Laminar boundary-layer flows with small buoyancy effects

Natural convection on horizontal, inclined, and vertical plates with variable surface temperature or heat flux

Effects of buoyancy forces in a forced laminar convection flow over a horizontal flat plate is analyzed. It is shown that the solutions may be expanded into power series in Grx/Rex2.5 whose first terms express the solution for the purely forced convection flow. A numerical example is given to show the effects of Grashof number on the velocity profile, the temperature profile, and the Nusselt number.

The effects of buoyancy-induced streamwise pressure gradients on laminar forced convective flow and heat transfer over a horizontal flat plate are studied analytically by the local similarity and local nonsimilarity methods of solution. Numerical results for the local surface heat transfer, wall shear stress, and velocity and temperature distributions are presented for gases having a Prandtl number of 0.7. It is found that both the local Nusselt number and the friction factor increase with increasing buoyancy forces for aiding flow and decrease with increasing buoyancy forces for opposing flow. With regard to the heat transfer results, significant buoyancy effects were encountered for Grx/Rex5/2 > 0.05 and < −0.03, respectively, for aiding and opposing flows. The buoyancy-affected velocity profiles for the aiding-flow case exhibited an overshoot beyond the free stream velocity. Results from previously reported series solutions and from an integral momentum/energy solution were found to be accurate only when the buoyancy effects are small. The present study provides results for intermediate range buoyancy force effects, which have not been reported previously.

Laminar mixed convection over horizontal flat plate embedded in a non-Darcian porous medium with suction and injection

Mixed convection boundary layer flow of a micropolar fluid on a horizontal flat plate with power law variation in surface temperature

An analysis is made of the effects of buoyancy forces in a laminar forced-convection flow on a vertical flat plate by using the perturbation method. The solutions are obtained up to the 3rd order approximation; accordingly, the range of applicability of the solution by the analysis is expanded. It is proved that solutions of the 1st report are applicable to a wider region of ξ for the fluids of Pr ≥1 in the case of friction factor and of all Prandtl numbers as to heat transfer, by comparing with the results of this paper. Furthermore, the friction factor and heat transfer coefficient are calculated, and it is shown that a linear relation exists between values. Also it is proved that the solution of energy equation Θ′(ξ, 0) can be presented by a similar formula, Θ′(ξ, 0) = -(0.664+0.48ξ)Pr1/3, (0≤ξ≤0.3), which is formulated in a purely forced-convection heat transfer problem.

An analysis of a laminar mixed convection boundary-layer flow of an optically dense viscous fluid along a highly heated permeable vertical flat plate in the presence of thermal radiation is performed. The radiative heat flux term is expressed using the Rosseland diffusion approximation. Here, the fluid density is assumed to vary exponentially with temperature. The dimensionless boundary layer equations are reduced to a convenient form by primitive variable transformation and then integrated numerically employing the implicit finite difference method along with the Gaussian elimination technique. Furthermore, the boundary-layer equations are also reduced to a set of nonsimilar equations with the help of the stream function formulation and are simulated by the implicit finite-difference Keller box method. The influence of different physical parameters on the velocity and temperature profiles, as well as on the shear stress and heat transfer rate, is shown and analyzed.

Natural convection near a corner of an arbitrary angle formed by two vertical flat plates with uniform surface heat flux

Starting from the differential equation of mass transfer in laminar flow and the appropriate boundary condition, expressions are derived for the rate of mass transfer from (a) a flat plate in a longitudinal fluid stream, (b) a vertical flat plate by natural convection, (c) the forward stagnation point of a sphere in a fluid stream. Only outward mass transfer is considered; this corresponds to blowing outwards from the plate at a rate inversely proportional to the boundary-layer thickness. The Kármán-Pohlhausen-Kroujiline method is used. Where appropriate the Prandtl or Schmidt number has been taken as 0⋅71. The calculations are valid for all mass-transfer processes for which a single diffusion coefficient can be ascribed to the diffusing property, but are particularly relevant to the combustion of liquid fuels, for which the outward mass-transfer rates are so high that important deviations occur from boundary-layer profiles without mass transfer. Despite the great temperature variations present in boundary layers with combustion, mean values for the fluid properties are assumed. In the case of natural convection, it is assumed that the body forces on the fluid in the boundary layer are everywhere zero; this leads to a less serious over-estimate of the buoyancy than the usual assumptions which are valid only for small temperature differences.

The linear stability of the laminar boundary layer flow of a Stokes wave in deep waters is investigated by means of a 'momentary' criterion of instability for unsteady flows. In the parameter range investigated, it is found that the flow is stable to 2-D perturbations. The least stable eigenmode of the resulting Orr-Sommerfield spectrum attains its maximum beneath the boundary layer of the Stokes wave. Moreover, an analysis of the associated pseudospectrum indicates that the laminar flow when modified by imperfections is unstable due to the non-normality of the Orr-Sommerfeld operator, and the unstable pseudoeigenmodes tend to peak within the boundary layer. The laminar flow of the Stokes wave is also stable to 3-D streamwise-independent perturbations. Instability is observed for the laminar flow with imperfections. The associated unstable pseudo-eigenmodes are streamwise vortical rolls similar to Langmuir cells. The laminar boundary layer flow of a Stokes wave appears to be stable to infinitesimal perturbations, but it may likely be unstable to finite perturbations, as in Poiseuille pipe flows. The present results are supportive of the recent experimental evidence of spontaneous occurrence of turbulence beneath unforced nonbreaking surface waves.

Correlations for laminar mixed convection on vertical, inclined and horizontal flat plates with uniform surface heat flux

An approach for evaluating aerosol particle deposition from a natural convection flow onto a vertical flat plate

Similarity Solution of Unsteady Combined Free and Force Convective Laminar Boundary Layer Flow about a Vertical Porous Surface with Suction and Blowing

On the solution of the convection equation in laminar boundary layer flows

An investigation is undertaken of the unsteady response of two-dimensional laminar free convection boundary layer flow of a viscous incompressible fluid along a semi-infinite vertical heated plate where the mean surface heat flux oscillates with a small amplitude about a steady profile. The buoyancy forces are favourable, resulting from a positive flux of heat from the surface of the plate into the fluid. The interaction of the time-periodic heat flux with the usual boundary-layer flow is examined by using a linearized theory. Solutions are obtained using three distinct methods, namely an extended series expansion method for low frequencies, an asymptotic series expansion method for high frequencies and a fully numerical finite difference method for general frequencies. Calculations have been carried out for a wide range of parameters to examine the solutions in terms of the amplitude and phase angle of the fluctuating parts of the surface shear stress and the surface temperature. It has been found that the amplitude and phase angle of both the shear stress and the surface temperature predicted by these three methods are in very good agreement in their respective ranges of validity.