Bioconvection mechanism using third-grade nanofluid flow with Cattaneo–Christov heat flux model and Arrhenius kinetics

This paper aims to study the effects of activation energy and thermal radiation in the bioconvection flow of nanofluid (third-grade nanofluid) containing swimming microorganisms in the presence of a heat source-sink past a stretching sheet. Brownian movement and thermophoresis diffusion are used in mathematical modeling. The given flow phenomenon is modeled in the form of governing partial differential equations. Furthermore, appropriate dimensionless transformation is used to transfer the governing system of PDEs into an ordinary one. The remodeled systems of ODEs are tackled numerically by bvp4c on Matlab with a shooting scheme in computational tool MATLAB. The bearing of prominently involved parameters on the numerical solution of velocity, temperature distribution, nanoparticles concentration and concentration of microorganisms is comprehensively discussed and elaborated through figures. It is established that velocity can be improved with a mixed convection aspect. Furthermore, the temperature and concentration of nanoparticles reduce against Prandtl number, also, large Peclet number declines the microorganisms field. The work contained in this paper has applications in nanotechnology, electrical and mechanical engineering, biomedicine, biotechnology, drug delivery, cancer treatment, food processing and various industries. No such work is yet reported, and it is good for the research in applied sciences.

Toward the Dynamical Convergence on the Jet Stream in Aquaplanet AGCMs

Systematic sensitivity of the jet position and intensity to horizontal model resolution is identified in several aquaplanet AGCMs, with the coarser resolution producing a more equatorward eddy-driven jet and a stronger upper-tropospheric jet intensity. As the resolution of the models increases to 50 km or finer, the jet position and intensity show signs of convergence within each model group. The mechanism for this convergence behavior is investigated using a hybrid Eulerian–Lagrangian finite-amplitude wave activity budget developed for the upper-tropospheric absolute vorticity. The results suggest that the poleward shift of the eddy-driven jet with higher resolution can be attributed to the smaller effective diffusivity of the model in the midlatitudes that allows more wave activity to survive the dissipation and to reach the subtropical critical latitude for wave breaking. The enhanced subtropical wave breaking and associated irreversible vorticity mixing act to maintain a more poleward peak of the vorticity gradient, and thus a more poleward jet. Being overdissipative, the coarse-resolution AGCMs misrepresent the nuanced nonlinear aspect of the midlatitude eddy–mean flow interaction, giving rise to the equatorward bias of the eddy-driven jet. In accordance with the asymptotic behavior of effective diffusivity of Batchelor turbulence in the large Peclet number limit, the upper-tropospheric effective diffusivity of the aquaplanet AGCMs displays signs of convergence in the midlatitude toward a value of approximately 107 m2 s−1 for the ∇2 diffusion. This provides a dynamical underpinning for the convergence of the jet stream observed in these AGCMs at high resolution.

Bounding the scalar dissipation scale for mixing flows in the presence of sources

We investigate the mixing properties of scalars stirred by spatially smooth, divergence-free flows and maintained by a steady source–sink distribution. We focus on the spatial variation of the scalar field, described by the dissipation wavenumber, ${k}_{d} $, that we define as a function of the mean variance of the scalar and its gradient. We derive a set of upper bounds that for large Péclet number ($\mathit{Pe}\gg 1$) yield four distinct regimes for the scaling behaviour of ${k}_{d} $, one of which corresponds to the Batchelor regime. The transition between these regimes is controlled by the value of $\mathit{Pe}$ and the ratio $\rho = {\ell }_{u} / {\ell }_{s} $, where ${\ell }_{u} $ and ${\ell }_{s} $ are, respectively, the characteristic length scales of the velocity and source fields. A fifth regime is revealed by homogenization theory. These regimes reflect the balance between different processes: scalar injection, molecular diffusion, stirring and bulk transport from the sources to the sinks. We verify the relevance of these bounds by numerical simulations for a two-dimensional, chaotically mixing example flow and discuss their relation to previous bounds. Finally, we note some implications for three-dimensional turbulent flows.

The diffusive strip method for scalar mixing in two dimensions

We introduce a new numerical method for the study of scalar mixing in two-dimensional advection fields. The position of an advected material strip is computed kinematically, and the associated convection–diffusion problem is solved using the computed local stretching rate along the strip, assuming that the diffusing strip thickness is smaller than its local radius of curvature. This widely legitimate assumption reduces the numerical problem to the computation of a single variable along the strip, thus making the method extremely fast and applicable to any large Péclet number. The method is then used to document the mixing properties of a chaotic sine flow, for which we relate the global quantities (spectra, concentration probability distribution functions (PDFs), increments) to the distributed stretching of the strip convoluted by the flow, possibly overlapping with itself. The numerical results indicate that the PDF of the strip elongation is log normal, a signature of random multiplicative processes. This property leads to exact analytical predictions for the spectrum of the field and for the PDF of the scalar concentration of a solitary strip. The present simulations offer a unique way of discovering the interaction rule for building complex mixtures which are made of a random superposition of overlapping strips leading to concentration PDFs stable by self-convolution.