Exact Solution of the Multi-layer Skin Bioheat Equation in Cylindrical Coordinates for Thermotherapy with Different Varying Heat Fluxes

2021 ◽  
Author(s):  
Mohamad Hasan Malekmohamadi ◽  
Hossein Ahmadikia ◽  
Mehdi Mosharaf-Dehkordi
Keyword(s):  
Exact Solution ◽  
Heat Fluxes ◽  
Bioheat Equation ◽  
Cylindrical Coordinates

scholarly journals An exact solution of a quasilinear Fisher equation in cylindrical coordinates

2008 ◽  
Vol 69 (12) ◽  
pp. 4803-4805 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
M.T. Mustafa ◽  
F.D. Zaman
Keyword(s):  
Exact Solution ◽  
Fisher Equation ◽  
Cylindrical Coordinates

Laminar convection of a radiating gas in a vertical channel

1971 ◽  
Vol 46 (3) ◽  
pp. 513-520 ◽  
Author(s):  
R. Greif ◽  
I. S. Habib ◽  
J. C. Lin
Keyword(s):  
Exact Solution ◽  
Natural Convection ◽  
Temperature Difference ◽  
Convective Flow ◽  
Vertical Channel ◽  
Heat Fluxes ◽  
Temperature Profiles ◽  
Dimensionless Velocity ◽  
Heated Channel ◽  
Laminar Convection

An exact solution is obtained for the problem of fully-developed, radiating, laminar convective flow in a vertical heated channel. The effect of radiation is to decrease the temperature difference between the gas and the wall, thereby reducing the influence of natural convection. Thus, the reduction in velocity occurring in a heated upflow is less for a radiating gas. Graphs are presented for the dimensionless velocity and temperature profiles and for the volume and heat fluxes.

Heat Transfer in Mini∕Microchannels With Combustion: A Simple Analysis for Application in Nonintrusive IR Diagnostics

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Ananthanarayanan Veeraragavan ◽  
Christopher P. Cadou
Keyword(s):  
Exact Solution ◽  
Temperature Distribution ◽  
Fourth Order ◽  
Heat Fluxes ◽  
Reacting Flow ◽  
Parallel Plates ◽  
Gas Temperature ◽  
Order Polynomial ◽  
Measured Absorption ◽  
Fourth Order Polynomial

An analytical solution for the temperature distribution in 2D laminar reacting flow between closely spaced parallel plates is derived as part of a larger effort to develop a nonintrusive technique for measuring gas temperature distributions in millimeter and submillimeter scale channel flows. The results show that the exact solution, a Fourier series, which is a function of the Peclet number, is approximated by second and fourth order polynomial fits to an R2 value of almost unity for both fits. The slopes of the temperature near the wall (heat fluxes) are captured to within 20% of the exact solution using a second order polynomial and to within 2% of the exact solution using a fourth order polynomial. The fits are used in a nonintrusive Fourier transform infrared spectroscopy technique and enable one to infer the temperature distribution along an absorbing gas column from the measured absorption spectrum. The technique is demonstrated in a silicon-walled microcombustor.

An Exact Solution for Classic Coupled Thermoelasticity in Cylindrical Coordinates

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
M. Jabbari ◽  
H. Dehbani ◽  
M. R. Eslami
Keyword(s):  
Exact Solution ◽  
Heat Source ◽  
Analytical Method ◽  
Loading Condition ◽  
Body Force ◽  
The Body ◽  
Cylindrical Coordinates ◽  
Coupled Thermoelasticity ◽  
Coupled Equations ◽  
Symmetric Loading

In this paper, the classic coupled thermoelasticity model of hollow and solid cylinders under radial-symmetric loading condition (r,t) is considered. A full analytical method is used, and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general forms, where no limiting assumption is used.

scholarly journals The solution of Problems Involving the Melting and Freezing of Finite Slabs by a Method due to Portnov

1964 ◽  
Vol 14 (2) ◽  
pp. 109-128 ◽  
Author(s):  
F. Jackson
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Temperature Distribution ◽  
Heat Fluxes ◽  
Poisson Integral ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Infinite Slab ◽  
The Face ◽  
Steady State Solutions

In a recent paper (1) Portnov used a form of Poisson integral to find the exact solution for the temperature distribution in a freezing semi-infinite slab occupying the region x > 0, and having an arbitrary time dependent temperature applied at the face x = 0. Previously, Boley (2) had used a method based on Duhamel's theorem to find solutions for problems involving melting, in both finite and semi-finite regions, caused by time dependent heat fluxes. Steady-state solutions have been investigated by Landau (3), Masters (4) and others (5).

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