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Fluid Mechanics Measurements in Non-Newtonian Fluids
Published in Richard J. Goldstein, Fluid Mechanics Measurements, 2017
Christopher W. Macosko, Paulo R. Souza Mendes
The rate δτ/δt is the interpolated convected time derivative of τ. When a = 1, we get the upper convected time derivative; when a = -1, δτ/δt becomes the lower convected time derivative; and for a = 0, the corotational time derivative is recovered. Using it, we obtain the interpolated Maxwell model: () τ+λ0δτδt=2μD
Choice of appropriate constitutive equations in modelling of injection moulding of rubber
Published in Per-Erik Austrell, Leif Kari, Constitutive Models for Rubber IV, 2017
V. Nassehi, G. Khodabakhshi, J. Clarke
is the upper convected time derivative of D¯¯,(∂D¯¯)/(∂t) is its local time derivative (which should be neglected in a viscometric flow). Here D¯¯=(1/2)[∇V¯+(∇V¯)T] is the symmetric and ω¯¯=(1/2)[∇V¯−(∇V¯)T] is the anti-symmetric part of the rate of deformation (or rate of strain) tensor. Therefore the CEF model relates explicitly the extra stress appearing in the equation of motion to the rate of strain (i.e. rate of deformation) within the fluid. As the rate of strain is defined in terms of velocity gradients this results in the elimination of the stress components from the equation of motion yielding a determinate set of equations which can be solved.
Cattaneo-Christov double diffusion based heat transport analysis for nanofluid flows induced by a moving plate
Published in Numerical Heat Transfer, Part A: Applications, 2023
We can examine the synthesis and utilization of thermal energy created across a reaction system using the modes of heat transport, such as diffusion, convection, radiation, and advection. Extensive research has been performed to better understand the flow and energy consumption pattern and the results have been applied to the aeronautical, medical, and mechanical scales. Researchers and scientists were able to develop technology such as heat sensors, radiators (heat exchangers), and so forth as a result of this collaboration. The Fourier model was altered by Cattaneo [20], who consolidated the thermal relaxation time characteristic, also referred to as the Maxwell–Cattaneo principle. To get an invariant model, Christov [21] modified Cattaneo’s approach by incorporating an upper-convected time derivative. Sarfraz et al. [22] studied the importance of Cattaneo–Christov heat flux for swirling flow over a rotating surface. Sarfraz et al. [23] analyzed the energy transport mechanism by using a heat source-sink. They modeled the problem of water conveying iron oxide and graphene nanoparticles past a stretching/spiraling surface. Studies related to the study and applications of Cattaneo–Christov heat flux are addressed in Refs. [24–27].
Significance of the Cattaneo–Christov theory for heat transport in swirling flow over a rotating cylinder
Published in Waves in Random and Complex Media, 2021
Mahnoor Sarfraz, Awais Ahmed, Masood Khan, M. Munawwar Iqbal Ch, Muhammad Azam
Through the modes of heat transport, i.e. diffusion, convection, radiation, and advection, we can scrutinize the production and applications of thermal energy generated throughout a system's reaction. To comprehend the flow and energy consumption pattern, numerous studies have been conducted, and their results are applied on aerospace, medicine and mechanical scale. In this way, researchers/scientists were able to develop technologies, such as heat sensors, radiators (heat exchangers), and so forth. Cattaneo [12] transformed the Fourier model by consolidating the thermal relaxation time characteristic, which is generally known as the Maxwell–Cattaneo principle. Christov [13] remodeled Cattaneo’s work by introducing an upper-convected time derivative to procure an invariant model. Ciarletta and Straughan [14] examined the uniqueness and stability of the Cattaneo–Christov theory. Straughan [15] reported that in heat convection, the Christov work linked with Cattaneo’s model heads intriguing consequences. Han et al. [16] showed a comparison between the traditional and advanced heat flux models. Hayat et al. [17] addressed the flow and thermal analysis in the stagnation region with thermal stratification and Cattaneo–Christov flux model. Reddy et al. [18] inquired about the influence of Cattaneo–Christov heat flux on Casson fluid. They concluded that energy transport in the Newtonian fluid was higher than in the non-Newtonian fluid. The thermal transport with a steady boundary layer flow was investigated by Li et al. [19]. Jakeer et al. [20] determined the mathematical importance of the heat transfer rate using the finite volume method for magneto-hybrid nanofluid. Acharya et al. [21] studied a modified model for Fourier-Fick’s for the energy distribution in Maxwell fluid flow. Further intriguing studies on the Cattaneo–Christov theory are considered in Refs. [22–25].
Heat transfer enhancement by pulsating flow of a viscoelastic fluid in a microchannel with a rib plate
Published in Nanoscale and Microscale Thermophysical Engineering, 2022
where ηs is the solvent viscosity coefficient and ηp is the polymer viscosity, λ is the relaxation time. represents the upper-convected time derivative. The temperature in the flow field is solved by energy equation: