HTF) velocity on the melting rate of the PCM were studied for configurations having between 0 and 18 fins. Results show that the overall heat transfer rate to the PCM increases with an increase in the HTF velocity. However, the effect of the HTF velocity was observed to be small in configurations having very few fins, owing to the large residual thermal resistance offered by the PCM. However, the effect of the HTF velocity becomes more pronounced with addition of fins; since the thermal resistance on the PCM side of the LHESS is significantly reduce by the large number of fins in the system.     

Effect of Conduction in Bottom Wall on B��nard Convection in a Porous Enclosure with Localized Heating and Lateral Cooling

Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length?? ${0.2\leq H \leq 0.9}$ , the wall thickness?? ${0.05\leq D \leq 0.4}$ , the thermal conductivity ratio?? ${0.8\leq K_{\rm r} \leq 9.8}$ , and the Biot number?? ${0.1\leq Bi \leq 1.1}$ . It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate.     

Pore-Scale Numerical Experiment on the Effect of the Pertinent Parameters on Heat Flux Splitting at the Boundary of a Porous Medium

Pore-scale heat and fluid flow simulation through reconstructed porous media is presented with the aim of investigating the physics of heat flux splitting at the boundary of porous media. As such, the effects of the solid to fluid thermal conductivity ratio, porosity, pore-scale Reynolds number, Prandtl number and heat conduction within the solid matrix are investigated. The results of the present study for heat transfer coefficient and pressure drop are compared with available experimental data and good agreement was observed. The validated results are then used to investigate the validity of the existing volume-averaged models. It was observed that while results based on the volume-averaged models are reasonably close to current predictions for $\varepsilon \le 0.7$ , the discrepancy between the two becomes notable for higher porosities. While existing models rely exclusively on porosity and thermal conductivity ratio, our newly proposed correlations show the effects of Reynolds number on the heat split mechanism for high porosities. On the other hand, the Prandtl number, at least for the range of parameters studies here, is found to be less influential on the boundary heat split mechanism.     

Effects of the number and distribution of fins on the storage characteristics of a cylindrical latent heat energy storage system: a numerical study

A numerical study of the effects of the number and distribution of fins on the storage characteristics of a cylindrical latent heat energy storage system (LHESS) was conducted. Due to the low thermal conductivity of phase change materials (PCMs) used in LHESS, fins were added to the system to increase the rate of heat transfer and charging. Finite elements were used to implement the developed numerical method needed to study and solve for the phase change heat transfer (melting of PCM) encountered in a LHESS during charging. The effective heat capacity method was applied in order to account for the large amount of latent energy stored during melting of the PCM and the moving interface between the solid and liquid phases. The effects of increasing the number and distribution of fins on the melting rate of the PCM were studied for configurations having between 0 and 27 fins for heat transfer fluid (HTF) velocities of 0.05 and 0.5?m/s. Results show that the overall heat transfer rate to the PCM increases with an increase in the number of fins irrespective of the HTF velocity. It was also observed that the total amount of energy stored after 12?h increases nearly linearly with the addition of fins up to 12 fins; further addition of fins increasing the total energy stored by ever smaller amounts.     

Conjugate Phase Change Heat Transfer in an Inclined Compound Cavity Partially Filled with a Porous Medium: A Deformed Mesh Approach

In this paper, the melting process of a PCM inside an inclined compound enclosure partially filled with a porous medium is theoretically addressed using a novel deformed mesh method. The sub-domain area of the compound enclosure is made of a porous layer and clear region. The right wall of the enclosure is adjacent to the clear region and is subject to a constant temperature of T_c. The left wall, which is connected to the porous layer, is thick and thermally conductive. The thick wall is partially subject to the hot temperature of T_h. The remaining borders of the enclosure are well insulated. The governing equations for flow and heat transfer, including the phase change effects and conjugate heat transfer at the thick wall, are introduced and transformed into a non-dimensional form. A deformed grid method is utilized to track the phase change front in the solid and liquid regions. The melting front movement is controlled by the Stefan condition. The finite element method, along with Arbitrary Eulerian–Lagrangian (ALE) moving grid technique, is employed to solve the non-dimensional governing equations. The modeling approach and the accuracy of the utilized numerical approach are verified by comparison of the results with several experimental and numerical studies, available in the literature. The effect of conjugate wall thickness, inclination angle, and the porous layer thickness on the phase change heat transfer of PCM is investigated. The outcomes show that the rates of melting and heat transfer are enhanced as the thickness of the porous layer increases. The melting rate is the highest when the inclination angle of the enclosure is 45°. An increase in the wall thickness improves the melting rate.

     

Thermal protection characteristics of a vertical rectangular cell filled with PCM/air layer

The present paper presents a numerical analysis concerning thermal protection characteristics of a vertical rectangular composite cell filled with a solid-liquid phase change material (PCM) and air layer. Inside the composite cell the PCM layer is separated from air layer by a solid partition of negligible thickness. The buoyancy-induced flows developed in both the air-filled layer and the molten PCM zone inside the PCM layer were modeled as two-dimensional laminar Newtonian fluid flow adhering to the Boussinesq approximation. Meanwhile, two-dimensional conduction heat transfer was accounted for the unmelted solid PCM region. Delineation is made via a parametric simulation of the effects of the pertinent parameters:Ste (Stefan number),Sc (subcooling factor),Ra (Rayleigh number), aspect ratio of composite cell,A, and relative thickness ratioA _p /A _a , on the transient thermal protection performance of the composite cell. Results demonstrate that by means of the latent-heat absorption inside the PCM layer, heat penetration across the composite cell can be greatly retarded over an effective duration until a critical instant until the melting front of PCM reaches the partition wall. Such an effective thermal protection duration is found to be a strong function ofRa, Ste, A _p /A _a , andA. In addition, the results of the transient heat transfer rate penetrating through the composite cell are examined as a function of the pertinent parameters of the problem.     

Effects of Bubbles on the Hydraulic Conductivity of Porous Materials – Theoretical Results

In a porous material, both the pressure drop across a bubble and its speed are nonlinear functions of the fluid velocity. Nonlinear dynamics of bubbles in turn affect the macroscopic hydraulic conductivity, and thus the fluid velocity. We treat a porous medium as a network of tubes and combine critical path analysis with pore-scale results to predict the effects of bubble dynamics on the macroscopic hydraulic conductivity and bubble density. Critical path analysis uses percolation theory to find the dominant (approximately) one-dimensional flow paths. We find that in steady state, along percolating pathways, bubble density decreases with increasing fluid velocity, and bubble density is thus smallest in the smallest (critical) tubes. We find that the hydraulic conductivity increases monotonically with increasing capillary number up to Ca 10^–2, but may decrease for larger capillary numbers due to the relative decrease of bubble density in the critical pores. We also identify processes that can provide a positive feedback between bubble density and fluid flow along the critical paths. The feedback amplifies statistical fluctuations in the density of bubbles, producing fluctuations in the hydraulic conductivity.     

Conjugate Natural Convection in a Porous Enclosure with Non-Uniform Heat Generation

Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 ???Ra ???1000), the internal heating and the local exponent parameters (0 ????? ???5), (1 ????? ???3), the wall to porous thermal conductivity ratio (0.44 ???Kr ???9.9) and the ratio of wall thickness to its width (0.02 ???D ???0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio.     

Thermal Analysis of Natural Convection Porous Fins

This work introduces a simple method of analysis to study the performance of porous fins in a natural convection environment. The method is based on using energy balance and Darcy’s model to formulate the heat transfer equation. The thermal performance of porous fins is then studied for three types of fins: long fin, finite-length fin with insulated tip and a finite-length fin with tip exposed to a known convection coefficient. It is found from the analysis that the effect of different design and operating parameters such as: Ra number, Da number, thermal conductivity ratio, Kr and length thickness ratio on the temperature distribution along the fin is grouped into one newly defined parameter called S_H. The effect of the variation of S_H on the porous fin thermal performance is established. The effect of varying the fin length and thermal conductivity ratio on the heat transfer rate from the fin is investigated and compared with that for a solid fin at certain conditions. It is found that the heat transfer rate from porous fin could exceed that of a solid fin. It is also found that increasing the fin length and effective thermal conductivity enhances the heat transfer from the fin up certain limit, where a further increase in these parameters adds no improvement to the fin performance. On Leave from Jordan University of Science and Technology, Irbid-Jordan     

Influence of variable permeability on combined free and forced convection flow past a semi-infinite vertical plate in a saturated porous medium

Combined free and forced convection flow of viscous incompressible fluid past a semi-infinite vertical plate embedded in a porous medium incorporating the variation of permeability and thermal conductivity are studied. Similarity solutions are obtained, for two cases namely uniform permeability (UP) and variable permeability (VP). Velocity and temperature profiles are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tabular form. The effects of the parameters Gr/Re ² (Gr – Grashof number, Re – the Reynolds number), (coefficient of viscositys of the fluid and porous medium), (the Darcy number), * (ratio of thermal conductivity of the solid to the liquid), Pr (the Prandtl number) and E (the Eckert number) on the flow field are discussed.     

The effect of short chain branching on the rheological and thermal properties of olefin: α-olefin copolymers

An important method of the modification of the properties of polyethylene and polypropylene is the copolymerisation with -olefins. The -olefin behaves as a short branch in the structure, and the rheological and thermal properties of copolymers change significantly. A new method is suggested to evaluate the rheological and thermal properties of copolymers on the basis of homopolymer properties, by introducing a short branch degree parameter. The zero shear viscosity, plateau modulus, fractional free volume, reptation tube diameter, glass transition temperature and thermodynamical melting point were calculated.     

Asymptotic and numerical transient analysis of the free convection cooling of a vertical plate embedded in a porous medium

This paper analyzes the cooling process of a vertical thin plate originated by a fluid-saturated porous medium, taking into account the effects of both longitudinal and transversal heat conduction in the plate. Due to the finite thermal conductivity of the plate, a longitudinal temperature gradient arises within it, which prevents any similarity solution in the boundary layer, changing the mathematical character of the problem from parabolic to elliptic, for large values of the suitable Rayleigh number. The energy balance equations are reduced to a system of two differential equations with two parameters: the nondimensional plate thermal conductivity and the aspect ratio of the plate . In order to obtain the evolution of the temperature of the plate as a function of time and position, the coupled balance equations are integrated numerically for several values of the parameters, including the cases of very good and poor conducting plates. The results obtained, are compared with an asymptotic analysis based on the multiple scales technique carried out for the case of a very good conducting plate. There is at the beginning a fast transient in nondimensional time scale of order followed by a slow nondimensional time scale of order unity, which gives the evolution of the cooling process. Good agreement is achieved even for values of the conduction parameter of order unity. The asymptotic solution allows us to give closed form analytical solution for the plate temperature evolution in time and space. The overall thermal energy of the plate decreases faster for smaller values of .     

Numerical homogenization of elastic and thermal material properties for metal matrix composites (MMC)

A two-scale material modeling approach is adopted in order to determine macroscopic thermal and elastic constitutive laws and the respective parameters for metal matrix composite (MMC). Since the common homogenization framework violates the thermodynamical consistency for non-constant temperature fields, i.e., the dissipation is not conserved through the scale transition, the respective error is calculated numerically in order to prove the applicability of the homogenization method. The thermomechanical homogenization is applied to compute the macroscopic mass density, thermal expansion, elasticity, heat capacity and thermal conductivity for two specific MMCs, i.e., aluminum alloy Al2024 reinforced with 17 or 30 % silicon carbide particles. The temperature dependency of the material properties has been considered in the range from 0 to \(500{\,}^\circ \mathrm {C}\), the melting temperature of the alloy. The numerically determined material properties are validated with experimental data from the literature as far as possible.     

The Effect of the Local Inertial Term on the Transient Free Convection from a Vertical Plate Inserted in a Semi-Infinite Domain Partly Filled with Porous Material

The transient hydrodynamics and thermal behaviours of the free convection from a vertical plate inserted in a semi-infinite domain partly filled with porous material are investigated. The role of the local macroscopic inertial term in the porous domain momentum equation is studied. It is found that the effect of the local inertial term on the domain behaviour is insignificant when Da < 1 × 10^–5 for all operating conditions. Also, the effect of the macroscopic inertial term is insignificant at large values of _R, where _R > 2.0, and over the entire ranges of _R, K_R and Pr (thermal diffusivity ratios, thermal conductivity ratios and Prandtl number, respectively).     

Constructal multi-scale structure of PCM-based heat sinks

This paper inquires the effectiveness of a PCM-based heat sink as a reliable solution to portable electronic devices. This sink is composed of a PCM with low thermal conductivity and fins to boost its conductivity. The optimization is subjected to fixed heat sink volume filled with PCM between vertical equidistant fins. New fins are installed in the unheated space existing in each enclosure which is not involved in thermal distribution from vertical fins to the PCM. Based on the same principle, new fins generations are augmented stepwise to the multi-scale structure. The steps of adding fins will continue up to the point that the objective function reaches its maximal value, i.e., maximizing the longest safe operation time without allowing the electronics to reach the critical temperature. The results indicate that in each length of the enclosure, the optimum volume fraction and the best fins distance values exist in which the heat sink performance becomes maximum, and adding more fins lowers the performance of the heat sink. Increasing the enclosure’s length by \(2^{n}\) does not change them. For an enclosure with constant length, the optimal number of steps for adding fins within the enclosure is a function of the fin thickness. The results indicate that increasing the thickness changes the optimal number of adding fins inside the enclosure (normally a decrease). As the fin thickness is lowered, there will be a higher effect by adding vertical fins in the enclosure. Numerical simulations cover the Rayleigh number range \(2\times 10^{5}\le \hbox {Ra}_{\mathrm{H}} \le 2.7\times 10^{8}\), where H is the heat sink height.     

Convection and heat transfer of elliptical tubes

Convection heat transfer (including natural and forced convection) of elliptical tubes had been studied system-atically. The experienced formula of heat transfer had been given. It presents fin efficiency of rectangular finned elliptical tube and optimized fin geometry (i.e. length/width ratio) and fin spacing for rectangular fin.

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Konvektion und Wärmeübergang an elliptischen Rohren

Zusammenfassung Konvektion und Wärmeübergang (sowohl bei freier als auch bei erzwungener Konvektion) an elliptischen Rohren wurden systematisch untersucht. Es wird eine aus dem Experiment abgeleitete Beziehung für den Wärmeübergang angegeben, die den Gütegrad elliptischer Rohre mit Rechteckrippen unter optimierter Rippengeometrie (Längen- zu Breitenverhältnis und Rippenabstand) beinhaltet. Stichworte: Konvektiver Wärmeübergang, Rippengütegrad, Elliptische Rohre mit Rechteckrippe.

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Nomenclature A length of a rectangular fin - A _F area of a fin - A _f overall fin area of per length - A _r tube surface of per length - B width of a rectangular fin - Gr Grashof number - N fin number of per length - Nu =hl/ Nusselt number - Pr Prandtl number - Ra =Gr·Pr Rayleigh number - Re =wl/ Reynolds number - S ₁ transverse tube pitch - S ₂ longitudinal tube pitch - w fluid velocity - a long axis of a ellipse - b short axis of a ellipse - c =a/b shape factor - d _e equivalent diameter - g acceleration of gravity - h heat exchange coefficient - l characteristic length - t fin spacing Greek symbols coefficient of thermal expansion - fin thickness - _fm area average fin efficiency - coefficient of fluid thermal conductivity - _f fin's thermal conductivity - kinematic viscosity     

Gas flow through an elliptical tube over the whole range of the gas rarefaction

A rarefied gas flow trough a long tube with an elliptical cross section is studied on the basis of the BGK kinetic model equation in the whole range of the Knudsen number varying from the free molecular regime to the hydrodynamic one. A wide range of the aspect ratio is considered. The mass flow rate is calculated as a function of the pressures on the tube ends.     

Mixed Convection Heat Transfer in the Annulus Between Two Concentric Vertical Cylinders Using Porous Layers

A numerical investigation of the steady-state, laminar, axi-symmetric, mixed convection heat transfer in the annulus between two concentric vertical cylinders using porous inserts is carried out. The inner cylinder is subjected to constant heat flux and the outer cylinder is insulated. A finite volume code is used to numerically solve the sets of governing equations. The Darcy–Brinkman–Forchheimer model along with Boussinesq approximation is used to solve the flow in the porous region. The Navier–Stokes equation is used to describe the flow in the clear flow region. The dependence of the average Nusselt number on several flow and geometric parameters is investigated. These include: convective parameter, λ, Darcy number, Da, thermal conductivity ratio, K _r, and porous-insert thickness to gap ratio (H/D). It is found that, in general, the heat transfer enhances by the presence of porous layers of high thermal conductivity ratios. It is also found that there is a critical thermal conductivity ratio on which if the values of Kr are higher than the critical value the average Nusselt number starts to decrease. Also, it found that at low thermal conductivity ratio (K _r ≈ 1) and for all values of λ the porous material acts as thermal insulation.