Incompressible Two-dimensional Boundary Layers Research Articles

A novel hybridity model for TiO2-CuO/water hybrid nanofluid flow over a static/moving wedge or corner

In this study, we are going to investigate semi-analytically the steady laminar incompressible two-dimensional boundary layer flow of a TiO2-CuO/water hybrid nanofluid over a static/moving wedge or corner that is called Falkner-Skan problem. A novel mass-based approach to one-phase hybrid nanofluid model that suggests both first and second nanoparticles as well as base fluid masses as the vital inputs to obtain the effective thermophysical properties of our hybrid nanofluid, has been presented. Other governing parameters are moving wedge/corner parameter (λ), Falkner-Skan power law parameter (m), shape factor parameter (n) and Prandtl number (Pr). The governing partial differential equations become dimensionless with help of similarity transformation method, so that we can solve them numerically using bvp4c built-in function by MATLAB. It is worthwhile to notice that, validation results exhibit an excellent agreement with already existing reports. Besides, it is shown that both hydrodynamic and thermal boundary layer thicknesses decrease with the second nanoparticle mass as well as Falkner-Skan power law parameter. Further, we understand our hybrid nanofluid has better thermal performance relative to its mono-nanofluid and base fluid, respectively. Moreover, a comparison between various values of nanoparticle shape factor and their effect on local heat transfer rate is presented. It is proven that the platelet shape of both particles (n1 = n2 = 5.7) leads to higher local Nusselt number in comparison with other shapes including sphere, brick and cylinder. Consequently, this algorithm can be applied to analyze the thermal performance of hybrid nanofluids in other different researches.

Non-similar solutions of the boundary layers equations with favorable and adverse pressure gradients, isothermal wall and slip boundary conditions: Application to Falkner–Skan gaseous flow

Abstract This article presents the non-similar solutions of the steady incompressible two-dimensional boundary layers equations of momentum and energy for Falkner–Skan gaseous flow with favorable and adverse pressure gradient under slip boundary conditions at a relatively low Mach number. By considering the slip boundary conditions at the fluid–wallinterface for the velocity and temperature, the non-dimensional boundary layer equations are solved numerically by using the centered implicit finite difference Keller Box methods. The results of the effects of different dimensionless parameters involved in the problem, namely the modified boundary layer Knudsen number, i.e., the slip parameter K and the shape parameter β on the local hydrodynamic and heat transfer characteristics of the flow are investigated and discussed. The results of these characteristics obtained from non-similar solutions are compared to those obtained from local similarity approach often used by several authors in the last decades. We show that for small shape parameter β and moderate or large values of the slip parameter, the self-similarity of the Falkner–Skan flows is generally lost because of slip boundary conditions. Therefore, the use of the local similarity approach may produce substantial errors for hydrodynamic and thermal characteristics of the flow as compared to non-similar solution. But in contrast, when β becomes larger than 2/3 up to 1, the flow regains its self-similarity character, in this case, the local similarity approach remains valid and may be used. While for β > 1 up to 2, the solutions of the boundary layer equations again become non-similar. Furthermore, a special attention was made to evaluate the separation point under rarefaction, the results show that the effect of slip parameter leads to decrease the separation point β s and it is concluded that separation of the boundary layer should be delayed in the slip flow regime.

A method for calculating the stability of boundary layers

Abstract A variable-step method is developed for the calculation of the two- and three-dimensional stability of compressible and incompressible two-dimensional boundary layers. The proposed method is compared with the computer code SUPORT and a finite-difference method. It is more efficient and requires less computer storage than both of these methods.

Multiscale model for turbulent flows

A is devised for computing general turbulent flows. The is an improvement over two-equation turbulence models in a critically important manner, that is, the new accounts for disalignment of the Reynolds-stress-tensor and the mean-strain-rate-tensor principal axes. The improved representation of the Reynolds-stress tensor has been accomplished through the introduction of a multiscale description of the turbulence, i.e., two energy scales are used corresponding to upper and lower partitions of the turbulence energy spectrum. A novel feature of the formulation is that the differential equation for the Reynolds-stress tensor is of first order, which in effect corresponds to what can be termed an algebraic stress model with convective terms. As a consequence of its mathematical simplicity, the is very efficient and easy to implement computationally. The is applied to a wide range of turbulent flows including homogeneous turbulence, compressible and incompressible two-dimensional boundary layers, and unsteady boundary layers including periodic separation and reattachment. Comparisons with corresponding experimental data show that the reproducesall salient features of the flows considered/Perturbation analysis of the viscous sublayer shows that integration through the sublayer can be accomplished with no special viscous modifications to the closure coefficients appearing in the model.

Effects of Gravity and Surface Tension Upon Liquid Jets Leaving Poiseuille Tubes

A method is developed for approximating the transverse velocity component in the incompressible two-dimensional boundary layer equations. The method is restricted to flows that are symmetrical in the transverse coordinate, and it facilitates easy numerical integration in such problems as the prediction of jet and wake flows. The prediction of velocity profiles and diameters for free exiting Poiseuille flows, under the influence of both gravity and surface tension, is then undertaken. Analytical results obtained by the present method are found to agree very closely with experiments. The experiments also show that, in low Weber number situations, contact angle at the exit plane can dominate the early relaxation of the exit profile.

Similarity conditions for heat transfer in incompressible two-dimensional laminar boundary layer flow

Similarity conditions are presented for the solution of some problems of heat transfer in incompressible two-dimensional boundary layer flow. The treatment holds for forced convection as well as for free convection. For free convection no a priori restriction is made with respect to geometry or temperature distribution of the solid surface. For forced convection the treatment is restricted to uniform bulk flow parallel to a flat surface of non-uniform temperature or heat flux. The results are summarized in some tables that facilitate comparison with older work.