A study for multi-layer skin burn injuries based on DPL bioheat model
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A study for multi‑layer skin burn injuries based on DPL bioheat model Rajneesh Kumar Chaudhary1 · Kabindra Nath Rai2 · Jitendra Singh1 Received: 19 August 2019 / Accepted: 15 June 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract In this paper, multi-layer skin burn injuries are studied using the DPL bioheat model when skin surface is subjected to different non-Fourier boundary conditions. A skin made of three layers known as epidermis, dermis, and subcutaneous layer. These layers assumed to be homogeneous and each layer studied separately. The metabolic heat varies linearly with temperature. The diffusion and evaporation of water in the multi-layer of skin increases heat loss in the skin layer. To solve the BVP of hyperbolic PDE, the FELWG method has been used. The whole analysis presented in a non-dimensional form and the results are shown graphically. In a particular case, the result obtained is compared with the exact solution and is in good agreement. The effects of relaxation time, layer thickness, different temperature, and non-Fourier boundary condition are analyzed at the temperature of the tissue related to the burning of the skin, and the three layers are discussed in detail. Keywords Dual-phase lagging (DPL) · Finite element Legendre wavelet Galerkin method (FELWGM) · Generalized nonFourier boundary condition · Multi-layer skin burn List of symbols cρ Specific heat/J kg−1 ◦C−1 k Thermal conductivity/W m−1 ◦C−1 t Time/s T Temperature/◦C Df Coefficient of water diffusion in tissue/m2 s−1 MW The molar mass of water/18 g mol−1 RH Relative humidity/% PW Vapor pressure of water/Pa r Space coordinate/m ΔHvap Enthalpy of water vaporization/2408 J kg−1 Δm Water vaporization rate from the skin surface/g m−2 s−1 Δr Body core distance from current tissue position/m 𝛿c The average distance of the momentum boundary layer/m 𝜌 Density of skin/kg m−3 * Jitendra Singh [email protected] Rajneesh Kumar Chaudhary [email protected] Kabindra Nath Rai [email protected] 1
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
Department of Mathematical Sciences, IIT-BHU, Varanasi 221005, India
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Ra Universal gas constant/8.314 J mol−1 ◦C−1 𝜏q Phase lag of heat flux/s 𝜏t Phase lag due to temperature gradient/s Tw Wall temperature at the boundary/◦C H Coefficient of reference heat transfer/W m−2 ◦C−1 qw Reference heat flux/W m−2 Ts Ambient temperature/◦C Qv Evaporation of water Qd Diffusion of water Subscripts and superscripts b Blood c Core a Air f Diffusion of water m Metabolic production s Surface of skin v Vaporization W Water Non‑dimensional variable Fo Non-dimensional time x Non-dimensional space coordinate Ki Kirchhoff number Bi Biot number Fot Non-dimensional phase lag due to temperature gradient Foq Non-dimensional phase lag of heat flux
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Pmo Non-dimensional coefficient of metabolic heat source Pf Non-dimensional coefficient of blood perfusion 𝜃 Non-d
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