Dual-Phase-Lag Heat Conduction Model in Thin Slab Under the Effect of a Moving Heating Source

Time‐dependent pressure‐driven flow in a horizontal cylinder filled with a bidisperse porous material

“…To obtain their corresponding expression in the time domain, we take their respective Laplace inverses. These, however, could be obviously difficult hence we employed a numerical method; the Riemann-Sum Approximation Method used by Khadrawi et al 29 and later by Jha and Isa. 30 This approach requires that the Laplace inverse of any function U y p ̅ ( , ) can be obtained from…”

“…To obtain their corresponding expression in the time domain, we take their respective Laplace inverses. These, however, could be obviously difficult hence we employed a numerical method; the Riemann‐Sum Approximation Method used by Khadrawi et al 29 and later by Jha and Isa 30 . This approach requires that the Laplace inverse of any function $$\mathop{U}\limits^{̅}(y,p)$$ can be obtained from $$$U(y,t)=\frac{{e}^{\varepsilon t}}{t}\left[\frac{1}{2}\bar{U}(y,\varepsilon )+Re\sum _{k=1}^{n}\bar{U}\left(y,\varepsilon +\frac{{ik}\pi }{t}\right){(-1)}^{k}\right],$$$ where $$Re$$ is the real part of the expression, $$i=\sqrt{-1}$$ is the imaginary number, and $$n$$ is the number of iterations used while $$\varepsilon $$ is the real part of the Bromwich contour used for inverting a function from the Laplace domain to its corresponding time domain.…”

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

“…Bioheat application [133,134] Laplace transformation technique [71,92,93,135,136] Cartesian, Cylindrical, Spherical 1-D, 2-D CV, DPL Hybrid method [93]. Moving heating source [136] Other analytical methods [137][138][139][140][141][142][143][144][145][146][147] Cartesian 1-D, 2-D, 3-D CV, DPL Fourier series [137]: Constant heat flux and constant temperature BC, [138,139]: fluctuating harmonic heating source. Spectral [140]: CV model, Chebyshev polynomials.…”

“…The axisymmetric problem of the CV non-Fourier model for the regions interior and exterior to a circular cylinder is investigated by using the methods of Laplace transformation and asymptotic analysis [135]. Also, the Laplace transformation technique is used to obtain the solution of the DPL model under the effect of a moving heat source [136] and the CV model in a radial one-dimensional heat conduction process for a hollow sphere [71].…”