Effective Thermal Conductivity Ratio Research Articles

MOMENTUM INTEGRAL METHOD FOR FORCED CONVECTION IN THERMAL NONEQUILIBRIUM POWER-LAW FLUID-SATURATED POROUS MEDIA

Forced convection heat transfer for power-law fluid flow in porous media was studied analytically. The analytical solutions were obtained based on the Brinkman-extended Darcy model for fluid flow and the two-equation model for forced convection heat transfer. As a closed-form exact velocity profile is unobtainable for the general power-law index, an approximate velocity profile based on the parabolic model is proposed by subscribing to the momentum boundary layer integral method. Heat transfer analysis is based on the two-equation model by considering local thermal nonequilibrium between fluid and solid phases and constant heat flux boundary conditions. The velocity and temperature distributions obtained based on the parabolic model were verified to be reasonably accurate and improvement is justified compared to the linear model. The expression for the overall Nusselt number was derived based on the proposed parabolic model. The effects of the governing parameters of engineering importance such as Darcy number, power-law index, nondimensional interfacial heat transfer coefficient, and effective thermal conductivity ratio on the convective heat transfer characteristics of non-Newtonian fluids in porous media are analyzed and discussed.

Effect of Particle Size on Thermal Conductivity of Nanofluid

Nanofluids, containing nanometric metallic or oxide particles, exhibit extraordinarily high thermal conductivity. It is reported that the identity (composition), amount (volume percent), size, and shape of nanoparticles largely determine the extent of this enhancement. In the present study, we have experimentally investigated the impact of Al2Cu and Ag2Al nanoparticle size and volume fraction on the effective thermal conductivity of water and ethylene glycol based nanofluid prepared by a two-stage process comprising mechanical alloying of appropriate Al-Cu and Al-Ag elemental powder blend followed by dispersing these nanoparticles (1 to 2 vol pct) in water and ethylene glycol with different particle sizes. The thermal conductivity ratio of nanofluid, measured using an indigenously developed thermal comparator device, shows a significant increase of up to 100 pct with only 1.5 vol pct nanoparticles of 30- to 40-nm average diameter. Furthermore, an analytical model shows that the interfacial layer significantly influences the effective thermal conductivity ratio of nanofluid for the comparable amount of nanoparticles.

Thermal characterization of a nanofluid comprising nanocrystalline ZrO2 dispersed in water and ethylene glycol

Nanofluids, comprising Y2O3-stabilized (partially; 3 mol%) ZrO2 nanoparticles (up to 2 vol%) dispersed in water and ethylene glycol, were developed. A suitable surfactant and stirring routine ensured uniformity and stability of dispersion. Thermal conductivity ratio of the nanofluids, measured using an indigenously developed thermal comparator device, showed a significant increase of up to 100% with only 1.5 vol% nanoparticles. Furthermore, it was analytically shown that shape factor and aspect ratio significantly influence the effective thermal conductivity ratio of nanofluids with comparable vol% nanoparticles. The study demonstrated that a nanofluid of nano-ZrO2 dispersed in water and ethylene glycol could be usefully applied in closed-loop single-phase heat transfer conditions, such as in refrigerators or microchannels.

Investigation on the Thermal Conductivity of 3-Dimensional and 4-Directional Braided Composites

It is vital to choose a factual and reasonable micro-structural model of braided composites for improving the calculating precision of thermal property of 3-D braided composites by finite element method (FEM). On the basis of new microstructure model of braided composites proposed recently, the model of FEM calculation for thermal conductivity of 3-dimennsional and 4-directional braided composites is set up in this paper. The curves of coefficient of effective thermal conductivity versus fiber volume ratio and interior braiding angle are obtained. Furthermore, comparing the results of FEM with the available experimental data, the reasonability and veracity of calculation are confirmed at the same time.

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio ( α s), inertial force parameter ( Γ), porosity ( ε), and the effective thermal conductivity ratio ( k r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α s and ε, while it decreases with increasing k r.

Forced convection of gaseous slip-flow in porous micro-channels under Local Thermal Non-Equilibrium conditions

Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn), Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio (KR) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (CfRe*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or KR increases; (2) increases as the Peclet number, Darcy number, or Biot number increases.

Analysis of microchannel heat sinks for electronics cooling

This paper presents an analytical and numerical study on the heat transfer characteristics of forced convection across a microchannel heat sink. Two analytical approaches are used: the porous medium model and the fin approach. In the porous medium approach, the modified Darcy equation for the fluid and the two-equation model for heat transfer between the solid and fluid phases are employed. Firstly, the effects of channel aspect ratio ( α s) and effective thermal conductivity ratio (k̃) on the overall Nusselt number of the heat sink are studied in detail. The predictions from the two approaches both show that the overall Nusselt number ( Nu) increases as α s is increased and decreases with increasing k̃. However, the results also reveal that there exists significant difference between the two approaches for both the temperature distributions and overall Nusselt numbers, and the discrepancy becomes larger as either α s or k̃ is increased. It is suggested that this discrepancy can be attributed to the indispensable assumption of uniform fluid temperature in the direction normal to the coolant flow invoked in the fin approach. The effect of porosity ( ε) on the thermal performance of the microchannel is subsequently examined. It is found that whereas the porous medium model predicts the existence of an optimal porosity for the microchannel heat sink, the fin approach predicts that the heat transfer capability of the heat sink increases monotonically with the porosity. The effect of turbulent heat transfer within the microchannel is next studied, and it is found that turbulent heat transfer results in a decreased optimal porosity in comparison with that for the laminar flow. A new concept of microchannel cooling in combination with microheat pipes is proposed, and the enhancement in heat transfer due to the heat pipes is estimated. Finally, two-dimensional numerical calculations are conducted for both constant heat flux and constant wall temperature conditions to check the accuracy of analytical solutions and to examine the effect of different boundary conditions on the overall heat transfer.

EFFECT OF ANISOTROPY IN PERMEABILITY AND EFFECTIVE THERMAL CONDUCTIVITY ON THERMAL PERFORMANCE OF AN ALUMINUM FOAM HEAT SINK

A numerical study has been carried out to investigate the thermal characteristics of an aluminum foam heat sink. An aluminum foam heat sink horizontally placed in a channel is modeled as a hydraulically and thermally anisotropic porous medium. A uniform heat flux is given from the bottom of the heat sink. Cold air is supplied from the top opening of the channel and exhausts to the channel outlet. Comprehensive numerical solutions are acquired to the governing Navier-Stokes and energy equations, using the Brinkman-Forchheimer extended Darcy model for the region of heat sink. It is assumed that the solid is in the local thermal equilibrium with the fluid. Details of flow and thermal fields are examined over wide ranges of the principal parameters: the Darcy number Da, the anisotropic permeability ratio K*(=K 2/K 1), and the anisotropic effective thermal conductivity ratio k*(=k 2/k 1). The results indicate that the anisotropy in permeability and effective thermal conductivity yields a significant change in the heat transfer rate. The same numerical approach that involves the anisotropic porous medium model is also applied to the thermal analysis of a conventional pin-fin heat sink.

On the local thermal equilibrium in microchannel heat sinks

In this paper, analytical solutions for temperature distributions in the microchannel heat sink are obtained by using both one-equation and two-equation models for heat transfer. From the analytical solutions, variables of engineering importance are identified as the Darcy number and the effective thermal conductivity ratio, and their effects are studied. To check the validity of the local thermal equilibrium assumption and the corresponding one-equation model, the relative temperature difference between the fluid and solid phases and the relative error for using the one-equation model are defined. The asymptotic behavior of the relative temperature difference between the phases is examined by using the order of magnitude analysis to confirm the applicability of the local thermal equilibrium assumption and the one-equation model. Finally, the relative error map is presented with respect to variables of engineering importance to identify the applicable region of the one-equation model in practical problems involving the microchannel heat sinks.

Forced Convection in Microstructures for Electronic Equipment Cooling

This paper reports analytical solutions for both velocity and temperature profiles in Microchannel heat sinks by modeling the Microchannel heat sink as a fluid-saturated porous medium. The analytical solutions are obtained based on the modified Darcy model for fluid flow and the two-equation model for heat transfer. To validate the porous medium model and the analytical solutions based on that model, the closed-form solution for the velocity distribution in the fully-developed channel flow and the numerical solutions for the conjugate heat transfer problem, comprising the solid fin and the fluid, are also obtained. The analytical solutions based on the porous medium model are shown to predict the volume-averaged velocity and temperature distributions quite well. Using the analytical solutions, the aspect ratio and the effective thermal conductivity ratio are identified as variables of engineering importance and their effects on fluid flow and heat transfer are studied. As either one of these variables increases, the fluid temperature is shown to approach the solid temperature. Finally, the expression for the total thermal resistance, derived from the analytical solutions and the geometry of the microchannel heat sink for which the thermal resistance of the heat sink is minimal, is obtained.

Computational fluid dynamics studies of fixed bed heat transfer

Fluid flow and heat transfer in a fixed bed of tube to particle ratio 2.86 were studied by solving the 3D Navier–Stokes and energy equations using a commercial finite element code, ANSYS/FLOTRAN. The geometry model consisted of an arrangement of eight spheres. Boundary conditions were given at the wall and the inlet, similar to an experimental setup, to determine the velocity and temperature at various locations. The main objective of this study was to use computational fluid dynamics (CFD) to obtain values for the dimensionless wall heat transfer coefficient, Nu w and the radial effective thermal conductivity ratio, k r/ k f, using air as the fluid. Nu w and k r/ k f were evaluated from the calculated temperatures at different locations in the bed by fitting these with the analytical solution of the usual two-dimensional pseudo-homogeneous model, using a non-linear least squares analysis. Results were obtained for Reynolds numbers in the range 9–1450. The Nu w and k r/ k f values showed reasonable qualitative agreement with both experimental values and values predicted by a model-matching theory based on experimental measurements. Studies were also carried out to verify the depth, pressure and wall temperature dependence of the effective heat parameters. The effect of the temperature profile measurement position above the bed on the estimated parameters, was investigated.