Bioheat Numberical problem

Biomedical Heat Transfer

Numerical problem

Due 04/07/16

Budget :20 USD only

Obtain a numerical solution by the method of finite volumes to the heating due to electric current circulation in the block shown in figure below. Solve the thermal problem for cartesian coordinates. The governing equation of the electrical part of this problem is, according to the theory developed in class (equation 2.21):

∇ · ∇(σV ) = 0

or, for cartesian coordinates and a constant electrical conductivity σ

The section to be analyzed has dimensions L =0.1 m by L =0.1 m, and has electrical conductivity σ = 0.188 S/m. The coordinate system is fixed in the upper right corner, as shown in figure. The shaded boundaries are electrically and thermally insulated, while the arrowed boundary represents a uniform current being injected into the section while the temperature there is kept at chilled water temperature. The right and bottom boundaries have a voltage equal to zero and temperatures equal to the basal temperature. The thermal properties of the tissue are k = 0.512 W/m·K, ρ = ρa = 1000kg/m3, C = Ca = 3600 J/kg·K and ω = 0.0005 s−1, and ˙qm=700 W/m3.

The boundary conditions for this electrical problem can be stated as:

V (0,y) = 0 for right face

V (x,L) = 0 for bottom boundary

= 0 for upper insulated boundary

For the left hand side boundary insulated sections

= 0 if y ≤ L/3 or y ≥ 2L/3

For left hand side boundary current injecting section

Amperes if L/3 ≤ y ≤ 2L/3

Use the solution for the electric problem obtained by the method of separation of variables to specify the external heat generation term of Pennes equation, and solve numerically the steady state thermal problem using the method of finite volumes. For the thermal problem the governing equation is Pennes bioheat equation for 2-D steady state cartesian coordinate problems

where the term ˙ql can be taken from the solution to HW 5, by taking

use the following boundary conditions for the thermal problem:

T(0,y) = Ta + q˙m/(ρaωCa) for right face

T(x,L) = Ta + q˙m/(ρaωCa) for bottom boundary

= 0 for upper insulated boundary

For the left hand side boundary insulated sections

= 0 if y ≤ L/3 or y ≥ 2L/3

For left hand side boundary current injecting section

T(0,y) = 5◦C if L/3 ≤ y ≤ 2L/3

Change the current density J leaving from the central part of the left hand side until you find a temperature of 100◦C at some point inside the tissue. Plot your results using matlab contour plots.

For that case, determine the percent of region of tissue where the temperature is above 60◦C.

Figure 1: Geometry of problem is in the attached file

also I'll attach related documents

Habilidades: Biotecnologia, Engenharia Elétrica, Sistemas de aquecimento, Matlab and Mathematica, Engenharia Mecânica

Veja mais: using geometry, problems geometry, problem geometry, point in geometry, part problem, no problem part 1, geometry solve for x, geometry problems, geometry find x, geometry find, geometry 2, find geometry, a point in geometry

Acerca do Empregador:
( 12 comentários ) Erie, United States

ID do Projeto: #10127923

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