Numerical investigation of natural convection in a square enclosure partially filled with horizontal layers of a porous medium

Two-dimensional buoyancy-induced flow and heat transfer inside a square enclosure partially occupied by copper metallic foam subjected to a symmetric side cooling and constant heat flux bottom heating was tested numerically. Finite Element Method was employed to solve the governing partial differential equations of the flow field and the Local Thermal Equilibrium model was used for the energy equation. The system boundaries were defined as lower heated wall by constant heat flux, cooled lateral walls, and insulated top wall. The three parameters elected to conduct the study are heater length (7 ≤ ζ ≤ 20 cm), constant heat flux (150 ≤ q″ ≤ 600 W m⁻²), and porous material thickness (5 ≤ H ≤ 20 cm). The porous material used was the copper metal foam of porosity = 0.9 and pore density PPI = 10, and saturated with a fluid of Prandtl number = 0.7. On the basis of the results obtained, it was concluded that at the porous layer thickness = 5 cm, the rate of heat transferred was (74.6%) higher than when the layer height was 20 cm (the cavity is fully filled) and at the same thickness it was found that the heat rate is (51.4%) higher than when using the half filling (H = 10 cm). Further, the local and mean Nusselt number is maximum when using the largest heater size and smallest porous layer thickness. Finally, better circulation and convective modes were observed at high values of heat flux.     

Effect of low thermal conductivity wick on the performance of compact loop heat pipe

The existing work deals with the evaluation of compact loop heat pipe by means of a low thermal conductivity sintered chrysotile wick to avoid large heat leaks as of the evaporator to the compensation chamber. Accordingly, a wick with low thermal conductivity (0.068–0.098 W/mK) chrysotile powder of a mean particle diameter of 3.4 μm is fabricated through sintering. Nine chrysotile wicks are sintered with different compositions of binders (bentonite and dextrin) and pore-forming agent NaCl at sintering temperatures of 500°C, 600°C, and 700°C with a sintering time of 30 min. The wick properties, for instance, porosity, permeability, wettability, and capillary rise are studied owing to sintering temperature. Consequently, it is observed that a pure chrysotile powdered wick at a sintering temperature of 600°C exhibits a high porosity of 61.8% with permeability 1.04 × 10⁻¹³ m² and a capillary rise of 4.5 cm in 30 s and is considered optimal. This optimal wick is used for performance evaluation in compact loop heat pipe and a decrease of 36.1% in thermal resistance is found when compared with copper mesh wick in a loop heat pipe. The lowermost thermal resistance originates to be 0.147 K/W at 120 W with wall temperature 57.7°C. This indicates that loop heat pipe with sintered chrysotile wick can operate at lower heat loads efficiently when compared with copper mesh wick and as heat load increases a chance of dry out condition occurs. The highest evaporative heat transfer coefficient obtained is 65.7 kW/m² K at a minimum heat load.     

Sintered porous heat sink for cooling of high-powered microprocessors for server applications

This paper experimentally investigates the sintered porous heat sink for the cooling of the high-powered compact microprocessors for server applications. Heat sink cold plate consisted of rectangular channel with sintered porous copper insert of 40% porosity and 1.44 × 10^?11 m² permeability. Forced convection heat transfer and pressure drop through the porous structure were studied at Re ? 408 with water as the coolant medium. In the study, heat fluxes of up to 2.9 MW/m² were successfully removed at the source with the coolant pressure drop of 34 kPa across the porous sample while maintaining the heater junction temperature below the permissible limit of 100 ± 5 °C for chipsets. The minimum value of 0.48 °C/W for cold plate thermal resistance (R_cp) was achieved at maximum flow rate of 4.2 cm³/s in the experiment. For the designed heat sink, different components of the cold plate thermal resistance (R_cp) from the thermal footprint of source to the coolant were identified and it was found that contact resistance at the interface of source and cold plate makes up 44% of R_cp and proved to be the main component. Convection resistance from heated channel wall with porous insert to coolant accounts for 37% of the R_cp. With forced convection of water at Re = 408 through porous copper media, maximum values of 20 kW/m² K for heat transfer coefficient and 126 for Nusselt number were recorded. The measured effective thermal conductivity of the water saturated porous copper was as high as 32 W/m K that supported the superior heat augmentation characteristics of the copper–water based sintered porous heat sink. The present investigation helps to classify the sintered porous heat sink as a potential thermal management device for high-end microprocessors.     

Evaluation of Jet Impingement,Spray and Microchannel Chip Cooling Options for High Heat Flux Removal

Thermal management for high heat flux removal from microelectronic chips is gaining critical importance in many earth-based and space-based systems. Heat fluxes greater than 1 MW/m² (100 W/cm²) have already been realized in high-end server applications, while cooling needs in next generation chips and advanced systems such as high-power electronics and electrical systems, pulsed power weapons systems, solid-state sensors, and phased-array radars are expected to reach 5–10 MW/m² (500–1000 W/cm²). After evaluating the contributions from different thermal resistances in the chip-to-ambient thermal path, this paper presents a critical review and research recommendations for three prominent contending technologies: jet impingement, spray cooling, and microchannel heat sinks.     

Filtration Gas Combustion in a Porous Ceramic Annular Burner for Thermoelectric Power Conversion

A numerical study of the combustion of lean methane/air mixtures in a porous media burner is performed using novelty geometry, cylindrical annular space. The combustion process takes place in the porous space located between two pipes, which are filled with alumina beads of 5.6 mm diameter forming a porosity of 0.4. The outer tube diameter of 3.82 cm is isolated; meanwhile the inner tube of 2 cm in diameter is covered by a continuous set of thermoelectric elements (TE) for transforming heat energy into electricity. To achieve and maintain the proper temperature gradient on TE, convective heat losses are considered from the TE. Computer simulations focus on the two-dimensional (2D) temperature analysis and displacement dynamics of the combustion front inside the reactor, depending on the values of the filtration velocity (0.1 to 1.0 m/s), the heat loss coefficient from the internal cylinder (400–1500 W/m²/K), and the fuel equivalence ratio (0.06– 0.5). The conditions that maximized the overall performance of the process of energy conversion are: 0.7 m/s of the filtration velocity, 0.363 of the fuel equivalence ratio and 1500 W/(m^2·K) of the heat transfer coefficient from the internal cylinder, to obtain 2.05 V electrical potential, 21 W of electrical power, and 5.64% of the overall process efficiency. The study shows that the cylindrical annular geometry can be used for converting the energy of combustion from lean gas mixtures into electricity, with a performance similar to the specified by manufacturers of thermoelectric elements (TE).     

A study of heat transfer in a circulating fluidized bed

An experimental investigation was carried out to study the effects of operating parameters on the local bed-to-wall heat transfer coefficient in a 4.5 m tall, 0.150 m diameter circulating fluidized bed with a bed temperature in the range of 65°C to 80°C, riser flow rate varying from 1400 litres/min to 2000 litres/min, bed inventory in the range of 15 kg to 25 kg of sand, and average sand sizes of 200 μm, 400 μm and 500 μm. A heat flux probe was attached to the riser wall at five different vertical locations for measuring the heat flux from the bed to the wall surface. From the present work, the heat transfer coefficient in the dilute phase was found to be in the range of 62 to 83 W/m²K, 51 to 74 W/m²K, and 50 to 59 W/m² K for sand sizes of 200 μm, 400 μm and 500 μm, respectively. Relevant mathematical correlations were developed to predict local heat transfer coefficient based on the results of the practical work.     

Crosswise stream of hydrogen-oxide (H2O) through a porous media containing copper nanoparticles

Transport theories in porous media are quite operative to analyse heat transferral phenomenon in biological tissues, reducing bio convective flow instabilities by means of porous media and many more. Inspired by these remarkable features, the present study is conducted to analyse heat transfer phenomenon for obliquely striking nanofluid through a porous media. Copper (Cu) nanoparticles are suspended in traditional Hydrogen Oxide based fluid. Scaling group of transformations is conveniently employed to reduce governing transport equations and is tackled numerically afterwards. Influence of nanoparticles volume fraction, stretching ratio and porosity parameter on physical measures of concern such as normal and tangential skin friction and corresponding heat flux at wall is portrayed. Streamline patterns are traced out to discover the influence of porosity factor on actual flow behavior. It was observed that solid volume fraction of copper nanoparticles enhanced the skin friction coefficients and heat flux. Increasing the porosity parameter leads to greater heat flux and tangential skin friction co-efficient.     

Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels

Fluid flow and convective heat transfer of water in sintered bronze porous plate channels was investigated numerically. The numerical simulations assumed a simple cubic structure formed by uniformly sized particles with small contact areas and a finite-thickness wall subject to a constant heat flux at the surface which mirrors the experimental setup. The permeability and inertia coefficient were calculated numerically according to the modified Darcy’s model. The numerical calculation results are in agreement with well-known correlation results. The calculated local heat transfer coefficients on the plate channel surface, which agreed well with the experimental data, increased with mass flow rate and decreased slightly along the axial direction. The convection heat transfer coefficients between the solid particles and the fluid and the volumetric heat transfer coefficients in the porous media predicted by the numerical results increase with mass flow rate and decrease with increasing particle diameter. The numerical results also illustrate the temperature difference between the solid particles and the fluid which indicates the local thermal non-equilibrium in porous media.     

Depth-averaged turbulent heat and fluid flow in a vegetated porous medium

In this article, the latest developments of porous media science are used in order to simulate heat and fluid flow in a non-flexible vegetated porous media. Vegetation porosity and density at the domain interior are redefined. The same strategy is then applied in order to define the boundary porosity near the bed and water surface. Regarding the vegetation arrangement in natural streams and flumes, three different models are suggested for calculating the porosity near other boundaries. The microscopic time-mean secondary force in momentum equations is modified for a vegetated porous media and its macroscopic form is derived. A dissipation source term is derived and, it is added to vorticity equation in order to take account of vegetation damping effect on secondary flows. The effect of this dissipation source term on the absolute magnitude of vorticity and velocity field is then investigated. Application of a high Reynolds number turbulence model to turbulent flow in partially vegetated open channels is numerically examined. A model is suggested for taking account of vegetation material on heat flux through walls in a vegetated porous media. The thermal diffusion due to the porosity gradient is modeled and, the contribution of this porosity-induced heat flux on temperature field is investigated. The effect of laminar thermal dispersion on temperature field is also investigated at low stem Reynolds number.     

Heat Transfer and Flow Pattern Characteristics for HFE-7100 Within Microchannel Heat Sinks

This study investigates the heat transfer characteristics and flow pattern for the dielectric fluid HFE-7100 within multiport microchannel heat sinks with hydraulic diameters of 480 μm and 790 μm. The test results indicate that the heat transfer coefficient for the smaller channel is generally higher than that of the larger channel. It is found that the heat transfer coefficients are roughly independent of heat flux and vapor quality for a modest mass flux ranging from 200 to 400 kg m^?2 s^?1 at a channel size of 480 μm and there is a noticeable increase of heat transfer coefficient with heat flux for hydraulic diameters of 790 μm. The difference arises from flow pattern. However, for a smaller mass flux of 100 kg m^?2 s^?1, the presence of flow reversal at an elevated heat flux for hydraulic diameters of 480 μm led to an appreciable drop of heat transfer coefficient. For a larger channel size of 790 μm, though the flow reversal is not observed at a larger heat flux, some local early partial dryout still occurs to offset the heat flux contribution and results in an unconceivable influence of heat flux. The measured heat transfer coefficients for hydraulic diameters of 790 μm are well predicted by the Cooper correlation. However, the Cooper correlation considerably underpredicts the test data by 35–85% for hydraulic diameters of 480 μm. The influence of mass flux on the heat transfer coefficient is quite small for both channels.     

Study of mixed convective heat transfer in a sintered porous channel

This investigation experimentally elucidates mixed heat convection in a rectangular channel with porous medium, and analyzes the cooling performance of electronics. The test sections are sintered copper granules with dimensions of 5 × 5 × 1 cm and average diameters of 0.704 mm and 1.163 mm. A porous channel is heated using air as the working fluid. The measured variables include the heat flux on the heat surface, the local wall temperature in the flow direction, the inlet/outlet pressure, and the flow rate. The boundary condition is that the heating surface of the lower plate of the test section is heated by an isothermal heat flux, while the other three sides are thermally insulated; the heat flux is between 0.23 and 1.86 Watt/cm². The mean air flow rate within a porous channel is between 0.3 and 4.0 m/s. The thermally developed region and the fully developed region are measured. This experiment is directed at understanding the influence on heat transfer based on the diameter of the sintered copper granules, Reynolds number, and heat flux. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(2): 64–77, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20050     

Non-uniform porosity and thermal dispersion effects on natural convection about a heated horizontal cylinder in an enclosed porous medium

A numerical solution has been obtained for transient two-dimensional natural convection from a heated horizontal cylinder embedded in an enclosed porous medium. Non-Darcian effects are taken into consideration in the momentum equation, while the thermal dispersion effect is taken into consideration in the energy equation. The wall effect on porosity is approximated by an exponential function and its effect on thermal dispersion is modeled by a dispersive length. The governing equations in terms of the stream function, vorticity, and temperature are expressed in a body-fitted coordinate system, which were solved numerically by the finite difference method. Results are presented for the streamlines and isotherms, tangential velocity and temperature distributions, as well as the average Nusselt numbers at different values of Rayleigh number, dimensionless particle diameter, and Prandtl number. The non-uniform porosity effect tends to increase the temperature gradient near the wall while the thermal dispersion effect increases the effective thermal conductivity, both resulting in an increase in surface heat flux. The effect of thermal dispersion on natural convection in porous media at low to moderate Rayleigh number is small. With nonuniform porosity and thermal dispersion effects taken into consideration, the predicted average Nusselt numbers are found to be in better agreement with experimental data.     

Metal foam heat sink for transmission window

A cooling device for transmission window of an accelerator based on aluminum foam with an inner heat production was investigated experimentally. Dissipation of heat flux up to 0.25 kW/cm² was obtained, by using porous metal with porosity of 40 pores per inch. Under these conditions, the difference between the temperatures of the wall and the bulk water did not exceed 45 K and the pressure difference per unit length was 20 bar/m. Image processing of thermal maps of the surface of the metal foam showed that boundary conditions with constant heat flux became more relevant for numerical model than those with constant temperature at high values of Reynolds numbers Re_K based on the permeability.     

An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media

The present experimental and numerical work investigates the effect of metallic porous materials, inserted in a pipe, on the rate of heat transfer. The pipe is subjected to a constant and uniform heat flux. The effects of porosity, porous material diameter and thermal conductivity as well as Reynolds number on the heat transfer rate and pressure drop are investigated. The results are compared with the clear flow case where no porous material was used. The results obtained lead to the conclusion that higher heat transfer rates can be achieved using porous inserts at the expense of a reasonable pressure drop. Also, it is shown that for an accurate simulation of heat transfer when a porous insert is employed its effective thermal conductivity should be carefully evaluated.     

The heat transfer characteristics of liquid cooling heat sink with micro pin fins

This paper numerically and experimentally investigated the liquid cooling efficiency of heat sinks containing micro pin fins. Aluminum prototypes of heat sink with micro pin fin were fabricated to explore the flow and thermal performance. The main geometry parameters included the diameter of micro pin fin and porosity of fin array. The effects of the geometrical parameters and pressure drop on the heat transfer performance of the heat sink were studied. In the experiments, the heat flux from base of heat sink was set as 300 kW/m². The pressure drop between the inlet and the outlet of heat sink was set < 3000 Pa. Numerical simulations with similar flow and thermal conditions were conducted to estimate the flow patterns, the effective thermal resistance. It was found that the effective thermal resistance would reach an optimum value for various pressure drops. It was also noted that the effective thermal resistance was not sensitive to porosity for sparsely packed pin fins.     

Heat transfer through fibrous assemblies incorporating reflective interlayers

Fibrous insulation has many applications including functional protective clothing, sleeping bags, buildings and construction, and aircrafts, particularly under extreme climatic conditions. It has been realized that reflective interlayers can be incorporated into the fibrous materials to block radiative heat transfer. However, since reflective interlayers generally have greater thermal conductivity than the bulk fibrous materials, the optimization of the construction of the fibrous insulation is important in maximizing the overall thermal insulation. In order to analyze this complex optimization problem, a two-flux radiative heat transfer model was built for the heat transfer through fibrous assemblies incorporating reflective interlayers. By using finite control volume method, the solution was obtained. After validation it was applied to predict the optimum constructional parameters of such an assembly for maximizing thermal insulation. It was found that (1) although extinction coefficient of Al-coated interlayer fibers decrease unidirectionally as the fiber diameter increases, the total heat flux first decreases and then increases with minimum heat flux at the fiber diameter of about 2 μm; Consequently, the thermal resistance reaches a maximum value when the fiber diameter d is about 2 μm; (2) the optimum construction is determined by the balance of the weakening of conductive thermal resistance and enhancement of the radiative thermal resistance as a result of incorporating thin reflective interlayers. For relatively thick reflective interlayer, the assembly with lower interlayer fiber volume fraction has a higher thermal resistance. On the other hand, for very thin reflective interlayers, relatively high fiber volume fraction is beneficial to the overall thermal insulation.     

Nucleate Boiling Enhancements on Porous Graphite and Microporous and Macro–Finned Copper Surfaces

Enhancements in nucleate boiling heat removal with dielectric liquids, by increasing either the bubbles nucleation sites density and/or the wetted surface area, are desirable for immersion cooling of high-power computer chips. This article presents the results of recent investigations of nucleate boiling enhancement of FC-72, HFE-7100, and PF-5060 dielectric liquids on porous graphite, copper microporous surfaces, and copper surfaces with square corner pins, 3 mm × 3 mm in cross-section and 2, 3, and 5 mm tall. All surfaces have a footprint measuring 10 × 10 mm. These investigations examined the effects of liquid subcooling up to 30 K and surface inclination, from upward-facing to downward-facing, on nucleate boiling heat transfer coefficient and critical heat flux. Natural convection of dielectric liquids for cooling chips while in the stand-by mode, at a surface average heat flux <20 kW/m², is also investigated for the different surfaces.     

Evaporative Cooling Heat Transfer of Water From Hierarchically Porous Aluminum Coating

A study of evaporative cooling of water was conducted using dual-scale hierarchically porous aluminum coating. The coating was created by brazing aluminum powders to a flat aluminum plate. The effects of particle size and thickness on evaporative heat transfer were investigated using average aluminum particle diameters of 27, 70, and 114 µm and average coating thicknesses of 560, 720, and 1200 µm. Constant ambient temperature of 24°C and relative humidity of 50% were provided throughout the study. Evaporative cooling tests on the coated surfaces were compared to the plain surface. Tested dual-scale porous coatings enhanced evaporative heat transfer significantly, compared to that of the plain surface, due to the effective wicking of water to the entire heated area. With particle size increase, both the wickability and dryout heat flux were significantly increased. The dryout heat flux with the particle size of 114 µm was 3.2 times higher than that with the particle size of 27 µm. At the fixed particle size of 70 µm the dryout heat flux increased as thickness increased, which resulted in the maximum dryout heat flux of 10.6 kW/m² and the maximum heat transfer coefficient of 251 W/m²K at the coating thickness of 1200 µm.     

Testing an external sodium receiver up to heat fluxes of 2.5 MW/m: Results and conclusions from the IEA-SSPS high flux experiment conducted at the central receiver system of the Plataforma Solar de Almeria (Spain)

During the IEA-SSPS High Flux Experiment conducted at the sodium-cooled central receiver system of the Plataforma Solar de Almeria (Spain), an increase of the 1.4 MW/m² design heat flux to a maximum of 2.5 MW/m² was accomplished by focusing all available heliostats on the Advanced Sodium Receiver's central panel. Receiver efficiency was measured in various independent tests from 0.8 MW to 3.5 MW with sodium inlet and outlet temperatures being , , and °C. The incoming flux distribution was measured with a radiometer bar and the receiver surface temperature distribution was recorded with an infrared camera system. These data were used to verify two different thermodynamic models. Receiver efficiency did not drop when operating the receiver under high peak and power levels but was found to even rise slightly over its design value of 90%. The experiment showed that current design upper flux, power and temperature limits have not yet been reached and that there is a promising potential for increasing annual thermal output.     

Enhancing heat transfer in the core flow by using porous medium insert in a tube

According to the concept of heat transfer enhancement in the core flow, porous media with a slightly smaller diameter to a tube are developed and inserted in the core of the tube under the constant and uniform heat flux condition. The flow resistance and heat transfer characteristics of the air flow for laminar to fully turbulent ranges of Reynolds numbers are investigated experimentally and numerically. There are three different porous media used in the experiments with porosity of 0.951, 0.966 and 0.975, respectively. The effect of porous radius ratio on the heat transfer performance is studied in numerical simulation. Both numerical and experimental results show that the convective heat transfer is considerably enhanced by the porous inserts of an approximate diameter with the tube and the corresponding flow resistance increases in a reasonable extent especially in laminar flow. It shows that the core flow enhancement is an efficacious method for enhancing heat transfer.