Analysis of two approaches for an adiabatic boundary condition in porous media

Purpose – The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed. Design/methodology/approach – Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium. Findings – The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕAfin increases and ϕAsub, ϕAcover decrease as Da decreases and k is held constant, ϕAsub increases and ϕAfin, ϕAcover decrease as k increases while Da is held constant; for Model B, ϕBfin increases and ϕBsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small. Research limitations/implications – Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases. Practical implications – Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement. Social implications – This work has important fundamental implications. Originality/value – In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.

Assessment of Prediction Capabilities of COCOSYS and CFX Code for Simplified Containment

The acceptable accuracy for simulation of severe accident scenarios in containments of nuclear power plants is required to investigate the consequences of severe accidents and effectiveness of potential counter measures. For this purpose, the actual capability of CFX tool and COCOSYS code is assessed in prototypical geometries for simplified physical process-plume (due to a heat source) under adiabatic and convection boundary condition, respectively. Results of the comparison under adiabatic boundary condition show that good agreement is obtained among the analytical solution, COCOSYS prediction, and CFX prediction for zone temperature. The general trend of the temperature distribution along the vertical direction predicted by COCOSYS agrees with the CFX prediction except in dome, and this phenomenon is predicted well by CFX and failed to be reproduced by COCOSYS. Both COCOSYS and CFX indicate that there is no temperature stratification inside dome. CFX prediction shows that temperature stratification area occurs beneath the dome and away from the heat source. Temperature stratification area under adiabatic boundary condition is bigger than that under convection boundary condition. The results indicate that the average temperature inside containment predicted with COCOSYS model is overestimated under adiabatic boundary condition, while it is underestimated under convection boundary condition compared to CFX prediction.

Unsteady Simulations of a Counter-Rotating Aspirated Compressor

An unsteady analysis of the MIT counter-rotating aspirated compressor (CRAC) has been conducted using the Numeca FINE™/Turbo 3D viscous turbulent solver with the Non-Linear Harmonic (NLH) method. All three blade rows plus the aspiration slot and plenum were included in the computational domain. Both adiabatic and isothermal solid wall boundary conditions were applied and simulations with and without aspiration were completed. Comparison of the aspirated case with data is good. When compared to the adiabatic boundary condition, the isothermal boundary condition solutions showed improvements in predicting stage performance, most notably at the endwalls. The aspiration has a significant impact on the flow field and provides a 4.2% increase in efficiency over the non-aspirated case. Although the slot and plenum had been designed to aspirate 1% of the inlet mass flow, the experiment and simulations show that it chokes at about 0.5%. Details of the aspiration flow path choking mechanism, which was previously not well understood, are presented.

Research on the Variation of Average Temperature of Heat Conduction Process under the Second Boundary Condition

The variation law of the average temperature with time in general case is derived by the differential equation of heat conduction which it is the reflection of the conservation of energy principle. The expression of the average temperature under the second boundary condition is given by the integral form of initial and boundary conditions. And what can be also derived are that the average temperature has a linear relationship with time when the boundary heat flux is constant, and it does not change with time under the adiabatic boundary condition.

Cross-sectional convection induced by an insulated boundary in a cylinder

When a long horizontal cylinder filled with fluid is differentially heated at the end walls at high Rayleigh number, A, the axial flow in the midsection consists of boundary layers at the top and bottom of the cylinder flowing in reverse directions, and the temperature is stably and linearly distributed in the vertical. Both the temperature is stably and linearly distributed in the vertical. Both the temperature and the flows are almost independent of the axial dimension. The adiabatic boundary condition on the cylinder requires temperature corrections which can induce cross-section boundary layers on the cylindrical wall and vertical internal boundary layers in the middle. Both types of boundary layers are O(A−¼) in width. Matching different boundary layers at the poles is achieved through additional A−⅙ and A−⅛ layers. The maximum boundary-layer velocity is calculated to be almost one-quarter of the axial velocity observed in experiments for A = 108.

Heat Transfer in Air Enclosures of Aspect Ratio Less than One

The heat transfer rates inside rectangular air enclosures of aspect ratios between 0.1 and 1.0 were investigated interferometrically for a Grashof number range between 2.64 × 106 and 5.45 × 106. The enclosures were composed of dissimilar temperature vertical walls and two types of ceilings and floors. One type was made from constant temperature plates kept at the vertical wall temperatures, and the other type was made of low thermal conductivity polyurethane foam rubber. The heat transfer characteristics and flow patterns within these two types of enclosures were found to be significantly different. For aspect ratios between 0.4 and 1.0 the isothermal ceiling and floor approximate an adiabatic boundary condition much better than foam because much less heat was interchanged between the floor (or ceiling) and the air in the enclosure.