scholarly journals Determination of a spacewise dependent heat source

2007 ◽  
Vol 209 (1) ◽  
pp. 66-80 ◽  
Author(s):  
Tomas Johansson ◽  
Daniel Lesnic
Keyword(s):  
Heat Source

An analytical approach of heat transfer modelling with thermal stresses in circular plate by means of Gaussian heat source and stress function

2021 ◽  
Author(s):  
Sangita Pimpare ◽  
Chandrashekhar Shalik Sutar ◽  
Kamini Chaudhari
Keyword(s):  
Boundary Condition ◽  
Heat Source ◽  
Circular Plate ◽  
Thermal Stresses ◽  
Research Work ◽  
Homogeneous Boundary Condition ◽  
Flux Boundary Condition ◽  
Differential Transform ◽  
The Mathematical Model

Abstract In the proposed research work we have used the Gaussian circular heat source. This heat source is applied with the heat flux boundary condition along the thickness of a circular plate with a nite radius. The research work also deals with the formulation of unsteady-state heat conduction problems along with homogeneous initial and non-homogeneous boundary condition around the temperature distribution in the circular plate. The mathematical model of thermoelasticity with the determination of thermal stresses and displacement has been studied in the present work. The new analytical method, Reduced Differential Transform has been used to obtain the solution. The numerical results are shown graphically with the help of mathematical software SCILAB and results are carried out for the material copper.

scholarly journals Determination of a time-dependent heat source under not strengthened regular boundary and integral overdetermination conditions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 809-814 ◽  
Author(s):  
Makhmud Sadybekov ◽  
Gulaiym Oralsyn ◽  
Mansur Ismailov
Keyword(s):  
Inverse Problem ◽  
Heat Source ◽  
Input Data ◽  
Nonlocal Boundary ◽  
Fourier Method ◽  
Time Dependent ◽  
Regular Boundary ◽  
Associated Functions ◽  
Integral Overdetermination

We investigate an inverse problem of finding a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is not complete. But the system of eigen- and associated functions forming a basis. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method.

Heat Generation in Laser Irradiated Tissue

1989 ◽  
Vol 111 (1) ◽  
pp. 62-68 ◽  
Author(s):  
A. J. Welch ◽  
J. A. Pearce ◽  
K. R. Diller ◽  
G. Yoon ◽  
W. F. Cheong
Keyword(s):  
Heat Source ◽  
Heat Generation ◽  
Near Infrared ◽  
Scattered Light ◽  
Incident Beam ◽  
Accurate Estimation ◽  
Optical Parameters ◽  
Infrared Wavelengths ◽  
Improved Model

Many medical applications involving lasers rely upon the generation of heat within the tissue for the desired therapeutic effect. Determination of the absorbed light energy in tissue is difficult in many cases. Although UV wavelengths of the excimer laser and 10.6 μm wavelength of the CO2 laser are absorbed within the first 20 μm of soft tissue, visible and near infrared wavelengths are scattered as well as absorbed. Typically, multiple scattering is a significant factor in the distribution of light in tissue and the resulting heat source term. An improved model is presented for estimating heat generation due to the absorption of a collimated (axisymmetric) laser beam and scattered light at each point r and z in tissue. Heat generated within tissue is a function of the laser power, the shape and size of the incident beam and the optical properties of the tissue at the irradiation wavelength. Key to the calculation of heat source strength is accurate estimation of the light distribution. Methods for experimentally determining the optical parameters of tissue are discussed in the context of the improved model.

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