Measurement of Temperature and Heat Flux Changes During the Fixing Process in Electrophotographic Machines

1996 ◽  
Vol 118 (1) ◽  
pp. 150-154 ◽  
Author(s):  
T. Mitsuya ◽  
K. Masuda ◽  
Y. Hori
Keyword(s):  
Heat Flux ◽  
Print Quality ◽  
Two Dimensional ◽  
Temperature Changes ◽  
One Dimensional ◽  
Temperature Heat ◽  
Rapid Temperature ◽  
Pressure Changes ◽  
The Relationship ◽  
Electrophotographic Printing

Increasingly higher speeds of modern electrophotographic printing force examination of the problem of retaining sufficient fixing strength without deterioration of print quality. In the nip region between the two rollers where fixing occurs, the significant parameters are temperature, heat flux, and pressure changes. Their optimization is necessary to maintain both speed and print quality. Difficulty in analyzing the relationship among these parameters occurs because of the complexity of two-dimensional phenomena in a rotating field and the rapidity of changes. Experimental equipment to measure relative heat flux in the nip region during rapid temperature changes was designed. Two sensors are installed in the heat roller. An adiabatic piece is buried under sensor 1. Sensor 2, without an adiabatic piece, detects temperature. Sensor 1 is electrically heated and always at the same temperature as sensor 2. Heat flux changes are obtained by noting the electric power supplied to sensor 1. The equipment was fabricated and measurements were made. They indicate an intermittent two-dimensional heat flux. Because of this, temperature decreases rapidly before the entrance to the nip region. Estimates of two-dimensional effects are made and modified for a one-dimensional case. From them, the temperature field in the nip region for actual fixing conditions is calculated.

scholarly journals Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Qingyue Gu ◽  
Jiwei Xu
Keyword(s):  
Expectation Maximization ◽  
Two Dimensional ◽  
Signal Distribution ◽  
Distributed Source ◽  
One Dimensional ◽  
Least Squares Estimators ◽  
Iterative Calculation ◽  
Symmetric Source ◽  
Relationship Of ◽  
The Relationship

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

Modeling of Mixed Convection Between Vertical Parallel Plates in Electric Equipment Immersed in High-Pr Liquids

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Parallel Plates ◽  
One Dimensional ◽  
Electric Equipment

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.

DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

Transient response of an erodable heat flux gauge using finite element analysis

2002 ◽  
Vol 216 (8) ◽  
pp. 701-706 ◽  
Author(s):  
D R Buttsworth
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Surface Temperature ◽  
Transient Response ◽  
Transient Heat Conduction ◽  
Two Dimensional ◽  
Element Analysis ◽  
Ic Engine ◽  
One Dimensional ◽  
Transient Heat Flux

The transient response of an erodable ribbon element heat flux gauge has been assessed using a two-dimensional finite element (FE) analysis. Such transient heat flux gauges have previously been used for measurements in internal combustion (IC) engines. To identify the heat flux from the measurements of surface temperature, it is commonly assumed that the heat transfer within these devices is one-dimensional. A corollary of the one-dimensional treatment is that only one value of the thermal product, , is needed for identification of the transient heat flux, even though erodable heat flux gauges are constructed from at least two different materials. The current results demonstrate that two-dimensional transient heat conduction effects have a significant influence on the surface temperature measurements made with these devices. For the ribbon element gauge and timescales of interest in IC engine studies, using a one-dimensional analysis (and hence a single value of ) will lead to substantial inaccuracy in the derived heat flux measurements.

Seepage flow in unconfined aquifers

1975 ◽  
Vol 71 (1) ◽  
pp. 181-192 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Flow Rate ◽  
Seepage Flow ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Unconfined Aquifers ◽  
Source Line ◽  
Theory Yield ◽  
The Relationship

The paper concerns one- and two-dimensional models of steady seepage flow in unconfined aquifers and the relationship between them. The first part gives a new proof of Charnyi's result that one- and two-dimensional theory yield the same value for the flow rate in a horizontal aquifer or porous bed between vertical ends and shows the extent to which it can be generalized to non-uniform or anisotropic media. The second part solves the highly two-dimensional problem of flow from a line source (line of springs) in an otherwise impermeable, sloping stratum and compares the result with the predictions of a one-dimensional Dupuit–Pavlovsky approach. Confirmatory experiments using the Hele Shaw analogue of seepage flow are also reported.

Measurement of Heat Flux From Fires

Volume 4 ◽  
2004 ◽  
Author(s):  
Cecilia S. Lam ◽  
Alexander L. Brown ◽  
Elizabeth J. Weckman ◽  
Walter Gill
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Unit Area ◽  
Inverse Heat Conduction ◽  
Thermal Impact ◽  
Temperature Changes ◽  
One Dimensional ◽  
Conduction Heat Transfer ◽  
Flux Measurements

Heat flux is an important parameter for characterization of the thermal impact of a fire on its surroundings. However, heat flux cannot be measured directly because it represents the rate of heat transfer to a unit area of surface. Therefore, most heat flux measurements are based on the measurement of temperature changes at or near the surface of interest [1,2]. Some instruments, such as the Gardon gauge [3] and the thermopile [2], measure the temperature difference between a surface and a heat sink. In radiation-dominated environments, this difference in temperature is often assumed to be linearly related to the incident heat flux. Other sensors measure a surface and/or interior temperature and inverse heat conduction methods frequently must be employed to calculate the corresponding heat flux [1,4]. Typical assumptions include one-dimensional conduction heat transfer and negligible heat loss from the surface. The thermal properties of the gauge materials must be known and, since these properties are functions of temperature, the problem often becomes non-linear.

scholarly journals The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation

2003 ◽  
Vol 2003 (4) ◽  
pp. 173-179 ◽  
Author(s):  
Vladimir V. Kulish ◽  
Vasily B. Novozhilov
Keyword(s):  
Heat Flux ◽  
Energy Transport ◽  
Local Heat ◽  
Local Temperature ◽  
Convolution Integral ◽  
Infinite Domain ◽  
One Dimensional ◽  
Local Heat Flux ◽  
The Relationship ◽  
Hyperbolic Heat Equation

The relationship between the local temperature and the local heat flux has been established for the homogeneous hyperbolic heat equation. This relationship has been written in the form of a convolution integral involving the modified Bessel functions. The scale analysis of the hyperbolic energy equation has been performed and the dimensionless criterion for the mode of energy transport, similar to the Reynolds criterion for the flow regimes, has been proposed. Finally, the integral equation, relating the local temperature and the local heat flux, has been solved numerically for those processes of surface heating whose time scale is of the order of picoseconds.

Multivariate analysis of montmorillonite

Clay Minerals ◽  
1965 ◽  
Vol 6 (1) ◽  
pp. 59-70 ◽  
Author(s):  
J. H. Rayner
Keyword(s):  
Multivariate Analysis ◽  
Similarity Coefficient ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
The Relationship

AbstractVarty & White's application of multivariate analysis to Grim & Kulbicki's measurements on montmorillonites has been re-examined and extended. Inconsistencies between their table of scored data and derived similarity table, and some unexplained errors in the similarity table, have only a small effect on their results. Similarities calculated from Grim & Kulbicki's data, using a different similarity coefficient, lead to a two dimensional representation which separates the groups of montmorillonites more clearly. The groups can be clearly separated even in a one dimensional representation, by changing the relationship between distance and similarity.

scholarly journals One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface

2021 ◽  
Vol 2090 (1) ◽  
pp. 012140
Author(s):  
Hideshi Ishida ◽  
Koichi Higuchi ◽  
Taiki Hirahata
Keyword(s):  
Heat Flux ◽  
Heat Exchanger ◽  
Model Equation ◽  
Computational Time ◽  
Two Dimensional ◽  
Fluid Interface ◽  
Thermal Equation ◽  
Fluid Equation ◽  
One Dimensional ◽  
Dimensional Equation

Abstract In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

Measurement of Straightness for Two-Dimensional Translatory Stage

2010 ◽  
Vol 437 ◽  
pp. 194-197
Author(s):  
Ryoshu Furutani ◽  
Masakazu Watanabe
Keyword(s):  
Laser Interferometer ◽  
Probe Method ◽  
Two Dimensional ◽  
Profile Error ◽  
Reference Mirror ◽  
One Dimensional ◽  
Dimensional Measurement ◽  
Adjustment Error ◽  
Profile Errors ◽  
The Relationship

The large scaled and high accurate 2D-stage is necessary for nanomanufacturing. In order to measure the position of stage, two direction sensors are used. These sensors measure the displacement from the metrological frame. However in nanometer application, as the profile error of metrological frame is comparable with the accuracy of 2D-stage, it is not negligible. Therefore the measuring result includes the displacement of stages and the profile error of metrological frame. So the multi-probe method is applied in one-dimensional measurement to separate the displacement error from the profile error of the metrological frame. In the multi-probe method, the zero adjustment error cannot be removed. So this article proposes a new method which separates the displacement of 2D-stage from the profile errors of the metrological frames in two directions. In this article, as the laser interferometer is used as the sensor, the measuring data is assumed as the shape of the axis of stages mixed with the profile error of the reference mirror in laser interferometer. The relationship during the measuring data, the shape of the axis and the profile error is described. The shape of axis of stage and the profile error of mirror are derived from the measuring result in experiment.

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