Heat flow algorithms

These equilibrium fluctuation estimates have been cross checked by using the heat flow algorithm (3.5). The results agree very well. It has been possible to find an interval where the heat field is large enough to prevail over thermal fluctuations and small enough not to violate the linear response relation (2.17). 

Comparison of the thermal conductivities of prolate (p) and oblate (o) nematic liquid crystals. The entries for zero field have been obtained by using the Green-Kubo relation (3.3). The entries for finite field have been obtained by applying the heat flow algorithm (3.5). Note that the EMD GK estimates and the NEMD estimates agree within the statistical error. 

Heat-flow algorithm for rigid polyatomic molecules... 

The availability of a phase space probability distribution for the steady state means that it is possible to develop a Monte Carlo algorithm for the computer simulation of nonequilibrium systems. The Monte Carlo algorithm that has been developed and applied to heat flow [5] is outlined in this section, following a brief description of the system geometry and atomic potential. 

Metropolis algorithm, Monte Carlo heat flow simulation, 70-71 molecular dynamics, 76-81... 

Monte Carlo simulations, heat flow, 67-81 dynamics, 75-81 Metropolis algorithms, 70-71 nonequilibrium molecular dynamics, 71-74 structure profiles, 74-75 system details, 67-70... 

In other work cyclic operation of a metal hydride refrigerator [3] was analyzed. With the help of mathematical model for calculation of transfer processes to HHP the algorithm of definition of optimum switching of heat flows in system has been developed at given cycle time. The algorithm is constructed from a condition of achievement of the maximal refrigerating effect (real COP) on unit of brought heat. 

A polynomial was fit to the calibration curve for the thermocouple by means of a minimization of the maximum deviation technique using the Nelder Mead sequential simplex minimization algorithm method.( 5,6, 7) The coefficients of this polynomial are stored in the analysis program and are used to convert thermocouple voltages to temperature values. Y values are converted to dH(t,T)/dt, the heat flow into and out of the sample in mcal/sec. The operator selects a baseline for the analysis by entering the temperatures of the beginning and end points of the baseline. A plot is produced of the raw data with the operator selected baseline shown as illustrated in Figure A. 

The other feature to note regarding the cascade in Fig. IIB is the point where the heat flow becomes zero. This is at an interval temperature of 75°C. This corresponds to the location of the pinch. Given that the interval temperature for the pinch is 75°C, the hot stream pinch temperature is therefore 80° C and the cold stream pinch temperature 70° C. This agrees with the location of the pinch from the composite curves. Thus, the problem table algorithm provides the information required for minimum hot and cold utility targets and the location of the pinch that is critical in the next step, which is to design to achieve the targets. 

Kunz RF, Siebert BW, Cope WK, Foster NF, Antal SP, Ettorre SM (1998) A coupled phasic exchange algorithm for three-dimensional multi-field analysis of heated flows with mass transfer. Computers Fluids 27(7) 741-768... 

It has turned out to be impossible thus far to derive simple NEMD algorithms with (mechanical) external fields analogous to the equilibrium case to determine self-diffusion or heat flow coefficients superimposed on the SLLOD dynamics of the system. ... 

A modification of the Newtonian MD scheme with the purpose of generating a thermodynamical ensemble at constant temperature is called a thermostat algorithm. The use of a thermostat ean be motivated by one (or a number) of the following reasons (i) to match experimental conditions (most condensed-phase experiments are performed on thermostatized rather than isolated systems) (ii) to study temperature-dependent processes (e.g., determination of thermal coefficients, investigation of temperature-dependent conformational or phase transitions) (iii) to evacuate the heat in dissipative non-equilibrium MD simulations (e.g., computation of transport coefficients by viscous-flow or heat-flow simulations) (iv) to enhance the efficiency of a conformational search (e.g., high-temperature dynamics, simulated annealing) (v)... 

The numerical solution of the energy balance and momentum balance equations can be combined with flow equations to describe heat transfer and chemical reactions in flow situations. The simulation results can be in various forms numerical, graphical, or pictorial. CFD codes are structured around the numerical algorithms and, to provide easy assess to their solving power, CFD commercial packages incorporate user interfaces to input parameters and observe the results. CFD... 

The advection—diffusion equation with a source term can be solved by CFD algorithms in general. Patankar provided an excellent introduction to numerical fluid flow and heat transfer. Oran and Boris discussed numerical solutions of diffusion—convection problems with chemical reactions. Since fuel cells feature an aspect ratio of the order of 100, 0(100), the upwind scheme for the flow-field solution is applicable and proves to be very effective. Unstructured meshes are commonly employed in commercial CFD codes. 

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