NUMERICAL SIMULATION OF THE HEAT CONDUCTION IN ELECTRICAL CABLES

2007 ◽  
Vol 12 (4) ◽  
pp. 425-439 ◽  
Author(s):  
Raimondas Čiegis ◽  
Audrius Ilgevičius ◽  
Heinz Liess ◽  
Mečislavas Meilūnas ◽  
Olga Suboč
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Mathematical Models ◽  
Radiation Effects ◽  
Mathematical Problem ◽  
Quantitative Description ◽  
Numerical Algorithms ◽  
Mobile Systems ◽  
Wire Conductor ◽  
Electrical Cables

The modelling of the heat conduction in electrical cables is a complex mathematical problem. To get a quantitative description of the thermo‐electrical characteristics in the electrical cables, one requires a mathematical model for it. It must involve the different physical phenomena occurring in the electrical cables, i.e. heat conduction, convection and radiation effects, description of heat sources due to current transitions. Since the space in mobile systems is limited and weight is always reduced, wire conductor sizes must be kept as small as possible. Thus the main aim is to determine optimal conductor cross‐sections for long standing loads. In this paper we develop and validate a set of mathematical models and numerical algorithms for the heat transfer simulation in cable bundles. The numerical algorithms are targeted to the two‐dimensional transient heat transfer mathematical models. Finally, a validation procedure for the coefficient validation of the differential equations is carried out. Results of numerical experiments are presented.

scholarly journals Modeling granular materials as compressible nonlinear fluids: Heat transfer boundary value problems

2006 ◽  
Vol 2006 ◽  
pp. 1-31 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Tran X. Phuoc
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Value Problems ◽  
Granular Materials ◽  
Radiation Effects ◽  
Boundary Value ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Flat Plates ◽  
Dimensionless Numbers

We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.

scholarly journals MATHEMATICAL MODELLING IN ELECTRICAL ENGINEERING

2005 ◽  
Vol 10 (3) ◽  
pp. 257-274
Author(s):  
L. Hacia
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Integral Equations ◽  
Current Density ◽  
Radiative Heat ◽  
Electrical Engineering ◽  
Fredholm Integral Equations ◽  
Conduction Theory

Various problems of electrical engineering lead to mathematical models being difference, differential or integral equations. In this paper some mathematical models in certain problems of electrical engineering are presented. Our considerations are restricted to the radiative heat transfer and density theory (Fredholm integral equations). Respecting time in current density problems we get integro‐differential equations or generally Volterra‐Predholm integral equations (heat‐conduction theory). The new numerical method for these equations is analysed. Daugelio elektros inžinerijos problemu sprendimui tenka sudaryti matematinius modelius, kurie dažniausiai būna aprašomi skirtuminemis, diferencialinemis ar integralinemis lygtimis. Šiame darbe apžvelgiami kai kurie modeliai, skirti konkrečiu elektros inžinerijos uždaviniu sprendimui. Apsiribojama šilumos perdavimo proceso su spinduliuote modeliavimu ir tankio pasiskirstymo teorija (Predholmo integralines lygtys) .Ivedus laika, lygtys tankiui tampa integr‐diferencialinemis arba Volteros‐Predholmo integralinemis lygtimis. Darbe pateikiamas ir nagrinejamas naujas skaitinis tokiu lygčiu sprendimo metodas.

scholarly journals The Single-Blow Problem Including the Effects of Longitudinal Conduction

1964 ◽  
Author(s):  
C. P. Howard
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Conduction ◽  
Transient Behavior ◽  
Step Change ◽  
Graphical Form ◽  
Compact Heat Exchanger ◽  
Fluid Temperature ◽  
Transfer Data ◽  
Method Of Calculation

The results are presented from a numerical finite-difference method of calculation for the transient behavior of porous media when subjected to a step change in fluid temperature considering the case where the longitudinal thermal heat conduction cannot be neglected. These results, given in tabular and graphical form, provide a useful means for evaluating the heat-transfer data obtained from the transient testing of compact heat-exchanger surfaces.

scholarly journals Effects of radiative heat transfer on the structure of turbulent supersonic channel flow

2011 ◽  
Vol 677 ◽  
pp. 417-444 ◽  
Author(s):  
S. GHOSH ◽  
R. FRIEDRICH ◽  
M. PFITZNER ◽  
CHR. STEMMER ◽  
B. CUENOT ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Radiation ◽  
Radiative Heat Transfer ◽  
Radiation Effects ◽  
Radiative Heat ◽  
Pure Water ◽  
Molecular Transport ◽  
Working Fluid ◽  
Mean Flow ◽  
Total Energy Balance

The interaction between turbulence in a minimal supersonic channel and radiative heat transfer is studied using large-eddy simulation. The working fluid is pure water vapour with temperature-dependent specific heats and molecular transport coefficients. Its line spectra properties are represented with a statistical narrow-band correlated-k model. A grey gas model is also tested. The parallel no-slip channel walls are treated as black surfaces concerning thermal radiation and are kept at a constant temperature of 1000 K. Simulations have been performed for different optical thicknesses (based on the Planck mean absorption coefficient) and different Mach numbers. Results for the mean flow variables, Reynolds stresses and certain terms of their transport equations indicate that thermal radiation effects counteract compressibility (Mach number) effects. An analysis of the total energy balance reveals the importance of radiative heat transfer, compared to the turbulent and mean molecular heat transport.

The heat/mass transfer to a finite strip at small Péclet numbers

1978 ◽  
Vol 86 (1) ◽  
pp. 49-65 ◽  
Author(s):  
R. C. Ackerberg ◽  
R. D. Patel ◽  
S. K. Gupta
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Shear Flow ◽  
Sodium Hydroxide Solution ◽  
Flow Direction ◽  
Mathematical Problem ◽  
Limiting Current ◽  
Transfer Rates ◽  
Uniform Shear ◽  
Uniform Shear Flow

The problem of heat transfer (or mass transfer at low transfer rates) to a strip of finite length in a uniform shear flow is considered. For small values of the Péclet number (based on wall shear rate and strip length), diffusion in the flow direction cannot be neglected as in the classical Leveque solution. The mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat-transfer rate from the strip are found. Experimental data on wall mass-transfer rates in a tube at small Péclet numbers have been obtained by the well-known limiting-current method using potassium ferrocyanide and potassium ferricyanide in sodium hydroxide solution. The Schmidt number is large, so that a uniform shear flow can be assumed near the wall. Experimental results are compared with our theoretical predictions and the work of others, and the agreement is found to be excellent.

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