Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

Heat capacities of ionic liquids as a function of temperature at 0.1 MPa. measurement and prediction

Heat capacities of nine ionic liquids were measured from (293 to 358) K by using a heat flux differential scanning calorimeter. The impact of impurities (water and chloride content) in the ionic liquid was analyzed to estimate the overall uncertainty. The Joback method for predicting ideal gas heat capacities has been extended to ionic liquids by the generation of contribution parameters for three new groups. The principle of corresponding states has been employed to enable the subsequent calculation of liquid heat capacities for ionic liquids, based on critical properties predicted using the modified Lydersen-Joback-Reid method, as a function of the temperature from (256 to 470) K. A relative absolute deviation of 2.9% was observed when testing the model against 961 data points from 53 different ionic liquids reported previously and measured within this study.

Transient Heat Conduction of Variable Stiffness Composite Laminate

Recent research on Variable Stiffness (VS) laminates, which are constructed by steering the fiber orientation as a spatial function of location, have shown to improve laminate performance under mechanical loads. Two distinct cases of stiffness variation can be achieved either by variation of the fiber orientation in the direction of the global x-axis, or perpendicular to it. In the present paper, thermal analysis of a VS laminate is performed to study the effect of steering fibers on transient heat conduction under uniform heat flux using finite element method. The goal of the present paper is a parametric study of the effect of variable stiffness properties on transient response including time to reach steady state and temperature profile. Also, stress resultants and maximum stress location are investigated under different boundary conditions. A FEM algorithm is applied to exactly incorporate the boundary conditions for stress resultant analysis.

Transient Heat Conduction of Variable Stiffness Composite Laminate

Recent research on Variable Stiffness (VS) laminates, which are constructed by steering the fiber orientation as a spatial function of location, have shown to improve laminate performance under mechanical loads. Two distinct cases of stiffness variation can be achieved either by variation of the fiber orientation in the direction of the global x-axis, or perpendicular to it. In the present paper, thermal analysis of VS laminate is performed to study the effect of steering fibers on transient heat conduction under uniform heat flux using finite element method. The goal of the present paper is a parametric study of the
effect of variable stiffness properties on transient response including time to reach steady state and temperature profile. Also, stress resultants and maximum stress location are investigated under different boundary conditions. A FEM algorithm is applied to exactly incorporate the boundary conditions.

Effect of Turbine Inlet Temperature on Rotor Blade Tip Leakage Flow and Heat Transfer

One of the most critical gas turbine engine components, the rotor blade tip and casing, is exposed to high thermal load. It becomes a significant design challenge to protect the turbine materials from this severe situation. The purpose of this paper is to study numerically the effect of turbine inlet temperature on the tip leakage flow structure and heat transfer. In this paper, the effect of turbine inlet temperature on the tip leakage flow structure and heat transfer has been studied numerically. Uniform low (LTIT: 444 K) and high (HTIT: 800 K) turbine inlet temperature, as well as non-uniform inlet temperature have been considered. The results showed the higher turbine inlet temperature yields the higher velocity and temperature variations in the leakage flow aerodynamics and heat transfer. For a given turbine geometry and on-design operating conditions, the turbine power output can be increased by 1.33 times, when the turbine inlet temperature increases 1.80 times. Whereas the averaged heat fluxes on the casing and the blade tip become 2.71 and 2.82 times larger, respectively. Therefore, about 2.8 times larger cooling capacity is required to keep the same turbine material temperature. Furthermore, the maximum heat flux on the blade tip of high turbine inlet temperature case reaches up to 3.348 times larger than that of LTIT case. The effect of the interaction of stator and rotor on heat transfer features is also explored using unsteady simulations. The non-uniform turbine inlet temperature enhances the heat flux fluctuation on the blade tip and casing.

Effect of turbine inlet temperature on blade tip leakage flow and heat transfer

One of the most critical gas turbine engine components, rotor blade tip and casing, are exposed to high thermal load. It becomes a significant design challenge to protect the turbine materials from this severe situation. As a result of geometric complexity and experimental limitations, Computational Fluid Dynamics (CFD) tools have been used to predict blade tip leakage flow aerodynamics and heat transfer at typical engine operating conditions. In this paper, the effect of turbine inlet temperature on the tip leakage flow structure and heat transfer has been studied numerically. Uniform low (LTIT: 444 K) and high (HTIT: 800 K) turbine inlet temperature have been considered. The results showed the higher turbine inlet temperature yields the higher velocity and temperature variations in the leakage flow aerodynamics and heat transfer. For a given turbine geometry and on-design operating conditions, the turbine power output can be increased by 1.48 times, when the turbine inlet temperature increases 1.80 times. Whereas the averaged heat fluxes on the casing and the blade tip become 2.71 and 2.82 times larger, respectively. Therefore, about 2.8 times larger cooling capacity is required to keep the same turbine material temperature. Furthermore, the maximum heat flux on the blade tip of high turbine inlet temperature case reaches up to 3.348 times larger than that of LTIT case. The effect of the interaction of stator and rotor on heat transfer features is also explored using unsteady simulations.

Combined Conduction-Convection-Radiation Heat Transfer of Slip Flow inside a Micro-channel Filled with a Cellular Porous Material

Combined conduction–convection–radiation heat transfer is investigated numerically in a micro-channel filled with a saturated cellular porous medium, with the channel walls held at a constant heat flux. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous–fluid system are studied by considering hydrodynamically fully developed flow and applying the Darcy–Brinkman flow model. One energy equation model based on the local thermal equilibrium condition is adopted to evaluate the temperature field within the porous medium. Combined conduction and radiation heat transfer is treated as an effective conduction process with a temperature-dependent effective thermal conductivity. Results are reported in terms of the average Nusselt number and dimensionless temperature distribution, as a function of velocity slip coefficient, temperature jump coefficient, porous medium shape parameter and radiation parameters. Results show that increasing the radiation parameter (Tr)(Tr) and the temperature jump coefficient flattens the dimensionless temperature profile. The Nusselt numbers are more sensitive to the variation in the temperature jump coefficient rather than to the velocity slip coefficient. Such that for high porous medium shape parameter, the Nusselt number is found to be independent of velocity slip. Furthermore, it is found that as the temperature jump coefficient increases, the Nusselt number decrease. In addition, for high temperature jump coefficients, the Nusselt number is found to be insensitive to the radiation parameters and porous medium shape parameter. It is also concluded that compared with the conventional macro-channels, wherein using a porous material enhances the rate of heat transfer (up to about 40 % compared to the clear channel), insertion of a porous material inside a micro-channel in slip regime does not effectively enhance the rate of heat transfer that is about 2 %.

On the filling factor of emitting material in the upper atmosphere of ε Eri (K2 V)

The emission measure distribution in the upper transition region and corona of e Eri is derived from observed emission-line fluxes. Theoretical emission measure distributions are calculated assuming that the radiation losses are balanced by the net conductive flux. We discuss how the area factor of the emitting regions as a function of temperature can be derived from a comparison between these emission measure distributions. It is found that the filling factor varies from ~0.2 in the mid-transition region to ~1.0 in the inner corona. The sensitivity of these results to the adopted ion fractions, the iron abundance and other parameters is discussed. The area factors found are qualitatively similar to the observed structure of the solar atmosphere, and can be used to constrain two-component models of the chromosphere. Given further observations, the method could be applied to investigate the trends in filling factors with indicators of stellar activity.

Multiphysics Simulation of Thermal Plasma Produced by Lightning Strike on Aircraft Structures

A novel numerical technique is proposed to model thermal plasma of microseconds/milliseconds time-scale effect. Modelling thermal plasma due to lightning strike will allow the estimation of electric current density, plasma pressure, and heat flux at the surface of the aircraft structure. These input data can then be used for better estimation of the mechanical/thermal induced damage on the aircraft structures for better protection systems design. Thermal plasma generated during laser cutting, electric (laser) welding and other plasma processing techniques have been the focus of many researchers. Thermal plasma is a gaseous state that consists from a mixture of electrons, ions, and natural particles. Thermal plasma can be assumed to be in local thermodynamic equilibrium, which means the electrons and the heavy species have equal temperature. Different numerical techniques have been developed using a coupled Navier Stokes – Heat transfer – Electromagnetic equations based on the assumption that the thermal plasma is a single laminar gas flow. These previous efforts focused on generating thermal plasma of time-scale in the range of seconds. Lighting strike on aircraft structures generates thermal plasma of time-scale of milliseconds/microseconds, which makes the previous physics used not applicable. The difficulty comes from the Navier-Stokes equations as the fluid is simulated under shock load, this introducing significant changes in the density and temperature of the fluid.

Investigation of thermal resistance and bridging in examples of contemporary and vernacular solid wall architecture

Contemporary architecture has tended to increase envelope insulation levels in an unceasing effort to reduce U-values. Traditional masonry architecture in contrast was devoid of insulation, except for the inherent insulative nature of vernacular materials. Also the consistency of the outer membrane of the building skin diminished any impact due to bridging. In contemporary highly insulated walls bridges are numerous due to the necessity to bind inner and outer structural skins through insulation layers. This paper examines thermal bridging in an example of contemporary façade design and compares it with an example of traditional vernacular architecture currently being researched which is characterized by a lack of bridging elements. Focus is given to heavy weight materials of high thermal mass, which appropriately for passive architecture help moderate fluctuations in internal temperature. In an extensive experimental study samples of highly insulated precast concrete sandwich panels and lime rendered masonry walls are tested in a guarded hot-box. The building construction methods are compared for static and dynamic thermal transmittance, via heat flux and surface temperature differential measurements. Focus is given to the differential heat loss due to the thermal bridging in the sandwich panels and its associated impact on overall heat loss relative to traditional masonry construction.

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.