Nonlinear effects of variable conductivities in thermistor-related problems: an explicit example

1990 ◽  
Vol 1 (3) ◽  
pp. 245-257
Author(s):  
J. H. Young ◽  
G. Tenti
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Distribution ◽  
Surface Temperature ◽  
Nonlinear Partial Differential Equations ◽  
Electrical Potential ◽  
Nonlinear Effects ◽  
Electrical Current ◽  
Electrical Heating ◽  
One Dimensional

The coupled nonlinear partial differential equations obeyed by the electrical potential and temperature distribution for a medium undergoing steady state electrical heating are applied to a one-dimensional rod having its surface temperature held constant as current is conducted along its length due to a potential difference maintained between its ends. Extension is given to the previously discussed class of solutions by the inclusion of a thermal conductivity which varies linearly with temperature. The resulting electrical current and resistance are found to be significantly influenced by the thermal conductivity of the medium. Molybdenum is identified as a material exemplifying such a thermal conductivity and the general effects are then numerically illustrated.

Quasi-Steady-State Temperature Distribution in Periodically Contacting Finite Regions

1981 ◽  
Vol 103 (4) ◽  
pp. 739-744 ◽  
Author(s):  
B. Vick ◽  
M. N. O¨zis¸ik
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Distribution ◽  
Interface Temperature ◽  
Quasi Steady State ◽  
Exact Analytical Solutions ◽  
One Dimensional ◽  
Steady State Temperature ◽  
Regular Cycle

Heat transfer across two surfaces which make and break contact periodically according to a continuous regular cycle is investigated theoretically and exact analytical solutions are developed for the quasi-steady-state temperature distribution for a two-region, one-dimensional, periodically contacting model. The effects of the Biot number, the thermal conductivity and thermal diffusivity of the materials and the duration of contact and break periods on the interface temperature and the temperature distribution within the solids are illustrated with representative temperature charts.

scholarly journals A one-dimensional spot welding model

2006 ◽  
Vol 2006 ◽  
pp. 1-24 ◽  
Author(s):  
K. T. Andrews ◽  
L. Guessous ◽  
S. Nassar ◽  
S. V. Putta ◽  
M. Shillor
Keyword(s):  
Thermal Conductivity ◽  
Spot Welding ◽  
Electrical Potential ◽  
Dissimilar Materials ◽  
Electrical Heating ◽  
Large Temperature ◽  
Dimensional Model ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Welding Processes

A one-dimensional model is proposed for the simulations of resistance spot welding, which is a common industrial method used to join metallic plates by electrical heating. The model consists of the Stefan problem, in enthalpy form, coupled with the equation of charge conservation for the electrical potential. The temperature dependence of the density, thermal conductivity, specific heat, and electrical conductivity are taken into account, since the process generally involves a large temperature range, on the order of 1000 K. The model is general enough to allow for the welding of plates of different thicknesses or dissimilar materials and to account for variations in the Joule heating through the material thickness due to the dependence of electrical resistivity on the temperature. A novel feature in the model is the inclusion of the effects of interface resistance between the plates which is also assumed to be temperature dependent. In addition to constructing the model, a finite difference scheme for its numerical approximations is described, and representative computer simulations are depicted. These describe welding processes involving different interface resistances, different thicknesses, different materials, and different voltage forms. The differences in the process due to AC or DC currents are depicted as well.

Steady-State Investigation of Vapor Deposited Micro Heat Pipe Arrays

1995 ◽  
Vol 117 (1) ◽  
pp. 75-81 ◽  
Author(s):  
A. K. Mallik ◽  
G. P. Peterson
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Surface Temperature ◽  
Heat Pipe ◽  
Effective Thermal Conductivity ◽  
Heat Pipes ◽  
Temperature Gradients ◽  
Bottom Surface ◽  
Micro Heat Pipe ◽  
Micro Heat Pipes

An experimental investigation of vapor deposited micro heat pipe arrays was conducted using arrays of 34 and 66 micro heat pipes occupying 0.75 and 1.45 percent of the cross-sectional area, respectively. The performance of wafers containing the arrays was compared with that of a plain silicon wafer. All of the wafers had 8 × 8 mm thermofoil heaters located on the bottom surface to simulate the active devices in an actual application. The temperature distributions across the wafers were obtained using a Hughes Probeye TVS Infrared Thermal Imaging System and a standard VHS video recorder. For wafers containing arrays of 34 vapor deposited micro heat pipes, the steady-state experimental data indicated a reduction in the maximum surface temperature and temperature gradients of 24.4 and 27.4 percent, respectively, coupled with an improvement in the effective thermal conductivity of 41.7 percent. For wafers containing arrays of 66 vapor deposited micro heat pipes, the corresponding reductions in the surface temperature and temperature gradients were 29.0 and 41.7 percent, respectively, and the effective thermal conductivity increased 47.1 percent, for input heat fluxes of 4.70 W/cm2. The experimental results were compared with the results of a previously developed numerical model, which was shown to predict the temperature distribution with a high degree of accuracy, for wafers both with and without the heat pipe arrays.

scholarly journals Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. M. Hamza ◽  
I. G. Usman ◽  
A. Sule
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Approximate Solutions ◽  
Variable Thermal Conductivity ◽  
Convection Flow

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

scholarly journals The Technology of Calculating the Optimal Modes of the Disk Heating (Ball)

2019 ◽  
Vol 5 (6) ◽  
pp. 1395-1406 ◽  
Author(s):  
Yury Alexandrovich Kostikov ◽  
Alexander Mikhailovich Romanenkov
Keyword(s):  
Thermal Conductivity ◽  
Optimal Control ◽  
Temperature Distribution ◽  
Heat Conduction Problem ◽  
Type Equation ◽  
Difference Approximation ◽  
Quadratic Functional ◽  
Differential Problem ◽  
Parabolic Boundary ◽  
One Dimensional

The paper considers the problem of optimal control of the process of thermal conductivity of a homogeneous disk (ball). An optimization problem is posed for a one-dimensional parabolic type equation with a mixed-type boundary condition. The goal of the control is to bring the temperature distribution in the disk (ball) to a given distribution in a finite time. To solve this problem, an algorithm is proposed that is based on the gradient method. The object of the study is the optimal control problem for a parabolic boundary value problem. Using the discretization of the original continuous differential problem, difference equations are obtained for which a numerical solution algorithm is proposed. Difference approximation of a differential problem is performed using an implicit scheme, which allows to increase the speed of calculations and provides the specified accuracy of calculation for a smaller number of iterations. An approximate solution of a parabolic equation is constructed using the one-dimensional sweep method. Using differentiation of the functional, an expression for the gradient of the objective functional is obtained. In this paper, it was possible to reduce the multidimensional heat conduction problem to a one-dimensional one, due to the assumption that the desired solution is symmetric. A formula is obtained for calculating the variation of a quadratic functional that characterizes the deviation of the current temperature distribution from the given one. The flowcharts and implementations of the algorithm are presented in the form of Matlab scripts, which clearly demonstrate the process of thermal conductivity and show the computation and application of optimal control in dynamics.

scholarly journals Thermal conductivity of porous ice in hailstone shells

1996 ◽  
Vol 42 (141) ◽  
pp. 195-200
Author(s):  
Guoguang Zheng ◽  
Roland List
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Distribution ◽  
Surface Temperature ◽  
Linear Dependence ◽  
Internal Heat ◽  
Density Range ◽  
Surface Temperature Distribution ◽  
Temperature Distributions ◽  
Evolving Surface

AbstractThe thermal conductivity and diffusivity of porous ice accreted on spherical and spheroidal hailstone models were measured over a density range of 620–915 kg m−3. By scanning the evolving surface temperature distributions during cooling in a cold airflow the thermal conductivity was varied in iterative fashion until the internal heat flux produced the correct surface temperature distribution. The results indicate a linear dependence of the thermal conductivity,ki, and diffusivity,αi, on density. For example, lowering the density by 10% lowerskiby 15%. Within the range of cloud conditions, the density variations affect the thermal parameters more than temperature does. The results also indicate a continuous decrease of the thermal conductivity from bulk ice via consolidated porous ice to loosely packed snow.

Air Temperature Distribution Inside of a Longitudinal Highway Tunnel: A Case Study

2012 ◽  
Vol 433-440 ◽  
pp. 6384-6389 ◽  
Author(s):  
Xing Han ◽  
Xu Zhang
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Air Temperature ◽  
State Theory ◽  
One Dimensional ◽  
Highway Tunnel ◽  
Temperature Enhancement ◽  
The One ◽  
General Method

With the development of tunneling technology and the increase of transportation, the mobiles are discharging more and more heat into the tunnel nowadays, which will cause the temperature enhancement. In this paper, general method of calculating the heat discharge is studied, and temperature distribution in the tunnels, which use different ventilation systems, is studied according to the one-dimensional steady state theory. One tunnel is taken for example to calculate the temperature distribution. The result can b e used in the relevant design and research.

Modelling of CW Laser Annealing of Multilayer Structures

1981 ◽  
Vol 4 ◽  
Author(s):  
I.D. Calder ◽  
R. Sue ◽  
Emad-Eldin A.A. Aly
Keyword(s):  
Phase Transition ◽  
Thermal Conductivity ◽  
Optical Properties ◽  
Steady State ◽  
Temperature Distribution ◽  
Thermal Model ◽  
Laser Annealing ◽  
Multilayer Structures ◽  
Cw Laser ◽  
Arbitrary Thickness

ABSTRACTA thermal model is developed for cw laser annealing of multilayer structures. Each layer has arbitrary thickness, thermal conductivity and optical properties. Steady state conditions with no phase transition are assumed. A procedure is presented for obtaining the temperature distribution in any system and explicit integral expressions are developed for the two and three layer cases. Results are calculated for the Si/glass and Si/SiO2 /Si systems.

scholarly journals On the thermal conductivity of some metal wires

1931 ◽  
Vol 131 (817) ◽  
pp. 320-335 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Thermal Conduction ◽  
Surrounding Medium ◽  
Electrical Current ◽  
Thermal Method ◽  
Electrical Method ◽  
Critical Account ◽  
The One ◽  
Metal Wires

The methods of investigating thermal conduction in metals and allots in which the steady state is employed fall into two groups (1) thermal, (2) electrical. In a previous paper use was made of the thermal method of which a brief critical account was given in that paper. In the present investigation the electrical method has been used. All the variants of this method employ a thin uniform cylinder headed by passing a steady electrical current through it, both ends of the cylinder being kept at the one constant temperature, that of the surrounding medium. The electrical method has several advantages:— ( a ) It is available for use with metals obtainable only in the form of a wire.

THE THERMAL CONDUCTIVITY OF SELECTED TROPICAL TIMBER SPECIES USING HOT BOX METHOD

2016 ◽  
Vol 78 (5-4) ◽  
Author(s):  
Raihana Mohamad Hata ◽  
Rohana Hassan ◽  
Haslin Idayu ◽  
Fadzil Arshad
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Steady State ◽  
Surface Temperature ◽  
Air Temperature ◽  
Timber Species ◽  
Steady State Condition ◽  
Tropical Timber ◽  
Box Method ◽  
Cold Chamber

In this study, thermal conductivity of selected tropical timber species was determined using hot box method. The test was conducted up until the heat flux, air temperature and surface temperature value at hot and cold chamber of hot box become constant. Each of the selected timber species represent hardwood and softwood as classified in MS 544: Part 2:2011. For this purpose, Chengal (Neobalanocarpus heimii – Dipteracarpaceae), Perupok (Lophopetalum spp. Celastraceae) Nyatoh (Sapotaceae) and Pulai (Alstonia spp. Apocynaceae) were tested. The thermal conductivity test was carried out based on BS EN ISO 8990:1996 standard. The thermal conductivity for Chengal, Perupok, Nyatoh and Pulai under steady state condition are 5.71 x 10-4, 3.595 x 10-4, 2.973 x 10-4 and 3.469 x 10-4 W/m2K respectively. Higher thermal conductivity value is significant with high density of materials.

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