Cross-current transfer processes in the non-steady state

1963 ◽  
Vol 272 (1349) ◽  
pp. 241-269 ◽  
Keyword(s):  
Steady State ◽  
Heat Exchanger ◽  
Steady States ◽  
The State ◽  
Current Transfer ◽  
Transfer Processes ◽  
Inlet Stream ◽  
Cross Current ◽  
Current Heat

The steady and non-steady states of cross-current transfer processes are analyzed mathematically for conditions where there is no mixing in either stream. Solutions are obtained which enable non-steady conditions to be followed quantitatively, whether they are caused by continuous or discontinuous regular or by random variations in the state of an inlet stream. As an illustrative example the response of a cross-current heat exchanger to a stepchange in the temperature of one of the inlet streams is calculated.

A numerical analysis of heat transfer in a cross-current heat exchanger with controlled and newly designed air flows

2018 ◽  
Vol 16 (1) ◽  
pp. 627-636 ◽  
Author(s):  
Witold Żukowski ◽  
Przemysław Migas ◽  
Monika Gwadera ◽  
Barbara Larwa ◽  
Stanisław Kandafer
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Flow Resistance ◽  
Substantial Part ◽  
Fluidised Bed ◽  
Air Chamber ◽  
Model Variant ◽  
Counter Current ◽  
Cross Current ◽  
Current Heat

AbstractSimulations of heat transfer between air and flue gases in a plate heat exchanger are presented. The device was designed for the heating of the air supplying a fluidised furnace for the combustion of wet sludge and wood crumbs. The locations of inlets and outlets and the geometry of the heat exchanger are determined by the construction of the furnace. The aim of the simulations was to increase effectiveness of heat transfer through the use of flow redirections with additional baffles placed in the air chamber. The results of the simulations showed that a substantial part of the heat exchanger without baffles is not used effectively. On the basis of a velocity profile, a temperature distribution and a wall heat flux, the geometry of the inter-plate space within the air chamber was modified by adding baffles. The unmodified exchangers had 77% efficiency in comparison to counter-current exchangers with the same heat transfer area. After the application of baffles, the efficiency increased to 83-91% depending on the construction used (one, two or three baffles). The best model variant of the exchanger with baffles led to the increase in the temperature of air supplying the fluidised bed by approximately 76 K in relation to the system without baffles . Unexpectedly, the presented modifications of the geometry of the system had very low influence of the flow resistance in the air chamber. The value of Δp for the system without baffles is almost the same as for the best model variant.

Countercurrent transfer processes in the non-steady state

1954 ◽  
Vol 225 (1161) ◽  
pp. 226-244 ◽  
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Heat Exchanger ◽  
General Solution ◽  
Wide Class ◽  
Distillation Process ◽  
Batch Distillation ◽  
Transfer Processes ◽  
Mass And Heat Transfer ◽  
Continuous Distillation

Countercurrent mass and heat-transfer operations are analyzed mathematically, taking into account column capacity, and a general solution is obtained which enables the course of non-steady conditions to be followed quantitatively for a wide class of processes. Absorption and extraction, continuous distillation and batch distillation, are treated in detail, and illustrative examples are provided of the behaviour of a typical heat exchanger and of a typical batch distillation process.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

scholarly journals A SIMPLE FIVE-STEP METHODOLOGY TO DETERMINE CONTROLLABILITY OF HEAT EXCHANGER NETWORKS USING STEADY-STATE INFORMATION

2011 ◽  
Author(s):  
Rodolfo Tellez ◽  
William Y. Svrcek ◽  
Brent R. Young
Keyword(s):  
Steady State ◽  
Heat Exchanger ◽  
Process Integration ◽  
Plant Design ◽  
State Information ◽  
Step Procedure ◽  
Heat Exchanger Networks ◽  
Propose Control Strategy ◽  
Optimum Heat ◽  
And Control

Process integration design methodologies have been developed and introduced to synthesise an optimum heat exchanger network (HEN) arrangement. However, controllability issues are often overlooked during the early stages of a plant design. In this paper we present a five-step procedure that involves the use of multivariable disturbance and control analyses based solely on steady-state information and with the purpose to assess process design developments and to propose control strategy alternatives appropriate and suitable for a HEN.

POVERTY TRAPS AND INFERIOR GOODS IN A DYNAMIC HECKSCHER–OHLIN MODEL

2012 ◽  
Vol 17 (6) ◽  
pp. 1227-1251 ◽  
Author(s):  
Eric W. Bond ◽  
Kazumichi Iwasa ◽  
Kazuo Nishimura
Keyword(s):  
Economic Theory ◽  
Steady State ◽  
World Economy ◽  
Steady States ◽  
The Other ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Multiple Steady States ◽  
The World ◽  
State Capital

We extend the dynamic Heckscher–Ohlin model in Bond et al. [Economic Theory(48, 171–204, 2011)] and show that if the labor-intensive good is inferior, then there may exist multiple steady states in autarky and poverty traps can arise. Poverty traps for the world economy, in the form of Pareto-dominated steady states, are also shown to exist. We show that the opening of trade can have the effect of pulling the initially poorer country out of a poverty trap, with both countries having steady state capital stocks exceeding the autarky level. However, trade can also pull an initially richer country into a poverty trap. These possibilities are a sharp contrast with dynamic Heckscher–Ohlin models with normality in consumption, where the country with the larger (smaller) capital stock than the other will reach a steady state where the level of welfare is higher (lower) than in the autarkic steady state.

Current transfer processes in a hydrated layer localized in a two-layer porous structure of nanosized ZrO2

2022 ◽  
Author(s):  
Yuriy Yu. Bacherikov ◽  
Petro M. Lytvyn ◽  
Sergii V. Mamykin ◽  
Olga B. Okhrimenko ◽  
Valentyna V. Ponomarenko ◽  
...  
Keyword(s):  
Porous Structure ◽  
Current Transfer ◽  
Transfer Processes ◽  
Hydrated Layer

scholarly journals Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks

1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Reaction Network ◽  
Steady States ◽  
Eigenvalue Analysis ◽  
Zero Eigenvalue ◽  
Positive Steady State ◽  
Positive Steady States ◽  
Positive Rate ◽  
System Of Inequalities

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.

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