On the Analogy Between the Calorimeter Problem and Some Granulate-Fluid Exchange Processes

1978 ◽  
Vol 100 (2) ◽  
pp. 319-323 ◽  
Author(s):  
J. Kern ◽  
J. W. Hemmings
Keyword(s):  
Energy Balance ◽  
Quantitative Comparison ◽  
Fluid Exchange ◽  
Short Contact ◽  
System Parameters ◽  
Error Diagram ◽  
Exchange Processes ◽  
Particulate Solids ◽  
Balance Solution

The solution to a generalized version of the classical calorimeter problem approximates the behavior of certain continuous exchange processes between particulate solids and a fluid. For modeling purposes, the much simpler energy-balance solution has obvious advantages, although it only holds for negligible intraparticle resistance and thus predicts too short contact times. An error diagram provides a quantitative comparison between those two results as a function of the two pertinent system parameters.

Prediction of Optimum Supplemental Heat for Piglets

2019 ◽  
Vol 62 (2) ◽  
pp. 321-342 ◽  
Author(s):  
Hugo F. M. Milan ◽  
Alex Sandro Campos Maia ◽  
Kifle G. Gebremedhin
Keyword(s):  
Energy Balance ◽  
Skin Temperature ◽  
Air Temperature ◽  
Computational Models ◽  
Thermal Environment ◽  
Learning System ◽  
Mechanistic Models ◽  
Neutral Zone ◽  
Hair Coat ◽  
System Parameters

Abstract. The thermal environment of farrowing facilities is generally controlled at the thermo-neutral zone for sows (15°C to 19°C). This imposes thermal challenges for newborn piglets, which are thermally comfortable at temperatures 10°C to 20°C higher (32°C to 35°C). To satisfy the energetic requirements of piglets, supplemental heat is installed in creep or brooder areas. In this study, we determined optimum supplemental heat requirements (supplied by heating lamps) for piglets based on energy balance as a function of air temperature and animal body weight. We also determined the zone of least thermoregulation of piglets for a given weight when supplemental heat is not provided. Energy balance was calculated using an ensemble of mechanistic models of bio-heat transfer that predicts hair-coat temperature, skin temperature, and skin heat flux. Inputs to the ensemble of mechanistic models include air temperature, black-globe temperature, rectal temperature, and system parameters (e.g., thickness of internal tissues and thermal conductivities). Input temperatures were predicted from measured air temperature in the pen and supplemental heat using machine learning. System parameters were measured or obtained from the literature and optimized using the Monte Carlo method. Ensemble predictions of hair-coat and skin temperature agreed within 3.5% with measured data. The ensemble-predicted zone of least thermoregulation agreed well with previous reports. Predicted optimum supplemental heat showed an exponential decay trend with increasing air temperature and/or animal weight. For air temperature between 15°C and 19°C, the predicted optimum supplemental heat was 266 to 344 W and 44 to 128 W for piglets weighing 1 kg and 20 kg, respectively. The predicted optimum supplemental heat was ~200 W lower for piglets at the end of the farrowing cycle (assuming weight of 20 kg) than at birth (assuming birth weight of 1 kg). Keywords: Bio-heat equation, Computational models, Ensemble learning, Piglets, Precision livestock farming, Supplemental heat, Thermo-neutral zone.

scholarly journals Changes of LISM Characteristics in the Heliospheric Interface

1984 ◽  
Vol 81 ◽  
pp. 28-31 ◽  
Author(s):  
Hartmut W. Ripken ◽  
Hans J. Fahr
Keyword(s):  
Solar System ◽  
Neutral Hydrogen ◽  
Solar Wind Plasma ◽  
Wind Vector ◽  
Hydrogen Atoms ◽  
Direct Inference ◽  
Degree Of Ionization ◽  
System Parameters ◽  
Exchange Processes ◽  
Heliospheric Interface

AbstractIt is possible to deduce LISM properties from observations of interstellar neutral gases in the inner solar system. Parameters accessible by this method are the interstellar wind vector and the densities and temperatures of hydrogen and helium, implying also the deduction of the relative abundance ratios and the degree of ionization in the LISM. Direct inference from observations, for example resonance luminescence measurements of Ly-alpha and He-58.4 nm radiation, yields values appropriate only for the inner solar system, i.e. for the regions within the heliopause dominated by the solar wind plasma.Particularly the subsonic LISM plasma interface ahead of the heliopause causes profound changes in the properties of the neutral LISM gas traversing this region. Mainly p-H charge exchange processes give rise to the destruction of primary hydrogen and the production of secondary hydrogen atoms, the net effect being a depletion of the neutral hydrogen component of the LISM by about 50%.Details on the depletion mechanisms, the hydrogen and oxygen extinctions, and the consequences for the Ly-alpha resonance luminescence intensity interpretations are presented.

Extended Semianalytic Method for Increasing and Decreasing Boundary Temperatures

1974 ◽  
Vol 14 (02) ◽  
pp. 152-164 ◽  
Author(s):  
H.G. Weinstein
Keyword(s):  
Energy Balance ◽  
Finite Difference ◽  
Computation Time ◽  
Test Problems ◽  
Coupling Equation ◽  
One Dimensional ◽  
Boundary Temperature ◽  
Balance Solution ◽  
Finite Difference Solution ◽  
Energy Equations

Abstract A semianalytic method developed earlier couples the overburden energy balance solution to reservoir equations by a single differential equation applicable at the reservoir/overburden boundary. The semi-analytic method is extended in this work to allow temperatures at the reservoir/overburden boundary to decrease, as well as increase, with time. Computer calculations on several test problems show a close agreement of the semianalytic method with the fully finite-difference solution. Both reservoir/overburden boundary temperature and heat flux into the overburden are accurately calculated. Because of its extended generality, the semi-analytic procedure should be quite useful in solving reservoir problems. It is expected that in addition to being useful in thermal simulation programs, it will also be applicable to aquifer, programs, it will also be applicable to aquifer, gas-cap, pseudorelative-permeability, and wellbore problems. The method is faster and requires problems. The method is faster and requires significantly less computer storage than the finite-difference solution. Introduction Thermal reservoir simulation programs, to avoid excessive storage and computation-time requirements, generally do not solve the material balance and energy balance simultaneously, Instead, there an two separate solution steps. First, the material balances are solved over the reservoir; then, with updated pressures and saturations, the energy balance is solved over the underburden/reservoir/ overburden system. However, problems with solution convergence and the treatment of mass transfer terms could be avoided by simultaneously solving the energy balance and the material balances (or equivalently, the pressure equation obtained by combining the material balances to eliminate saturation). A recent paper showed how variational methods could be applied to eliminate the energy-balance solution in the overburden, and thus avoid the problems enumerated above. Included in the model problems enumerated above. Included in the model were a three-dimensional variational principle and an overburden temperature approximation proportional to the solution of the one-dimensional heat conduction equation. However, only the case of a monotonicallyincreasingreservoir/overburden boundary temperature was treated. Using a variational principle complementary to Weinstein's, Chase and O'Dell considered the flow of heat both into and out of the overburden. Their variational equation was one-dimensional, and the assumed overburden temperature function was a one-dimensional cubic polynomial, chosen because of its simplicity. Because the variational model was one-dimensional, no account could be taken of conduction parallel to the reservoir/overburden boundary. Thus, their results are restricted to situations where convection parallel to the reservoir dominates conduction. Chase and O'Dell derived two coupled nonlinear differential equations for the two free parameters of their model. An analytic solution was obtained for increasing boundary temperatures; however, the two equations had to be integrated numerically for decreasing boundary temperatures. To calculate their heat loss vector they had to perform an inner iteration with respect to both perform an inner iteration with respect to both temperature and time. Solving the parameter equations and solving for the heat flux vector were both time-consuming, leading to only a "moderate" savings in computation time over the fully finite-difference model. On the test problems they studied, the model showed increasing errors as the simulation proceeded through the soak and backflow periods. Presumably, these errors would continue to periods. Presumably, these errors would continue to grow if additional heat-flow reversals were invoked. The model to be described here has alleviated the shortcomings in Chase and O'Dell's procedure. This paper describes a generalized semianalytic method paper describes a generalized semianalytic method of handling the energy balance solution in the overburden (and underburden). This solution results in a single overburden energy coupling equation that can be solved easily in conjunction with the reservoir pressure and energy equations. The coupling equation pressure and energy equations. The coupling equation is general, whether reservoir/overburden boundary temperature increases or decreases with time, or increases at some boundary locations while decreasing at others. The paper presents the mathematical development of the extension of the original method to increasing and decreasing temperature problems. SPEJ P. 152

scholarly journals THEORY OF EVAPOTRANSPIRATION: 1. Transpiration and its quantitative description

2011 ◽  
Vol 59 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Anatolij Budagovskyi ◽  
Viliam Novák
Keyword(s):  
Energy Balance ◽  
Differential Equations ◽  
Water Vapour ◽  
Quantitative Description ◽  
Vertical Transport ◽  
System Of Equations ◽  
Plant Canopy ◽  
Basic Information ◽  
Exchange Processes

THEORY OF EVAPOTRANSPIRATION: 1. Transpiration and its quantitative descriptionBasic information about the evapotranspiration and its components is presented. System of equations describing the transport of water and energy in the soil - plant continuum is analyzed. The system of five differential equations with five unknowns is proposed, describing transport of heat and water vapour within the plant canopy, including exchange processes among the leaves and the atmosphere, vertical transport of the heat, water vapour and the energy balance.

A Semi-Analytic Method for Thermal Coupling of Reservoir and Overburden

1972 ◽  
Vol 12 (05) ◽  
pp. 439-447
Author(s):  
H.G. Weinstein
Keyword(s):  
Energy Balance ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Homogeneous Medium ◽  
Energy Coupling ◽  
Thermal Recovery ◽  
Test Problems ◽  
Coupling Equation ◽  
Balance Solution ◽  
Energy Equations

Abstract A semianalytic method of handling the energy balance solution in the overburden has been developed. The method results in a single overburden energy coupling equation applicable at the reservoir - overburden boundary. This feature facilitates simultaneous solution of the pressure and energy equations in the reservoir. Test problems show the semianalytic method to compare favorably with the fully finite-difference technique. Both reservoir - overburden boundary temperature and the important factor of beat transfer into the overburden are accurately predicted by the method. predicted by the method. The semianalytic procedure may have considerable usefulness in the solution of reservoir problems. The method can definitely be applied in thermal simulation programs. Other anticipated applications are to an aquifer underlying a reservoir, an overlying gas cap, or to increasing definition in the vicinity of a wellbore. In each of these applications, the semianalytic procedure is expected to be considerably faster than the finite - difference solution. Introduction In thermal reservoir simulation programs, the material balances are solved over the reservoir; the energy balance is solved over the underburden-reservoir-overburden system. Hence, to avoid excess storage and computation time requirements, the material and energy balances are generally not solved simultaneously. In many cases it would be desirable to solve simultaneously the material balances (or equivalently, the pressure equation obtained by combining the material balances to eliminate saturation) and the energy balance. Problems with solution convergence and the treatment of mass transfer terms could be avoided in this way. This paper describes a semianalytic method of handling the energy balance solution in the overburden (and underburden). This solution results in a single overburden energy coupling equation that can be solved easily in conjunction with the reservoir pressure and energy equations. pressure and energy equations. The paper presents the mathematical development of the method and shows results for several test problems. The problems are similar to those encountered in thermal recovery processes. They compare the semianalytic method with the fully finite-difference procedure and, in one of the problems, with a completely analytic procedure and, in one of the problems, with a completely analytic solution. THEORY GOVERNING EQUATION AND BOUNDARY CONDITIONS Consider the overburden (and underburden) to be a homogeneous medium. The energy balance for the overburden can then be written as follows: (1) where is the density, C is the heat capacity, and khx, khy, khz, are the thermal conductivities in the x, y, z directions, respectively. The initial and boundary conditions for Eq. 1 are (2) Here we assume 0 x a, 0 y b to be the lateral extent of the reservoir and overburden, and 0 z to be the vertical extent of the overburden. SPEJ P. 439

scholarly journals First results and interpretation of energy-flux measurements over Alpine permafrost

2000 ◽  
Vol 31 ◽  
pp. 275-280 ◽  
Author(s):  
Catherine Mittaz ◽  
Martin Hoelzle ◽  
Wilfried Haeberli
Keyword(s):  
Energy Balance ◽  
Energy Exchange ◽  
Swiss Alps ◽  
High Mountain ◽  
Frozen Ground ◽  
Near Surface ◽  
Exchange Processes ◽  
Significant Difference ◽  
First Results ◽  
Coarse Surface

AbstractThe interaction of energy-exchange processes between the atmosphere and the Earth surface determines the surface temperature regime. It is of fundamental importance to the question whether frozen ground exists at a given site and how rapidly it may decay in response to a climatic perturbation. To further our understanding of these processes, measurements concerning near-surface energy-exchange processes were initiated in January 1997 on creeping permafrost at a high mountain site, Murtèl-Corvatsch, upper Engadin, Swiss Alps. Data on all important energy-balance fluxes were collected. In this paper, we present ground-temperature and energy-balance measurements from Murtèl-Corvatsch for a 2 year period, 1997–99. We will examine the relative importance of the energy-balance components and discuss special problems relating to the coarse surface layer. The results indicate a non-zero energy budget, with a positive deviation of up to 78 W m 4 in winter and a negative deviation of up to –130 W nT2 in summer. We propose that this overall imbalance of the energy-exchange fluxes, as well as the significant difference between mean annual surface and ground temperatures/can be explained by unmeasured advective energy fluxes that occur within the layer of large boulder blocks at the top of the permafrost.

Dynamics and Stability of Towed Flexible Cylinders: Theory and Experiments

2014 ◽  
Author(s):  
Mojtaba Kheiri ◽  
Michael P. Païdoussis ◽  
Marco Amabili
Keyword(s):  
Numerical Solutions ◽  
Integration Method ◽  
Time Integration ◽  
Dynamical Behaviour ◽  
Quantitative Comparison ◽  
Flexible Cylinder ◽  
System Parameters ◽  
Time Integration Method ◽  
Overall Stability ◽  
Theory And Experiments

In this paper, a newly developed nonlinear model is used to predict the dynamical behaviour and stability of a typical towed flexible cylinder. The numerical solutions are obtained via a time-integration method and also via the AUTO software. The effect of some system parameters on the local and overall stability and dynamics of the system is also investigated. Some experiments are then described which were designed to illustrate the dynamical behaviour of towed flexible cylinders and to test the theory. The experimental observations are generally in qualitative agreement with the nonlinear theory. Quantitative comparison of various quantities, e.g. the instability thresholds, between experiment and theory, based on the estimated values of some of the theoretical nondimensional parameters, is also fairly good.

Quantifying urban river–aquifer fluid exchange processes: A multi-scale problem

2007 ◽  
Vol 91 (1-2) ◽  
pp. 58-80 ◽  
Author(s):  
Paul A. Ellis ◽  
Rae Mackay ◽  
Michael O. Rivett
Keyword(s):  
Urban River ◽  
Scale Problem ◽  
Fluid Exchange ◽  
Multi Scale ◽  
Exchange Processes

Gravity Flow of Solids down Vertical Pipes

1969 ◽  
Vol 184 (3) ◽  
pp. 1-6
Author(s):  
I. R. McDougall
Keyword(s):  
Experimental Data ◽  
Pressure Difference ◽  
Theory And Practice ◽  
Air Pressure ◽  
Gravity Flow ◽  
Flow Rates ◽  
System Parameters ◽  
Basic Assumptions ◽  
Particulate Solids

Only a small amount of literature has been published on the gravity flow of particulate solids down pipes. Earlier work showed that in such conditions considerable volumes of air could be entrained with the solids, often resulting in considerable air-pressure difference across the ends of the pipe. A model is developed which makes possible prediction of the pressure differences for known flow rates from system parameters. Considering the rather large number of basic assumptions required and the paucity of experimental data, the agreement between theory and practice is fairly good. The model, however, throws little light on the problem of predicting solids flow rates, emphasizing that further work, both theoretical and experimental, is needed.

Effects of Ambipolar Diffusion on Prominence Thread Models

1994 ◽  
Vol 144 ◽  
pp. 315-321 ◽  
Author(s):  
M. G. Rovira ◽  
J. M. Fontenla ◽  
J.-C. Vial ◽  
P. Gouttebroze
Keyword(s):  
Energy Balance ◽  
Transition Region ◽  
Ambipolar Diffusion ◽  
Line Profiles ◽  
Balance Equations ◽  
Model Calculations ◽  
Partial Frequency ◽  
Frequency Redistribution ◽  
Partial Frequency Redistribution ◽  
Theoretical Structure

AbstractWe have improved previous model calculations of the prominence-corona transition region including the effect of the ambipolar diffusion in the statistical equilibrium and energy balance equations. We show its influence on the different parameters that characterize the resulting prominence theoretical structure. We take into account the effect of the partial frequency redistribution (PRD) in the line profiles and total intensities calculations.

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