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Purpose The purpose of this study is to investigate the Cattaneo-Christov double diffusion, multiple slips and Darcy-Forchheimer’s effects on entropy optimized and thermally radiative flow, thermal and mass transport of hybrid nanoliquids past stretched cylinder subject to viscous dissipation and Arrhenius activation energy. Design/methodology/approach The presented flow problem consists of the flow, heat and mass transportation of hybrid nanofluids. This model is featured with Casson fluid model and Darcy-Forchheimer model. Heat and mass transportations are represented with Cattaneo-Christov double diffusion and viscous dissipation models. Multiple slip (velocity, thermal and solutal) mechanisms are adopted. Arrhenius activation energy is considered. For graphical and numerical data, the bvp4c scheme in MATLAB computational tool along with the shooting method is used. Findings Amplifying curvature parameter upgrades the fluid velocity while that of porosity parameter and velocity slip parameter whittles down it. Growing mixed convection parameter, curvature parameter, Forchheimer number, thermally stratified parameter intensifies fluid temperature. The rise in curvature parameter and porosity parameter enhances the solutal field distribution. Surface viscous drag gets controlled with the rising of the Casson parameter which justifies the consideration of the Casson model. Entropy generation number and Bejan number upgrades due to growth in diffusion parameter while that enfeeble with a hike in temperature difference parameter. Originality/value To the best of the authors’ knowledge, this research study is yet to be available in the existing literature.

In this paper we consider a Banach spaces-based fully-mixed variational formulation that has been recently proposed for the coupling of the stationary Brinkman–Forchheimer and double-diffusion equations, and develop the first reliable and efficient residual-based a posteriori error estimator for the 2D and 3D versions of the associated mixed finite element scheme. For the reliability analysis, and due to the nonlinear nature of the problem, we employ the strong monotonicity of the operator involving the Forchheimer term, in addition to inf-sup conditions of some of the resulting bilinear forms, along with a stable Helmholtz decomposition in nonstandard Banach spaces, which, in turn, having been recently derived, constitutes another distinctive feature of the paper, and local approximation properties of the Raviart–Thomas and Clément interpolants. On the other hand, inverse inequalities, the localization technique through bubble functions, and known results from previous works, are the main tools yielding the efficiency estimate. Finally, several numerical examples confirming the theoretical properties of the estimator and illustrating the performance of the associated adaptive algorithms, are reported. In particular, the case of flow through a 2D porous media with an irregular channel networks is considered.

Purpose This paper aims to present the effect of entropy generation on the unsteady flow of upper-convected Maxwell nanofluid past a wedge embedded in a porous medium in view of buoyancy force. Cattaneo-Christov double diffusion theory simulates the processes of energy phenomenon and mass transfer. Meanwhile, Brownian motion, thermophoresis and convective boundary conditions are discussed to further visualize the heat and mass transfer properties. Design/methodology/approach Coupled ordinary differential equations are gained by appropriate similar transformations and these equations are manipulated by the Homotopy analysis method. Findings The result is viewed that velocity distribution is a diminishing function with boosting the value of unsteadiness parameter. Moreover, fluid friction irreversibility is dominant as the enlargement in Brinkman number. Then controlling the temperature and concentration difference parameters can effectively regulate entropy generation. Originality/value This paper aims to address the effect of entropy generation on unsteady flow, heat and mass transfer of upper-convected Maxwell nanofluid over a stretched wedge with Cattaneo-Christov double diffusion, which provides a theoretical basis for manufacturing production.

While the Kuroshio is known to be a nutrient stream, as these nutrients are in dark subsurface layers, they are not immediately available for photosynthesis unless they are supplied to the sunlit surface layers. Recent microstructure observations have revealed that strong diapycnal mixing caused by the Kuroshio flowing over topographic features and double diffusion in the subsurface layers of the Kuroshio. However, it is still unclear how much nutrient flux can be provided by these microscale mixing processes. In this study, using an autonomous microstructure float and nutrient samplings, nutrient flux caused by the Kuroshio over the Izu Ridge, and that caused by double diffusion in the Kuroshio Extension are quantified. The nitrate diffusive flux is estimated to be > 1 mmol N m - 2 day - 1 over a distance, 20–30 km near the Izu Ridge and > 0.1 mmol N m - 2 day - 1 , which persists further downstream direction over 100 km along the Kuroshio, increasing the subsurface chlorophyll-a concentration in the region 200 km downstream. The double-diffusion-induced nitrate flux is estimated to be 1- 10 mmol N m - 2 day - 1 in the pycnostad 26– 26.5 kgm - 3 of the Kuroshio Extension, suggesting that whether this double-diffusion-induced nutrient flux in the subsurface layers can ultimately contribute to surface primary production depends on additional eddy up- and northward fluxes.

A study for MHD (magnetohydrodynamic) impacts on the rotating flow of Casson nanofluids is considered. The concentration and temperature distributions are related along with the double diffusion Cattaneo–Christov model, thermophoresis, and Brownian motion. The governing equations in the 3D form are changed into dimensionless two-dimensional form with the implementation of suitable scaling transformations. The variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled nonlinear partial differential problem. The variation patterns of Sherwood number, Nusselt number, skin friction coefficients, velocities, concentration, and temperature functions are computed to reveal the physical nature of this examination. It is seen that higher contributions of the magnetic force, Casson fluid, and rotational fluid parameters cause to raise the temperature like thermophoresis and Brownian motion does but causes slowing the primary as well as secondary velocities. The FEM solutions showing an excellent correlation with published results. The current study has significant applications in the biomedical, modern technologies of aerospace systems, and relevance to energy systems.

The aim of this study is to better understand diffusive convection (DC) and its role in the upper ocean dynamic environment and sea ice melting in the Canada Basin. Based on a moored dataset with 6737 profiles collected from August 2003 to August 2011 in the upper layer of the Canada Basin, DC between the warm and salty Atlantic Water (AW) and the colder and less salty Lower Halocline Water (LHW) were investigated. The moorings were designated at four stations: A, B, C, and D, located at the southwestern, southeastern, northeastern, and northwestern parts of the basin, respectively. During the observation period, the temperature, salinity, and depth of the AW and LHW exhibited unique temporal variations. The temperature and salinity of the AW varied among stations, with a decreasing trend from northwest to southeast, consistent with the propagation path of the AW in the Canada Basin. The temperature and salinity of the LHW were similar at all stations. The AW and LHW cores were located between depths of 320–500 m and 160–300 m, respectively, and both gradually deepened over time. Distinct DC staircase structures were observed between the AW and LHW, more pronounced at stations C and D than at stations A and B, which is speculated to be related to eddies at stations A and B during the observation period. The vertical heat fluxes through the DC staircase layer at stations C and D (FHc_C and FHc_D) were estimated using an empirical formula. FHc_C ranged from 0.05 to 0.94 W/m2, and FHc_D ranged from 0.05 to 0.6 W/m2, with the maximum probability value for both at approximately 0.2 W/m2. The effective diffusivities at these two stations (KT_C and KT_D) are similar, ranging from 2 × 10−6 to 3 × 10−5 m2/s, with the highest probability occurring at 6 × 10−6 m2/s. Both the probability density function of the heat flux and the effective diffusivity skewed towards larger values and obey a lognormal distribution, indicating turbulence intermittency of the DC staircase in the Canada Basin. These finding offers new insights into the heat transport and turbulence in the DC staircase, and then bring a deeper understanding of sea ice melting in the Canada Basin.

Purpose The purpose of this paper is to investigate the two-dimensional stagnation-point flow, heat and mass transfer of an incompressible upper-convected Oldroyd-B MHD nanofluid over a stretching surface with convective heat transfer boundary condition in the presence of thermal radiation, Brownian motion, thermophoresis and chemical reaction. The process of heat and mass transfer based on Cattaneo–Christov double-diffusion model is studied, which can characterize the features of thermal and concentration relaxations factors. Design/methodology/approach The governing equations are developed and similarly transformed into a set of ordinary differential equations, which are solved by a newly approximate analytical method combining the double-parameter transformation expansion method with the base function method (DPTEM-BF). Findings An interesting phenomenon can be found that all the velocity profiles first enhance up to a maximal value and then gradually drop to the value of the stagnation parameter, which indicates the viscoelastic memory characteristic of Oldroyd-B fluid. Moreover, it is revealed that the thickness of the thermal and mass boundary layer is increasing with larger values of thermal and concentration relaxation parameters, which indicates that Cattaneo–Christov double-diffusion model restricts the heat and mass transfer comparing with classical Fourier’s law and Fick’s law. Originality/value This paper focuses on stagnation-point flow, heat and mass transfer combining the constitutive relation of upper-convected Oldroyd-B fluid and Cattaneo–Christov double diffusion model.

The fractional anisotropy (FA) that can be derived from diffusion tensor imaging (DTI), is ambiguous because it not only depends on the tissue microstructure but also on the axon or fiber orientation distribution within a voxel. Measures of the microscopic diffusion anisotropy, like the microscopic anisotropy index (MA) that can be determined with so-called double-wave-vector (DWV) or double diffusion encoding (DDE) imaging, are independent of this orientation distribution and, thus, offer a more direct and undisguised access to the tissue structure on a cellular or microscopic scale. In this study, FA and MA measurements were performed in a group of aged (>60y), healthy volunteers and compared to the data obtained recently for a group of young (<33y), healthy volunteers to reveal age-related differences. The coefficients-of-variation (CV) determined for the aged group were considerably lower for MA than for FA in average and in most of the 16 ROIs analyzed due to lower between-subject variations of MA. FA differences between the young and the aged group were in line with previous DTI studies. MA was also decreased in the aged group but in more of the 16 ROIs and with a higher significance. Furthermore, MA differences were also observed in frontal brain regions containing fiber crossings that did not reveal significant FA differences, i.e. MA seems to provide a better sensitivity to detect microstructural changes in such regions. In some non-cortical gray matter structures like the putamen, FA was increased but MA was decreased in the aged group which could indicate a coherent fiber orientation in the aged group related to the loss of crossing or fanning fibers. In conclusion, MA not only could improve the detectability of differences of the tissue microstructure but, in conjunction with FA, could also help to identify the underlying changes. •The microscopic diffusion anisotropy (MA) was measured in aged, healthy subjects.•MA values are larger and more consistent between subjects and regions than FA.•MA may be more sensitive to detect changes of the tissue microstructure than FA.•Age-related MA differences are obtained from a comparison with young subjects.•Combining FA and MA can help to characterize changes of the tissue microstructure.

Double diffusion occurs when the fluid density depends on two components that diffuse at different rates (e.g. heat and salt in the ocean). Double diffusion can lead to an up-gradient buoyancy flux and drive motion at the expense of potential energy. Here, we follow the work of Lorenz ( Tellus , vol. 7 (no. 2), 1955, pp. 157–167) and Winters et al.  ( J. Fluid Mech. , vol. 289, 1995, pp. 115–128) for a single-component fluid and define the background potential energy (BPE) as the energy associated with an adiabatically sorted density field and derive its budget for a double-diffusive fluid. We find that double diffusion can convert BPE into available potential energy (APE), unlike in a single-component fluid, where the transfer of APE to BPE is irreversible. We also derive an evolution equation for the sorted buoyancy in a double-diffusive fluid, extending the work of Winters & D’Asaro ( J. Fluid Mech. , vol. 317, 1996, pp. 179–193) and Nakamura ( J. Atmos. Sci. , vol. 53 (no. 11), 1996, pp. 1524–1537). The criterion we develop for a release of BPE can be used to analyse the energetics of mixing and double diffusion in the ocean and other multiple-component fluids, and we illustrate its application using two-dimensional simulations of salt fingering.

Double-diffusive convection, in which a fluid is acted upon by two fields (such as temperature and salinity) that affect the density, has been widely studied in areas as diverse as the oceans and stellar atmospheres. Assuming classical Fickian diffusion for both heat and salt, the evolution of temperature and salinity are governed by parabolic advection–diffusion equations. In reality, there are small extra terms in these equations that render the equations hyperbolic (the Maxwell–Cattaneo effect). Although these corrections are nominally small, they represent a singular perturbation and hence can lead to significant effects when the underlying differences of salinity and temperature are large. In this paper, we investigate the linear stability of a double-diffusive fluid layer and show that amending Fick's law for the temperature, or the salinity, alone can lead to new modes of oscillation and to very large changes in the preferred wavelength of oscillatory convection at onset. In particular, the salt finger regime of classical double diffusion is here replaced by Maxwell–Cattaneo oscillations when the salt concentration is very high. The more complicated case when both laws are amended is left to a future paper, now in preparation.