Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy

Abstract

Objective function k Thermal conductivity, W/m °C L Length, m M Number of nodes at spatial coordinate N Number of temporal measurements q ′′ (t) Surface heat flux, W/m 2 q m Metabolic heat generation, W/m 3 T (x, t) Temperature, °C �T (x, t) Sensitivity problem, °C t Temporal coordinate, s W (T ) Convective heat exchange with blood flow, W/m 3 x Spatial coordinate, m Y (t) Measured temperature, °C Greek symbols β Search step size γ Conjugate coefficient δ Dirac delta function ε Convergence criterion ζ Transformed time coordinate, s (x, t) Adjoint function µ Random variable ρ Density, kg/m 3 σ Standard deviation of the measurement errors τ Thermal relaxation time, s ω Perfusion rate of blood, m 3 /s/m 3 Subscript b Blood c Conduction heat transfer es Estimated value ex Exact value f Final value initial Initial value

A computational study of biomagnetic fluid flow in a channel in the presence of obstacles under the influence of the magnetic field generated by a wire carrying electric current

“…Biomagnetic fluids' behaviour in the presence of magnetic fields has become an interesting area for many researchers. Cell separation (Haik, Pai, & Chen, 1999a;Miltenyi, Müller, Weichel, & Radbruch, 1990), targeted drug delivery (Crane et al, 2004;Cregg, Murphy, & Mardinoglu, 2012;Lu, Wei, Ma, Yang, & Chen, 2012;Yellen et al, 2005;Yu, Chen, Chen, & Zhou, 2008), wound healing due to the effects of magnetic fields (Henry, Concannon, & Yee, 2008;Nursal et al, CONTACT S. Morteza Mousavi smorteza_mousavi@yahoo.com 2006), and cancer treatment with magnetic hyperthermia (Baghban & Ayani, 2017;Lahiri, Ranoo, & Philip, 2017;Liangruksa, Ganguly, & Puri, 2011) are some applications of this field in the medical and biomedical engineering. Blood is the most characteristic biomagnetic fluid.…”