At the outset, this work aims to carried out an analytical investigation of forced convection by establishing a laminar flow into circular duct under convective boundary conditions third type for non-Newtonian nanofluid, fluid containing TiO2 uniformly dispersed in aqueous solution with 0.5wt% CMC solutions (Carboxymethyl Cellulose) is used as working fluid. The viscous dissipation effects are ...

Simple, e cient and accurate nite di erence methods are introduced for 3D unsteady viscous incompressible ows in the vorticity-vector potential formulation on non-staggered grids. Two di erent types of methods are discussed. They di er in the implementation of the normal component of the vorticity boundary condition and consequently the enforcement of the divergence free condition for vorticity...

Sensitive boundary condition dependence (BCD) is reported in a convectively unstable system with noise, where the amplitude of generated oscillatory dynamics in the downstream depends sensitively on the boundary value. This BCD is explained in terms of the decrease (relaxation) of the comoving Lyapunov exponent (characterizing the convective instability) from upstream to downstream [K. Fujimoto...

where the symbols ∆, ∇, and ∇· stand for the Laplacian, gradient, and divergence operators, respectively (∆u is the vector of components ∆ui); the number μ is a viscous constant; f is a given vector function; β = (U,V)t is a given C1 function. The system (1.1) may be obtained by linearizing the steady-state barotropic compressible viscous Navier-Stokes equations without an ambient flow (see [8,...

In thermal convection, coherent flow structures emerge at high Rayleigh numbers as a result of intrinsic hydrodynamic instability and self-organization. They range from small-scale thermal plumes that are produced near both the top and the bottom boundaries to large-scale circulations across the entire convective volume. These flow structures exert viscous forces upon any boundary. Such forces ...