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ABSTRACT
Thermal analysis of tissue phantoms subjected to short pulse laser irradiation has been presented. The transient radiative transfer equation (RTE) has been solved using a novel separation of variables-based discrete transfer method (DTM) recently developed by the present authors (Nirgudkar et al. [Citation21]). As an advancement, the solution of RTE has been coupled with Pennes’ bioheat transfer equation for determining the temperature distribution. Homogenous as well as phantoms embedded with optical inhomogeneity have been considered. The numerical model has been verified against the results available in the literature. This study clearly reveals the influence of the nature of the embedded inhomogeneity and its relative contrast on the resultant temperature distribution inside the body of the tissue phantom.
Nomenclature
| a | = | anisotropy factor |
| c | = | velocity of light in medium |
| Cv | = | specific heat |
| G | = | incident intensity |
| I | = | intensity |
| k | = | thermal conductivity |
| M | = | number of discrete directions |
| = | unit vector normal to the surface | |
| p | = | scattering phase function |
| q | = | heat flux |
| s | = | distance travelled by beam |
| = | unit vector in s direction | |
| t | = | time |
| T | = | temperature |
| tp | = | pulse width of laser |
| Greek symbols | = | |
| σs | = | Stefan-Boltzmann's constant |
| β | = | extinction coefficient |
| ∈ | = | emissivity |
| θ, ϕ | = | polar and azimuthal angle |
| κ | = | absorption coefficient |
| μ, ζ | = | Direction cosines in x and y direction |
| ρ | = | density |
| σ | = | scattering coefficient |
| τ | = | optical thickness |
| Ω | = | solid angle |
| ω | = | scattering albedo |
| ωb | = | blood perfusion rate |
| Subscripts | = | |
| 0 | = | reference or incident value |
| av | = | average |
| b | = | blood/black body |
| c | = | collimated |
| d | = | diffused |
| w | = | wall |
| Superscripts | = | |
| D | = | downstream |
| m | = | index for a discrete direction |
| U | = | upstream |
| * | = | non-dimensional parameter |
Nomenclature
| a | = | anisotropy factor |
| c | = | velocity of light in medium |
| Cv | = | specific heat |
| G | = | incident intensity |
| I | = | intensity |
| k | = | thermal conductivity |
| M | = | number of discrete directions |
| = | unit vector normal to the surface | |
| p | = | scattering phase function |
| q | = | heat flux |
| s | = | distance travelled by beam |
| = | unit vector in s direction | |
| t | = | time |
| T | = | temperature |
| tp | = | pulse width of laser |
| Greek symbols | = | |
| σs | = | Stefan-Boltzmann's constant |
| β | = | extinction coefficient |
| ∈ | = | emissivity |
| θ, ϕ | = | polar and azimuthal angle |
| κ | = | absorption coefficient |
| μ, ζ | = | Direction cosines in x and y direction |
| ρ | = | density |
| σ | = | scattering coefficient |
| τ | = | optical thickness |
| Ω | = | solid angle |
| ω | = | scattering albedo |
| ωb | = | blood perfusion rate |
| Subscripts | = | |
| 0 | = | reference or incident value |
| av | = | average |
| b | = | blood/black body |
| c | = | collimated |
| d | = | diffused |
| w | = | wall |
| Superscripts | = | |
| D | = | downstream |
| m | = | index for a discrete direction |
| U | = | upstream |
| * | = | non-dimensional parameter |
