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Reaction–Diffusion Modeling
Published in Ranjit Kumar Upadhyay, Satteluri R. K. Iyengar, Spatial Dynamics and Pattern Formation in Biological Populations, 2021
Ranjit Kumar Upadhyay, Satteluri R. K. Iyengar
The hyperbolic system (2.9) and (2.10) is a reaction–Cattaneo (RC) system. This RC system can also be obtained from extended irreversible thermodynamics [88]. Al-Ghoul [4], Al-Ghoul and Eu [5] have derived such systems from generalized hydrodynamic theory. Differentiating (2.9) with respect to t and (2.10) with respect to x and eliminating the mixed derivative, we obtain τϕtt+[1−τF′(ϕ)]ϕt=Dϕxx+F(ϕ).
Viscosity of Nanofluid Systems: A Critical Evaluation of Modeling Approaches
Published in K.R.V. Subramanian, Tubati Nageswara Rao, Avinash Balakrishnan, Nanofluids and Their Engineering Applications, 2019
Amir Varamesh, Abdolhossein Hemmati-Sarapardeh
Based on extended irreversible thermodynamics, Lebon and Machrafi [53] proposed a new approach to calculate the viscosity of nanofluids. The model was introduced as an extension of Einstein [20] model by considering the flowing elements including effects of a layer surrounding nanoparticles and a thermodynamic description of the role of size impacts. Lebon and Machrafi [53] presented Eq. (6.44) by coupling of the effects of liquid layering, nanoparticle’s size, and volume fraction. The obtained results by the model were in good agreement with molecular dynamic simulation and experimental data. () μnf=μbf1+2.5φ(1+h/r)31+4π2φ2(1+h/r)2(l2/r2).
Nonlinear Rheology of Giant Micelles
Published in Raoul Zana, Eric W. Kaler, Giant Micelles, 2007
Jorge E. Puig, Fernando Bautista, J. Felix Armando Soltero, Octavio Manero
Extended irreversible thermodynamics (EIT) can provide an approach to derive hydrodynamic equations that govern the flow-induced concentration changes produced by inhomogeneous stresses in a complex fluid.144 One of the most relevant effects arising from these inhomogeneous flows is manifested in flow-induced concentration fluctuations. In addition, it has been demonstrated that the generalized extended Gibbs free energy variation with shear rate provides a criterion to predict the stress plateau under shear-banding flow.112 The criterion of bands coexistence is the equality of the extended Gibbs free energy of the bands when normal stresses can be neglected. The predicted stress plateau coincides remarkably well with experimental data.
Blood Flow Effects in Thermal Treatment of Three-Dimensional Non-Fourier Multilayered Skin Structure
Published in Heat Transfer Engineering, 2021
Mohammad Jamshidi, Jafar Ghazanfarian
When the local equilibrium is considered, the wave-like behavior of the dual-phase-lag heat conduction model can result in violation of the second law of thermodynamics [26, 27]. But, this paradox is resolved by taking into account additional forces like the heat flux vector in the generalized Gibbs space in the framework of extended irreversible thermodynamics. Hence, the extension of the classical thermodynamics results in local equilibrium in non-Fourier heat transfer, and consequently makes the dual-phase-lag heat conduction model consistent with the second law of thermodynamics [28]. Heat transport in laser irradiation process [29], nano-electronic devices, and complex media such as bio-tissues are some well-known examples of fast process. Since the non-Fourier heat transport occurs rapidly and transiently, it is not difficult to consider that the local equilibrium gets abandoned [30, 31].
New general decay results for a Moore–Gibson–Thompson equation with memory
Published in Applicable Analysis, 2020
Wenjun Liu, Zhijing Chen, Dongqin Chen
The MGT equation is one of the equations of nonlinear acoustics describing acoustic wave propagation in gases and liquids [1–3]. Equation (1) arises from modeling high frequency ultrasound waves accounting for thermal flux and molecular relaxation times [4–6]. According to revisited extended irreversible thermodynamics, thermal flux relaxation leads to the third-order derivative in time while molecular relaxation leads to non-local effects governed by memory terms. Because of the wide range of applications such as the medical and industrial use of high intensity ultrasound in lithotripsy, thermotherapy, ultrasound cleaning, etc., there have been a large amount of studies in this research field.
A generalized thermoelastic problem due to nonlocal effect in presence of mode I crack
Published in Journal of Thermal Stresses, 2020
Thermoelastic coupling is a thorough, but challenging issue. Nevertheless, it is challenged presently for thermoelastic analysis of the emerging structures having cracks, where the size effect of both heat conduction and deformation is strong. In this work, size-dependent thermoelasticity is formulated by combining nonlocal heat conduction and nonlocal elasticity with the aids of extended irreversible thermodynamics and generalized free energy. The most significant thing is the effect of nonlocality on the vertical and horizontal stresses in the vicinity of the crack. In terms of theoretical developments and numerical computations, the following remarks are addressed.The present problem is formulated in the framework of 3P lag model subjected to a nonlocal medium. According to this new nonlocal theory of thermoelasticity, we need to construct a new classification to the materials according to the elastic nonlocality parameter e0.Significant effect of the nonlocal parameter is noticed in the distribution of the displacement components. It is seen that the maximum and minimum values of the displacements strongly dependent on the vertical distance.Presence of nonlocality has the tendency to diminish the magnitude of the profile of stress components within the medium.The magnitude of the stress components increases with the increase of the vertical distance.In the distribution of temperature, there is no effect of nonlocality beyond the length of the crack.