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This paper is aimed to throw a light on the steady boundary layer flow and heat transfer of a non-Newtonian Casson fluid over an exponentially permeable shrinking sheet in the presence of exponentially moving free stream with convective boundary condition. Using similarity transformations, the self-similar forms of the governing equations are obtained and then solved numerically by shooting technique. Dual solutions of the problem are also obtained. It is found that wall temperature gradient decreases with the increasing values of convective parameter. It is interesting to note that as suction and the fluid material parameter increase, wall temperature gradient decreases. [ABSTRACT FROM AUTHOR]

We explore theoretically non-Kolmogorov scaling and dissipation laws by employing continuous symmetry group transformations on statistical model equations for planar turbulent plume. The dissipation laws for mean turbulent K. E. ( k ¯ ) and mean thermal intensity ( k θ ¯) at infinite Reynolds number limit are obtained as ϵ ∼ ( k ¯) 3 / 2 / ( δ u R e δ u m ) , ϵ θ ∼ ( k ¯) 1 / 2 ( k θ ¯) / ( δ u R e δ u m ) , where the exponent m = 3 a 2 / ( a 1 + a 2 ) preferably belongs to [−3/2, 1], a1, a2 the dilation symmetry group parameters. Here R e δ u is the local Reynolds number based on plume velocity width δu. The Kolmogorov dissipation law will hold only when k ¯ ∼ u ¯ 2 ∼ u ′ v ′ ¯ , which implies the same streamwise variations of Reynolds stresses, while non-Kolmogorov dissipation can hold only when k ¯ ∼ u ¯ 2 ≁ u ′ v ′ ¯ indicating different streamwise variations of Reynolds stresses. When m = −3/2, the plume scales as a non-equilibrium exponential function of streamwise distance x, while for m ∈ (−3/2, 0) ∪ (0, 1], there exist multiple non-equilibrium power law scalings and classical equilibrium scaling corresponds to m = 0. The turbulent kinetic energy dissipation law for m ≈ 1 is reported both experimentally and theoretically in axisymmetric turbulent wake and planar jet. When m = 1, the plume velocity and temperature widths (δu, δT) grow as ∼(x + a)2/5, centerline mean velocity grows as u ¯ c ∼ (x + a) 1 / 5 , and mean temperature decays as θc ∼ (x + a)−3/5, with a being a virtual origin. The non-equilibrium dissipation scaling instigates a variation of plume entrainment coefficient with streamwise distance. In particular, the region where dissipation scaling with exponent m = 1 holds, the entrainment coefficient in planar plume varies as ∼(x + a)−3/5, whereas the entrainment coefficient reported recently in planar jet varies as ∼(x + a)−1/3. [ABSTRACT FROM AUTHOR]

We report a symmetry model for turbulence intermittency. This is obtained by the compositions of continuous symmetry group transformations of statistical turbulent spectral equation at infinite Reynolds number limit. Flow evolution under group compositions yields velocity structure function exponents that depend on the dilation symmetry group parameter c 1 (≠ 0) and a random parameter m. The random parameter m is associated with energy distribution. Since the correction to the space-filling Kolmogorov cascade is small, the value of m ∈ [ 0. 7 , 1). The asymptotic structures are filaments having dimension one, so c 1 is found to be related with m by c 1 = − 3 / 4 ln (1 − m). The present model therefore depends only on m , and c 1 can be ascertained uniquely for m ∈ [ 0. 7 , 1). It is found that the velocity structure function exponents ζ p , p = 0 , 1 , 2 , ... in present symmetry model agree well with the existing experimental, direct numerical simulation results and different phenomenological models for m ∈ [ 0. 7 5 , 0. 8 5 ]. For these values of m , the correction to Kolmogorov space-filling, universal − 5 / 3 law, belongs to the range [ − 0. 0 5 0 9 2 9 5 , − 0. 0 2 9 1 7 5 ] , and the fractal dimension for the support set lies in [ 2. 8 7 1 5 7 , 2. 9 3 2 2 4 ]. [ABSTRACT FROM AUTHOR]

In this work we study the pattern of bifurcations and intermittent-chaos of non-Newtonian couple-stress shallow fluid layer subject to heating from below. The couple-stress parameter delays onset of convection, synchronizes chaotic behavior, and decreases the heat transfer . Some global aspects of the dynamics such as homoclinic bifurcations and transition to chaos are explored. The effects of particle size on the intermittent-chaos regime at particular normalized Rayleigh number, say $$r=166.1$$ , are investigated. With the increase in couple-stress parameter, the present Lorenz-like system synchronizes to a steady state via a series of periodic solutions interspersed with intervals of chaotic behaviors. [ABSTRACT FROM AUTHOR]

The paper is concerned to find the distribution of the chemically reactant solute in the MHD flow of an electrically conducting viscous incompressible fluid over a stretching surface. The first order chemical reaction and the variable solute distribution along the surface are taken into consideration. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of non-linear self-similar ordinary differential equations by using scaling group of transformations. An exact analytic solution is obtained for the velocity field. Using this velocity field, we obtain numerical solution for the reactant concentration field. It reveals from the study that the values of concentration profile enhances with the increase of the magnetic field and decreases with increase of Schmidt number as well as the reaction rate parameter. Most importantly, when the solute distribution along the surface increases then the concentration profile decreases. [ABSTRACT FROM AUTHOR]

An updated numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses is developed. A shear-thinning fluid modelling the deformation dependent viscosity of blood is considered for the characterization of generalized Newtonian behaviour of blood. The arterial model is treated as two-dimensional and axisymmetric with an outline of the stenosis obtained from a three-dimensional casting of a mildly stenosed artery. The full Navier-Stokes equations governing blood flow are written in the dimensionless form and the solution is accomplished by finite time-step advancement through their finite difference staggered grid representations. The marker and cell (MAC) method comprising the use of a set of marker particles moving with the fluid is used for the purpose. Results are obtained for three differently shaped stenoses - irregular, smooth and cosine curve representations. The present results do agree well with those of existing investigations in the steady state, but contrary to their conclusions the present findings demonstrate that the excess pressure drop across the cosine and the smooth stenoses is caused by neither their smoothness nor their higher degree of symmetry relative to the irregular stenosis, but is rather an effect of area cover with respect to the irregular stenosis. This effect clearly prevails throughout the entire physiological range of Reynolds numbers. Further the in-depth study in flow patterns reveals the development of flow separation zones in the diverging part of the stenosis towards the arterial wall, and they are influenced by non-Newtonian blood rheology, distensibility of the wall and flow unsteadiness in order to validate the applicability of the present model. [ABSTRACT FROM AUTHOR]

We establish theoretically multitude scaling laws of a self-similar (statistical) axisymmetric turbulent wake. At infinite Reynolds number limit, the flow evolves as general power law and a new exponential law of streamwise distance, consistent with the criterion of equilibrium similarity hypothesis. We found power law scalings for components of the homogeneous dissipation rate (ϵ) obeying the non-Richardson-Kolmogorov cascade as ϵ u ∼ k u 3 / 2 / ( l R e l m ) , ϵ v ∼ k v 3 / 2 / l , k v ∼ k u / R e l 2 m , 0 < m < 3. Here ku and k v are the components of the Reynolds normal stress, l is the local length scale, and Rel is the Reynolds number. The Richardson-Kolmogorov cascade corresponds to m = 0. For m ≈ 1, the power law agrees with non-equilibrium scaling laws observed in recent experiments of the axisymmetric wake. On the contrary, the exponential scaling law follows the above dissipation law with different regions of existence for power index m = 3. At finite Reynolds number with kinematic viscosity ν, scalings obey the dissipation laws ϵu ∼ νku/l2 and ϵ v ∼ ν k v /l2 with k v ∼ k u / R e l n . The value of n is preferably 0 and 2. Different possibilities of scaling laws and symmetry breaking process are discussed at length. [ABSTRACT FROM AUTHOR]