A. Lakhssassi et al. / Natural Science 2 (2010) 131-138

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138

depth-dependent thermal conductivity (plots (2)).

3.2. Effect of Surface Heating

The effects of surface heating (when the surface of the

living tissue is maintained at different constant tempera-

ture) on the temperature distribution and on the location

of the peak temperature have been studies and observed

when the initial temperature is either a decreasing func-

tion of depth

(Figure 5(a) and (b)) or an increasing

function of depth

(Figure 5(c) and (d)). The plots

of this figure are obtained with 1/ 4200000

and

(, )(0.005,0.02).

Figure 5(a) gives the depth at

which the temperature peak occurs at a given time while

Figure 5(b) gives the time at which the temperature peak

at a given depth occurs. Figure 5(a) shows that the tem-

perature peak does not depend on the surface tempera-

ture. These two plots also show that the magnitude of

peak temperature does not depend on the surface tem-

perature: the magnitude of peak temperature is the same

for all three surface temperatures. As we can see from

Figures 5(c) and (d), the depth (Figure 5(c) and the

time (Figure 5(d) from which the variation of the tem-

perature suddenly changes do not depend on the surface

temperature. Many other information about the tempera-

ture distribution in the living tissue can be obtained from

Figure 5. For example, it is seen from plots (a) and (b)

that the width of the peak temperature increases with the

surface temperature: the higher the surface temperature is,

the higher is the width of the peak temperature.

4. CONCLUSIONS

In this work, we present a numerical investigation of a

1D bioheat transfer equation with either depth-dependent

or temperature-dependent thermal conductivity and with

temperature-dependent blood perfusion. An implicit un-

conditional numerical scheme of the Crank-Nicholson

type is constructed and used to solve the nonlinear bio-

heat transfer equation with given initial and boundary

conditions. We found that blood perfusion decreases the

temperature in living tissue. It is also shown that the lo-

calization and the magnitude of peak temperature do not

depend on the surface temperature, while its width in-

creases with surface temperature. The computation pre-

sented in this paper can be used to predict the tempera-

ture distribution in living tissue during many bioheat

transfer processes. The method used in this paper has

potential to provide the temperature distribution in tissue

in the absent of heat flux.

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