Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues

Processes

Piran Goudarzi¹  Mikhail A. Sheremet²  Mohammad Ghalambaz³  Awatef Abidi⁴  Seyed Abdollah Mansouri Mehryan⁵ 

[1] Department of Mechanical Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran;Laboratory on Convective Heat and Mass Transfer, Tomsk State University, 634050 Tomsk, Russia;Metamaterials for Mechanical, Biomechanical and Multiphysical Applications Research Group, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam;Physics Department, College of Sciences Abha, King Khalid University, Abha City 61421, Saudi Arabia;Young Researchers and Elite Club, Yasooj Branch, Islamic Azad University, Yasooj 7591493686, Iran;

关键词: inverse fractional non-Fourier;    fractional heat conduction;    parameter estimations;    tissues;   

DOI  :  10.3390/pr9111877

来源: DOAJ

【 摘 要 】

In this work, the relaxation parameter (τ) and fractionality order (α) in the fractional single phase lag (FSPL) non-Fourier heat conduction model are estimated by employing the conjugate gradient inverse method (CGIM). Two different physics of skin tissue are chosen as the studied cases; single and three-layer skin tissues. Single-layer skin is exposed to laser radiation having the constant heat flux of Q_in. However, a heat pulse with constant temperature is imposed on the three-layer skin. The required inputs for the inverse problem in the fractional diffusion equation are chosen from the outcomes of the dual phase lag (DPL) theory. The governing equations are solved numerically by utilizing implicit approaches. The results of this study showed the efficiency of the CGIM to estimate the unknown parameters in the FSPL model. In fact, obtained numerical results of the CGIM are in excellent compatibility with the FSPL model.

【 授权许可】

Unknown