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Analytical analysis of the dual-phase-lag model of bioheat transfer equation during transient heating of skin tissue

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Abstract

Dual-phase-lag model of bioheat transfer equation is utilized in treating the transient heat transfer problems in skin tissue considering prevalent heating conditions in thermal therapy applications, namely, pulse train and periodic heat flux. Comparisons between the presented analytical results for limiting cases and previous studies display an excellent agreement. The effects of temperature gradient relaxation time on the tissue temperature, damage, and also on the blood perfusion in skin tissue are studied.

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Abbreviations

A 0 :

Frequency factor (s−1)

c :

Specific heat of tissue (J kg−1 K−1)

c b :

Specific heat of blood (J kg−1 K−1)

C :

Thermal wave speed (m s−1)

E a :

Activation energy of denaturation reaction (J mol−1)

k :

Tissue thermal conductivity (W m−1 K−1)

l :

Bromwich contour integration line

L :

Tissue slab length (m)

q :

Heat flux density (W m−2)

q 0 :

Incident heat flux amplitude (W m−2)

Q m :

Metabolic heat generation (W m−3)

R :

Universal gas constant (J mol−1 K−1)

s :

Laplace domain parameter

t :

Time variable (s)

T :

Tissue temperature (°C)

T 0 :

Initial tissue temperature (°C)

T b :

Blood temperature (°C)

U :

Unit Step function

w b :

Blood perfusion rate (s−1)

x :

Coordinate variable (m)

α:

Tissue thermal diffusivity (m2 s−1)

Γ :

Dimensionless temperature gradient relaxation time (Eq. 11)

Γ i :

Dimensionless incident heat flux exposure time

θ :

Dimensionless tissue temperature

Λ :

Dimensionless heat flux relaxation time (Eq. 11)

Λ 0 :

Dimensionless blood perfusion rate

λ :

Eigenvalues

ξ :

Dimensionless coordinate

ξ L :

Dimensionless tissue slab length

ρ :

Tissue mass density (kg m−3)

ρ b :

Blood mass density (kg m−3)

τ i :

Duration time of pulse train heat flux (s)

τ q :

Heat flux relaxation time (s)

τ T :

Temperature gradient relaxation time (s)

τ 1 :

Dimensionless heat flux relaxation time (Eq. 28)

τ2 :

Dimensionless temperature gradient relaxation time (Eq. 28)

φ :

Dimensionless metabolic heat generation (Eq. 28)

ψ :

Dimensionless metabolic heat generation (Eq. 11)

ω :

Incident heat flux frequency (s−1)

Ω :

Damage parameter

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Isfahan, 81746-73441, Isfahan, Iran

    Hossein Askarizadeh & Hossein Ahmadikia

Authors
  1. Hossein Askarizadeh
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  2. Hossein Ahmadikia
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Correspondence to Hossein Ahmadikia.

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Askarizadeh, H., Ahmadikia, H. Analytical analysis of the dual-phase-lag model of bioheat transfer equation during transient heating of skin tissue. Heat Mass Transfer 50, 1673–1684 (2014). https://doi.org/10.1007/s00231-014-1373-6

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