Thermal Math Modeling and Analysis of an Electronic Assembly

2000 ◽  
Vol 123 (4) ◽  
pp. 372-378 ◽  
Author(s):  
K. N. Shukla
Keyword(s):  
Temperature Distribution ◽  
Integral Transform ◽  
Three Dimensional ◽  
Thermal Characteristics ◽  
Circuit Board ◽  
Heat Sources ◽  
The Finite Element Method ◽  
Modeling And Analysis ◽  
Discrete Surface ◽  
Integral Transform Technique

This paper presents a mathematical model for a three-dimensional thermal analysis of a circuit board with multiple heat dissipating sources. The model considers the three-dimensional flat plate with discrete surface heat sources and integral transform technique is employed to determine the temperature distribution. The calculation procedure for the thermal characteristics of a circuit board, with surface mounted components, is presented and the solution is compared with those obtained from the finite element method. Also, the temperature distribution of a two-layered circuit board is presented in terms of Green’s function.

scholarly journals Thermoelastic Behavior Inthin Hollow Cylinder using Internal Moving Heat Source

2019 ◽  
Vol 9 (2) ◽  
pp. 2578-2583
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Boundary Conditions ◽  
Hollow Cylinder ◽  
Infinite Series ◽  
Thermal Stresses ◽  
Integral Transform ◽  
Elastic Problem ◽  
Moving Heat Source ◽  
Integral Transform Technique

A hollow cylinder having cylindrical hole at the center has been examined under the temperature variation condition. This composition deals with study of temperature distribution in thin hollow cylinder and corresponding stresses. The author has worked to carry out the transient thermo elastic problem for evaluation of temperature distribution, displacement and thermal stresses of a thin hollow cylinder. The known non homogeneous boundary conditions are applied to obtain the solution of this problem. The integral transform technique yields the solution to the problem. The analysis contains an infinite series. The variation of said parameters observed and analyzed by using necessary graphs

SEMINUMERICAL MODEL TO STUDY TEMPERATURE DISTRIBUTION IN PERIPHERAL LAYERS OF ELLIPTICAL AND TAPERED SHAPED HUMAN LIMBS

2010 ◽  
Vol 10 (01) ◽  
pp. 57-72 ◽  
Author(s):  
MAMTA AGRAWAL ◽  
NEERU ADLAKHA ◽  
KAMALRAJ PARDASANI
Keyword(s):  
Temperature Distribution ◽  
Three Dimensional ◽  
Axial Direction ◽  
Temperature Profiles ◽  
Series Method ◽  
The Finite Element Method ◽  
Biophysical Parameters ◽  
Metabolic Heat ◽  
Metabolic Heat Generation ◽  
Fourier Series Method

In this article, a seminumerical approach has been developed to study temperature distribution in peripheral layers of tapered shaped human limbs, which are elliptical in shape. The model is three-dimensional which incorporates the important biophysical parameters such as blood mass flow rate, thermal conductivity and rate of metabolic heat generation. Appropriate boundary conditions have been framed using biophysical conditions. The finite element method has been employed along radial and angular directions and Fourier series method along axial direction to obtain temperature profiles in the region. The results have been used to study relationships among various physical and physiological parameters. MATLAB 7.0 has been used to simulate the model and obtain numerical results.

scholarly journals ANALYTICAL MODEL OF TEMPERATURE DISTRIBUTION OVER AN ELECTRONIC CIRCUIT BOARD

2003 ◽  
Vol 2 (1) ◽  
Author(s):  
V. V. Vlassov
Keyword(s):  
Temperature Distribution ◽  
Electronic Circuit ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Circuit Board ◽  
Multiple Sources ◽  
Temperature Dependent ◽  
Closed Expression ◽  
Driver Plate ◽  
Steady State Heat

The thermal model of an electronic circuit board with installed heat dissipating components is presented as a two-dimension steady-state heat conduction problem with multiple sources distributed over a rectangular region. The corresponding energy equation includes a source term and a temperature-dependent term to account for linear heat transfer in z-direction. Boundary conditions are of first type with unique temperature along the perimeter. The integral-transform technique is applied to obtain closed-form integral solution. Assuming that all dissipated components have a rectangular contact area with the plate, multiple integrals for each dissipated sub-region are easily found. A temperature map over the board is calculated from the closed expression with a triple sum of series with respect to each coordinate and source. The error is evaluated by the estimation of the truncated terms. The solution was applied to obtain the temperature distribution over the electronic Driver Plate of the CEP block of the CIMEX Brazilian experiment for flight qualifying of the Optical Block Detector Assembling.

scholarly journals Analytical study of the temperature distribution in solids subjected to nonuniform moving heat sources

2013 ◽  
Vol 17 (3) ◽  
pp. 687-694 ◽  
Author(s):  
Mohamed Hamraoui ◽  
Mounir Chbiki ◽  
Najib Laraqi ◽  
Luis Roseiro
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Power Dissipation ◽  
Relative Velocity ◽  
Analytical Study ◽  
Three Dimensional ◽  
Total Power ◽  
Heat Sources ◽  
Reference Case ◽  
Made In

We propose in this paper an analytical study of the temperature distribution in a solid subjected to moving heat sources. The power dissipated by the heat sources is considered nonuniform. The study was made in steady state. The model is three-dimensional. It is valid regardless of the relative velocity of the source. We have considered three cases of semi-elliptic distribution of the power with: (i) the maximum at the center of the source, (ii) the maximum at the inlet of the source, (iii) the maximum at the output of the source. These configurations simulate the conformity imperfection of contact due to wear and / or the non-uniformity of contact pressure in frictional devices. We compare the temperature change for these different scenarios and for different relative velocities, considering the same total power dissipation. The reference case is that of a uniform source dissipating the same power.

scholarly journals ANALYTICAL MODEL OF TEMPERATURE DISTRIBUTION OVER AN ELECTRONIC CIRCUIT BOARD

2003 ◽  
Vol 2 (1) ◽  
pp. 32 ◽  
Author(s):  
V. V. Vlassov
Keyword(s):  
Temperature Distribution ◽  
Electronic Circuit ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Circuit Board ◽  
Multiple Sources ◽  
Temperature Dependent ◽  
Closed Expression ◽  
Driver Plate ◽  
Steady State Heat

The thermal model of an electronic circuit board with installed heat dissipating components is presented as a two-dimension steady-state heat conduction problem with multiple sources distributed over a rectangular region. The corresponding energy equation includes a source term and a temperature-dependent term to account for linear heat transfer in z-direction. Boundary conditions are of first type with unique temperature along the perimeter. The integral-transform technique is applied to obtain closed-form integral solution. Assuming that all dissipated components have a rectangular contact area with the plate, multiple integrals for each dissipated sub-region are easily found. A temperature map over the board is calculated from the closed expression with a triple sum of series with respect to each coordinate and source. The error is evaluated by the estimation of the truncated terms. The solution was applied to obtain the temperature distribution over the electronic Driver Plate of the CEP block of the CIMEX Brazilian experiment for flight qualifying of the Optical Block Detector Assembling.

An Inverse Method for Controlling the Temperature Distribution and Identification of the Conductivity of Thick Cylindrical Shells

2011 ◽  
Author(s):  
Hossein Rastgoftar ◽  
Faissal A. Moslehy
Keyword(s):  
Temperature Distribution ◽  
Heat Conduction Equation ◽  
Inverse Method ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Heat Diffusion ◽  
The Finite Element Method ◽  
Steady State Heat ◽  
Boundary Surfaces

The paper presents an inverse method for control of temperature distribution in thick cylindrical shells. Since the thickness is large enough, three-dimensional heat diffusion equations must be considered. To control the temperature distribution, the heat fluxes at the boundary surfaces of the cylindrical shell are assigned values such that the desired temperature distribution, which satisfies the steady state heat conduction equation, will be achieved. Furthermore, a Lyapunov-based method for identification of the conductivity of the cylinder is presented, and the estimated conductivity is updated such that it converges to the exact value. The numerical results are obtained by the finite element method (FEM), which include the heat flux at the surfaces of the cylinder. These results are shown to be in excellent agreement with the analytical solution.

Integral Transforms for Three-Dimensional Steady Turbulent Dispersion in Rivers and Channels

2005 ◽  
Author(s):  
Felipe P. J. de Barros ◽  
Renato M. Cotta
Keyword(s):  
Turbulent Flows ◽  
Integral Transform ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Computational Effort ◽  
Velocity Fields ◽  
Turbulent Dispersion ◽  
Test Case ◽  
Solution Convergence ◽  
Integral Transform Technique

A three-dimensional steady-state mathematical model is considered for predicting the fate of dissolved contaminants in rivers and channels under turbulent flows. The model allows for variable velocity fields and non-uniform turbulent diffusivities. Making use of the Generalized Integral Transform Technique (GITT), a hybrid numerical-analytical solution is then obtained. The solution convergence behavior is investigated and the criterion for reordering the terms in the infinite series is discussed, with the aim of reducing the computational effort associated with the double eigenfunction expansion. A test case is presented to illustrate the proposed approach.

scholarly journals Three-Dimensional Unsteady State Temperature Distribution of Thin Rectangular Plate with Moving Point Heat Source

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yogita M. Ahire ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Heat Source ◽  
Rectangular Plate ◽  
Thermal Stresses ◽  
Integral Transform ◽  
Three Dimensional ◽  
Unsteady State ◽  
Point Heat Source ◽  
Thin Rectangular Plate ◽  
Special Case ◽  
Integral Transform Technique

This paper deals with the study of thermal stresses in thin rectangular plate subjected to point heat source which changes its place along x-axis. Governing heat conduction equation has been solved by using integral transform technique. Results are obtained in the form of infinite series. As a special case, aluminum plate has been considered and results for thermal stresses have been computed numerically and graphically.

Analytical Solution for Temperature Distribution in Microwave Heating of Rectangular Objects

2011 ◽  
Author(s):  
Mohammad Robiul Hossan ◽  
Prashanta Dutta
Keyword(s):  
Dielectric Properties ◽  
Temperature Distribution ◽  
Microwave Heating ◽  
Processing Time ◽  
Integral Transform ◽  
Three Dimensional ◽  
Sample Thickness ◽  
Microwave Source ◽  
Salmon Fillet ◽  
Close Form

Microwave heating is extremely popular as a household method for warming up foodstuffs quickly. However the industrial application of this convenient, pollution free heating technique is very limited because of its non-uniform temperature distribution with hot and cold spots. The temperature distribution in microwave heating depends on the electromagnetic frequency, processing time, size and shape, and dielectric properties of the object being heated. In this paper, we present a close form analytic solution for temperature distribution in a three dimensional rectangular block under microwave processing. With the knowledge of electric field distribution from Maxwell’s equation, a three dimensional, unsteady, non-homogenous energy equation containing a microwave source term is solved by the integral transform technique. The effects of various parameters such as sample thickness, electromagnetic frequencies, dielectric properties, and processing time are studied for a salmon fillet. The results indicate that the proper integration of incident frequencies, dielectric properties, sample thickness and processing time could provide homogenous temperature distribution in a salmon fillet under microwave heating.

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