Laminar natural convection in water near the density extremum along a vertical plate with sinusoidal surface temperature variation

Summary. The steady laminar boundary-layer flow along a vertical plate immersed in water at 4°C is studied. The plate temperature varies sinusoidally with x between 0°C and 8°C, where the density of water varies parabolically and is almost symmetrical about 4°C. The results are obtained with the direct numerical solution of the boundary layer equations taking into account the temperature dependence of all water thermophysical properties (, , and c_p). It is found that the amplitude of oscillation of temperature gradient and wall shear stress remains constant with x, in contrast to previous studies concerning fluids with constant thermophysical properties and linear density-temperature relationship, where the amplitude of these quantities changes with x. It was also found that there is an inner boundary layer near the plate with periodic characteristics and that the velocity boundary layer thickness increases with x.     

Mixed convection flow near an axisymmetric stagnation point on a vertical cylinder

The mixed convection flow near an axisymmetric stagnation point on a vertical cylinder is considered. The equations for the fluid flow and temperature fields reduce to similarity form that involves a Reynolds number R and a mixed convection parameter λ, as well as the Prandtl number σ. Numerical solutions are obtained for representative values of these parameters, which show the existence of a critical value λ _c  = λ _c (R, σ) for the existence of solutions in the opposing (λ < 0) case. The variation of λ _c with R is considered. In the aiding (λ > 0) case solutions are possible for all λ and the asymptotic limit λ → ∞ is obtained. The limits of large and small R are also treated and the nature of the solution in the asymptotic limit of large Prandtl number is briefly discussed.     

Mixed convection in vertical internal flow of a micropolar fluid

The theory of micropolar fluids due to Eringen is used to formulate a set of equations for the flow and heat transfer characteristics of the combined convection micropolar flow in vertical channels. It is found that the microstructure and substructure parameters have significant effects on the flow and thermal fields. By making the Newtonian solvent more and more micropolar, it is possible to obtain drag reduction as well as reduced heat transfer characteristics.     

Mixed convection around a horizontal circular cylinder immersed in a Darcy flow

The forced and free mixed convection problem around a horizontal circular cylinder in a fluid-saturated porous medium is investigated at small Peclet number with Gr/Re = O(1). The Darcy flow model is used for the velocity field. The method of matched asymptotic expansions is used to obtain asymptotic solutions for small Peclet number. It is shown that, up to the present order of approximation, natural convection has no effects on the temperature field, and the effects of the parameter Gr/Re on the velocity field are examined in detail.     

Influence of free convection on the rate of aerosol precipitation from a laminar gas stream

Results of experiments and computational estimates are presented which show that turbulization of a stream under the influence of free convection can substantially intensify aerosol deposition on channel walls from a laminar gas stream.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 1, pp. 44–49, July, 1977.     

Mixed convection boundary-layer on a vertical cylinder embedded in a saturated porous medium

Summary The mixed convection boundary layer on a vertical circular cylinder embedded in a saturated porous medium is considered. It is found that the flow depends on the parameter =R _a /P _e whereR _a andP _e are the Rayleigh number and Peclet number respectively. gives the ratio of the velocity scale for free convection to that for the forced convection. When is small the solution is, to a first approximation, obtained by a known heat conduction problem. The flow near the leading edge is considered and it is shown that a solution is possible only for ₀, ₀–1.354, and that a stable finite-difference solution away from the leading edge can be obtained only if –1; with <–1 there is a region of reversed flow near the cylinder. The finite-difference scheme is unable to give a satisfactory solution at very large distances from the leading edge, and to overcome this difficulty a simple approximate solution is developed. This solution shows that at large distances along the cyclinder, forced convection eventually becomes the dominant mechanism for heat transfer. This is also confirmed by an asymptotic solution of the full boundarylayer problem.Nomenclature a radius of cylinder - g acceleration of gravity - K permeability of the porous medium - N _u non-dimensional Nusselt number - r radial coordinate - non-dimensionalr=r/a - R _a Rayleigh number=(g T)Ka/ - P _e Peclet number=U ₀ a/ - T temperature - T _w temperature of the cylinder (constant) - T ₀ temperature of the ambient fluid (constant) - T temperature difference=T _w –T ₀ - u Darcy's law velocity in thex direction - U ₀ velocity of the outer flow - v Darcy's law velocity in ther-direction - x coordinate measuring distance along the cylinder - X non-dimensionalx,=x(aP _e )^–1 - equivalent thermal diffusivity - coefficient of thermal expansion - ratio of free to forced convection=R _a /P _e - viscosity of the convective fluid - density of the ambient fluid - non-dimensional temperature - stream function With 2 Figures     

Mixed convection flow in a porous medium bounded by two vertical walls

The aim of the investigation is to study the fully developed mixed convection flow in a porous medium bounded by two vertical walls having a linear axial temperature variation. Solution of the governing second order simultaneous differential equations, derived by non-dimensionalising the momentum and energy equations, has been obtained by converting them into a fourth order differential equation. It has been found that the fourth order differential equation has five different solutions depending upon the values of the Darcy number, Rayleigh number and ratio of the effective viscosity of the porous domain to the viscosity of the fluid. Graphical representation of the analytical solution shows that the flow is of parabolic type only for higher Darcy number whereas there is a reverse type of motion for lower Darcy numbers. The effect of the ratio of the effective viscosity of the porous matrix to the viscosity of the fluid is to decrease the velocity field.     

Turbulent transition of a laminar boundary layer in the axisymmetric flow of a jet over plane surfaces normal to the stream

Results are presented of experimental investigations of the hydrodynamics of the wall boundary layer on a plate over which an axisymmetric jet flows transversely. The conditions of existence and transition to turbulent of the laminar boundary layer are determined.     

Mixed convection boundary layer flow on a vertical surface in a saturated porous medium

Summary The flow of a uniform stream past an impermeable vertical surface embedded in a saturated porous medium and which is supplying heat to the porous medium at a constant rate is considered. The cases when the flow and the buoyancy forces are in the same direction and when they are in opposite direction are discussed. In the former case, the flow develops from mainly forced convection near the leading edge to mainly free convection far downstream. Series solutions are derived in both cases and a numerical solution of the equations is used to describe the flow in the intermediate region. In the latter case, the numerical solution indicates that the flow separates downstream of the leading edge and the nature of the solution near this separation point is discussed.     

Mixed convection with viscous dissipation in a vertical channel filled with a porous medium

Summary The fully developed laminar mixed convection flow in a vertical plane parallel channel filled with a porous medium and subject to isoflux ÷ isothermal wall conditions is investigated assuming that (i) the Darcy law and the Boussinesq approximation hold, (ii) the effect of viscous dissipation is significant, and (iii) the average flow velocity U _m (as an experimentally accessible quantity) is prescribed. It is shown that under these conditions both upward (U _m > 0) and downward (U _m < 0) laminar flow solutions may exist as long as U _m does not exceed a maximum value U _{m, max}. The velocity field can either be unidirectional or bidirectional. Moreover, bidirectional flow configurations are possible also for U _m = 0. A remarkable feature of the problem is that for U _m < U _{m, max} even two solution branches (dual solutions) exist, which merge when U _m approaches its maximum value U _{m, max}. The mechanical and thermal characteristics of the flow configurations associated with the dual solutions are investigated in the paper analytically and numerically in detail.     

Special features of free convection in water at temperatures below 277° K

An analysis of the parametric equations and of experimental investigations has shown the existence of a minimum in the heat transfer by free convection in water at temperatures below 277° K, for positive temperature heads, not exceeding 16°. A physical interpretation of the observed effect is given. The displacement of the heat-transfer minimum as a function of the temperature head is given.     

Effect of a temperature gradient on the heat transfer during laminar natural convection along a vertical wall

Results are shown of calculations and of an experimental study concerning the heat transfer during laminar natural convection along a vertical wall, in the general case when the temperature excess varies along the wall height according to an arbitrary law.     

Transient free convection flow of water at 4°C past a semi-infinite vertical plate

Transient free convection flow of water at 4°C past an isothermal semi-infinite vertical plate, when its density is maximum, is analysed by employing an explicit finite-difference technique. The transient velocity and temperature, the average skin-friction and the average Nusselt number are shown graphically for Prandtl number Pr=11.4 (4°C) and 7.0 (20°C). It has ben observed that when the density of water is maximum, it takes more time to reach its steady state. Also the average skin-friction decreases considerably when the water is at 4°C, as compared to that at 20°C. The average Nusselt number increases at small values of time and decreases at large values of time when the water is at 4°C.     

Heat and mass transfer in a binary laminar boundary layer with free convection on a vertical porous surface

An approximate analytical solution of heat and mass transfer in a binary laminar boundary layer with free convection on a vertical surface is presented. The numerical solution is compared with an approximate analytical solution obtained by another method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 19–28, July, 1971.     

Free convection in the laminar boundary layer flow of a thermomicropolar fluid past a vertical flat plate with suction/injection

Summary The effect of suction/injection in the laminar free convection flow of a thermomicropolar fluid past a nonuniformly heated vertical flat plate has been considered. The conditions under which similarity exists have been examined. The resulting system of non-linear ordinary differential equations has been solved numerically after transforming the infinite domain of boundary layer coordinate into a finite domain. The effects of variation of the boundary condition parameter and suction/injection parameter on the velocity, microrotation and temperature fields and the heat transfer coefficient have been studied graphically. The skin-friction parameter and the gradient of microrotation on the wall have been tabulated. It is found that there is significant increase in velocity, skin-friction and the heat transfer coefficient with the decreasing concentration of microelements.With 4 Figures