Piecewise Constant Temperature Research Articles

Analysis of electromagnetic interference emission in domestic induction cooker

In this paper, a systematic procedure has been developed to analyze electromagnetic interference (EMI) emission of actual domestic induction cookers under normal operation condition. The induction cooker is divided into two subsystems: one is a printed circuit board (PCB) with some discrete components, and the other is induction heating (IH) system consisting of flux concentrators, concentric coils and a vessel made of ferromagnetic material. By using an equivalent impedance of the IH system, two subsystems are separately modeled and analyzed. In the PCB subsystem, parasitic effects of the lumped components are modelled, and a multi‐port network is developed to solve excitations at the IH system and each discrete component. In the IH subsystem, an electromagnetic‐thermal analysis is conducted. Based on the temperature distribution on the vessel, an approximate model of the vessel with the linear material and the piecewise constant temperature is built up. Simulation and measurement results are given to validate the proposed analysis approach.

Irreversible Brownian Heat Engine

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine $$\eta =1-\sqrt{{T_{c}/T_{h}}}$$ [23]. On the other hand, the maximum power efficiency of the engine approaches $$\eta ^{MAX}=1-({T_{c}/T_{h}})^{1\over 4}$$ . It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.

Model of the process with piecewise-constant extremals to minimize losses of vitamins during the melting of melons and gourds

The extension of periods of storage of fruits of gourds is an urgent task processing industry. The most developed and available for injection is a method of dehydration of raw materials due to supply of heat transfer fluids. In addition to solid dry frame in raw materials is 80–90% water. In the period of moisture removal from raw material changes of thermal-physical and structural-mechanical and physicochemical characteristics. The ratio of water and dry matter in vegetative raw materials largely determines the modes of drying and storage conditions of the finished product. During drying, there are a number of limitations: the drying temperature should not exceed the degradation temperature of vitamins and proteins, and the magnitude of course, the moisture content of the product depends on the reaction prevention malonodinitrile sugars at the critical moisture content. An important problem of the drying of production is quality control stages of drying, the dynamics of which is quite difficult to describe using mathematical models. The main factors of optimization of industrial drying processes is preservation of valuable components of the feedstock, the drying time, energy and resource conservation. Development of effective control algorithm for the process of dehydration of raw materials described in the article on the example of drying of slices of melon. Experimental approach a two-stage process of drying of melon varieties Taman, the proposed regression model with the relaxation-based on humidity and content of vitamin C from the variable in time temperature and pressure, based on the available literature and own experimental data. According to the optimal control of the drying process to search for the thermobaric regime that maximizes the vitamin C content at the end of the drying, under specified conditions, the humidity. The main findings are the solution of the problem for the case of piecewise constant temperature and pressure in the separate N steps each 2 stages of experimental drying slices of melon.

On Multilayer Modeling of Radiative Transfer for Use With the Multisource k-Distribution Method for Inhomogeneous Media

A nonisothermal medium is modeled using the multilayer approach in which the continuous temperature distribution in a one-dimensional system as modeled as being piecewise constant. This has been shown to provide accurate results for a surprisingly small number of layers. Analysis is performed on a nonisothermal gray medium to attempt to characterize the ways in which the errors introduced by the multilayer modeling change with various physical parameters namely, the optical thickness and the temperature or emissive power gradient. A demonstration is made of how the multisource k-distribution method is capable of evaluating the heat flux within a one-dimensional system with piecewise constant temperature distribution with line-by-line accuracy with a significant decrease in computational expense. The k-distribution method for treating the spectral properties of an absorbing–emitting medium represents a powerful alternative to line-by-line calculations by reducing the number of radiative transfer equation (RTE) evaluations from the order of a million to the order of 10 without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact. However, when no appropriate reference temperature can be defined, the method results in errors. The multisource k-distribution method extends the k-distribution method to problems with piecewise constant temperature and optical properties.

A multi-source full spectrum k-distribution method for 1-D inhomogeneous media

The k-distribution method for treating the spectral properties of an absorbing–emitting medium represents an alternative to line-by-line calculations. It reduces the number of RTE evaluations from the order of a million to the order of ten without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact. However, when no appropriate reference temperature can be defined, the method results in errors. There have been several attempts to implement corrections to the k-distribution method to extend its application to inhomogeneous media by modeling the effects of temperature, pressure, and concentration gradient. Some of these techniques are effective at reducing these errors, but none successfully extend the k-distribution method to inhomogeneous media in a way that retains the analytical guarantee of line-by-line accuracy. The Multi-Source Full Spectrum K-Distribution Method (MSFSK) introduced here manages to attain this goal for 1-dimensional domains with piecewise constant temperature distributions by applying the superposition principle to the original RTE before applying the k-distribution transformation to decompose the problem into a set of sub-problems each of which is able to be solved exactly via the ordinary or modified full spectrum k-distribution method.

Effect of thermal inhomogeneity on the performance of a Brownian heat engine

We explore the effect of thermal inhomogeneity on the performance of a Brownian heat engine by considering exactly solvable models. We first consider a Brownian heat engine which is modeled as a Brownian particle in a ratchet potential moving through a highly viscous medium driven by the thermal kick it receives from a linearly decreasing background temperature. We show that even though the energy transfer due to kinetic energy is neglected, Carnot efficiency cannot be achieved at quasistatic limit. At quasistatic limit, the efficiency for such a Brownian heat engine approaches the efficiency of endoreversible engine η = 1 − √T c /T h [F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)]. Moreover, the dependence of the current, the efficiency and the coefficient of performance of the refrigerator on the model parameters is also explored via Brownian dynamic simulations and analytically. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature [M. Asfaw, M. Bekele, Eur. Phys. J. B 38, 457 (2004), M. Asfaw, M. Bekele, Physica A 384, 346 (2007)]. Furthermore, for a Brownian heat engine driven by a piecewise constant temperature, we show that systematic removal of the inhomogeneous medium leads to a homogeneous medium with a uniform temperature where the effect of temperature inhomogeneity is replaced by an effective load.

Temperature distributions in a periodically stratified layer with a vertical dug well

The stationary problems of heat conduction in a periodically stratified layer with a vertical cylindrical hole is considered. The lateral surface of the hole is kept at a given piece-wise constant temperature. The boundary planes at zero temperature are taken into account, and the ideal thermal contact between the composite constituents is assumed. The problem within the homogenized model with microlocal parameters is solved.

A Multi-Source Full Spectrum K-Distribution Method for 1-D Inhomogeneous Media

The k-distribution method for treating the spectral properties of an absorbing-emitting medium represents an alternative to line-by-line calculations which reduces the number of RTE evaluations from the order of a million to the order of ten without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact. However, when no appropriate reference temperature can be defined, the method results in errors. There have been several attempts to implement corrections to the k-distribution method to extend its application to inhomogeneous media by modelling the effects of temperature, pressure, and concentration gradient. Some of these techniques are very effective at reducing these errors, but none successfully extend the k-distribution method to inhomogeneous media in a way that retains the analytical guarantee of line-by-line accuracy. The Multi-Source Full Spectrum K-Distribution Method (MSFSK) introduced here manages to attain this goal for 1-dimensional domains with piecewise constant temperature distributions by applying the superposition principle to the original RTE before applying the k-distribution transformation to decompose the problem into a set of sub-problems each of which is able to be solved exactly via the ordinary or modified full spectrum k-distribution method.

The extended Graetz problem with piecewise constant wall temperature for laminar and turbulent flows through a concentric annulus

The effect of axial heat conduction on the heat transfer is of importance if the flow Peclet number is small or if the axial extension of the heating zone is small. This paper therefore presents an analytical solution to the extended Graetz problem in a concentric annulus with piecewise constant temperature at the outer wall. The solution is based on a selfadjoint formalism which results from the decomposition of the elliptic energy equation into two first-order partial differential equations. The gained solution is exact and simple.The need of regarding the axial heat conduction is displayed by evaluating the analytical solution.

Toward Polymer Product Design. I. Dynamic Optimization of Average Molecular Weights and Polydispersity Index in Batch Free Radical Polymerization

In the polymer industry, product quality is usually determined by the molecular weight distribution of polymer products. We propose a comprehensive study of polymer product design through dynamic optimization of average molecular weights and the polydispersity index in batch free radical polymerization. After analyzing and validating the modified Stickler−Panke−Hamielec (SPH) model, this paper extends the model to achieve product design with a specified polymer molecular weight distribution for various optimization goals. Conversion maximization under isothermal conditions was studied first. We concluded that dynamic optimization is useful to obtain desired products. However, some specifications of polymer molecular weight distribution cannot be achieved under isothermal conditions. Therefore, optimization with piecewise constant temperature profiles was also studied to extend the range of product specifications. Considering the practical requirement for productivity in engineering applications, reaction ...

Optimal potentials for temperature ratchets

In a spatially periodic temperature profile, directed transport of an overdamped Brownian particle can be induced along a periodic potential. With a load force applied to the particle, this setup can perform as a heat engine. For a given load, the optimal potential maximizes the current and thus the power output of the heat engine. We calculate the optimal potential for different temperature profiles and show that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures, the optimal potential leads to a divergent current. This divergence, being an effect of both the overdamped limit and the infinite temperature gradient at the interface, would be cut off in any real experiment.

Model-based optimization of temperature and feed control strategies for glycerol production by fed-batch culture of osmophilic yeast Candida krusei

In this study, the optimization of temperature and feed control strategies for glycerol production by fed-batch culture of osmophilic yeast Candida krusei was investigated to maximize the final yield whilst to control the residual glucose at a low concentration. For the purposes of convenient control performance and easy numerical solution, the entire fermentation process was proposed being divided into multi-subintervals. In each subinterval, temperature was controlled constantly; while glucose and corn steep liquor were fed in pulse form at each start. Both piecewise-constant temperature (PCT) and discrete-pulse feed (DPF) control strategies were optimized by the complex method of Box based on previous macro-kinetic model and verified experimentally in a 600 ml airlift loop reactor. It was found that, by model-based optimization of only DPF control strategies, the final glycerol yield were significantly improved compared with those by previous empirical strategies. The yield could be improved further by optimization of both PCT and DPF control strategies and by selecting the first half of the whole fermentation process as the control emphasis. The optimization approach proposed appeared promising to solve the multivariable control problem in many fermentation processes.

Piecewise constant triangular cooling schedules for generalized simulated annealing algorithms

We investigate how to tune a generalized simulated annealing algorithm with piecewise constant cooling schedule to get an optical convergence exponent. The optimal convergence exponent of generalized simulated annealing algorithms has been computed by Catoni and Trouve. It is reached only with triangular sequences of temperatures, meaning that different finite sequences are used, depending on the time resource available for computations (expressed by an overall number of iterations). We show first that it is possible to get close to the optimal convergence exponent uniformly over suitably bounded families of energy landscapes using a fixed number of temperature steps. Then we show that, letting the number of steps increase with the time resource, we can build a cooling schedule which is universally robust with respect to the convergence exponent: a fixed triangular sequence of temperatures gives an optimal convergence exponent for any energy landscape. Piecewise constant temperature sequences are often used in practice: in favourable cases, the use of the same temperature during a large number of iterations allows tabulating the exponential penalties appearing in the transition matrix, thus sparing a significant amount of computer time. The proofs we give rely on Freidlin and Wentzell's closed formulas for the exit time and point from subdomains of time homogeneous Markov chains.