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Transport Effects and Dynamic Behavior at Interfaces
Published in Van P. Carey, Liquid-Vapor Phase-Change Phenomena, 2020
The extremely high heat transfer coefficients typically associated with vaporization and condensation processes make it possible to transfer thermal energy at high heat flux levels with relatively low driving temperature differences. The ability to handle high heat flux levels is particularly important in applications such as electronics cooling and power system thermal control. A question of central interest in such applications is “What is the highest heat flux possible in a given vaporization or condensation process?”
Transport Effects and Dynamic Behavior At Interfaces
Published in Van P. Carey, Liquid-Vapor Phase-Change Phenomena, 2018
The extremely high heat transfer coefficients typically associated with vaporization and condensation processes make it possible to transfer thermal energy at high heat flux levels with relatively low driving temperature differences. The ability to handle high heat flux levels is particularly important in applications such as electronics cooling and power system thermal control. A question of central interest in such applications is “What is the highest heat flux possible in a given vaporization or condensation process?”
Steady-State Heat Conduction
Published in Michael R. Gosz, Finite Element Method, 2017
In order to derive the steady-state heat equation, it is helpful to observe Figure 5.1. The figure illustrates a solid body defined by the interior volume Ω and outer surface Γ. The body is subjected to a prescribed temperature distribution over a portion of the surface labeled ΓT. In addition, a heat flux distribution is prescribed over the portion of the boundary labeled Γq. A heat flux is a vector quantity that describes the amount of energy flowing through a unit area per unit time. Hence the flux vector, q, at a point on the surface has the SI units of Joules per meter squared per second, i.e., J/(m2 · s). In the sign convention adopted here, positive flux points out of the body. Heat can also be generated (or dissipated) internally by means of a heat source distribution S(X1, X2, X3) inside Ω. The heat source has units of energy per unit volume per unit time, i.e., J/(m3 · s). The relevant quantities and associated units for steady-state heat conduction are summarized in Table 5.1. Note that in the table we have used the unit Watt instead of Joules per second, i.e., W = J/s.
On the gradient tracking problem for a bilinear reaction–diffusion equation excited by distributed bounded controls
Published in Journal of Control and Decision, 2023
El Hassan Zerrik, Abderrahman Ait Aadi, Mohamed Ouhafsa
The notion of gradient controllability was initiated by Zerrik et al. (1999) and aimed to control the gradient of a system instead of the state. There are many reasons for introducing this notion: it generalises the notion of controllability, in the sense that if a system is controllable it is gradient controllable and the converse is not in general true. Indeed, there exists systems that are not controllable but gradient controllable (see Zerrik et al., 1999). Moreover controlling a gradient of a system costs fewer than controlling the state of the system. Additionally, the gradient controllability provides a means to deal with many problems from the real word, for instance, the problem of thermal insulation where the purpose is to keep a constant temperature of the system with regards to the outside environment assumed to be with fluctuating temperature. Thus, one has to regulate the system temperature in order to vanish the exchange thermal flux. This is the case inside a car where one has to change the level of the internal air conditioning with respect to the external temperature. As we cannot always have external measurements, we use a sensor to measure the flux, which is a transducer producing a signal that is proportional to the local heat flux.
Experimental study of using Aerogel insulation for residential buildings
Published in Advances in Building Energy Research, 2022
Mohamed T. Elshazli, Mohammad Mudaqiq, Tao Xing, Ahmed Ibrahim, Brian Johnson, Jinchao Yuan
Temperature vs time results for each wall were recorded and plotted as shown in Figure 7. Then, the heat transfer was observed through calculating the heat flux. Heat flux is the transmission of energy through a surface area and it is expressed in watts per square metre. Heat flux occurs whenever there are temperature differences. The diagram in Figure 6 shows how heat transfer and the factors affecting heat flux. Heat flux was calculated using the following equation. where: K = thermal conductivity (W/(m.K), Btu /(hr oF ft2/ft))A = area (m2, ft2)T1 = temperature 1 (°C, °F)T2 = temperature 2 (°C, °F)x = material thickness (m, ft)
Discrete Element Analysis of Heat Transfer in the Breeder Beds of the European Solid Breeder Blanket Concept
Published in Fusion Science and Technology, 2019
M. Moscardini, S. Pupeschi, Y. Gan, F. A. Hernández, M. Kamlah
Figure 8 shows the influence of the helium pressure at 4, 2, 1, and 0.1 bars on the temperature profiles generated for the same assembly under standard conditions (see Sec. II.B). As expected, an increase of the temperature is obtained when the gas pressure decreases. While slight increases of about 1.7% and 5% occur in terms of the peak temperatures when the gas pressure is reduced from 4 to 2 bars and 1 bar, respectively, the peak temperature increases by about 52% when the gas pressure decreases down to 0.1 bar. At 1 and 0.1 bar the temperature limit of 920°C is overcome reaching maximum temperatures of 933°C and 1350°C, respectively. This behavior is due to the Smoluchowski effect, which determines a reduction of the thermal conductivity of the confined gas with the pressure. This leads to a reduction of the conductance in the thermal contacts; thus, a lower heat flux is exchanged between particles.