Free convection of highly viscous liquid along a vertical finite plate with constant heat flux

On the basis of asymptotic analysis of the complete Navier-Stokes and energy equations, using the Prandtl number as the basic parameter of the expansion, the form of the velocity profile of free-convective flow is determined at large Prandtl numbers.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 1, pp. 59–63, January, 1985.     

Free convective heat transfer at a vertical semiinfinite plate

The effect of the boundary layer at the leading edge on heat transfer near a vertical semiinfinite heated plate is determined by means of matched asymptotic expansions. The criterial relation for air is in good agreement with existing experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 1, pp. 32–39, July, 1977.     

Numerical study of an unsteady free convective magnetohydrodynamic flow of a dissipative fluid along a vertical plate subject to a constant heat flux

A new method is presented to solve the transient free convection MHD flow of a dissipative fluid along a semi-infinite vertical plate with mass transfer, the surface of which is exposed to a constant heat flux. The non-linear system of partial differential equations is numerically solved by means of the network simulation method, based on the thermo–electric analogy. This method permits the direct visualisation and evolution of the local and/or integrated transport variables (temperatures, velocities, concentrations and fluxes) at any point or section of the medium. At the same time, the solution for both transient and steady-state problems is obtained, the only requirement being finite-difference schemes for the spatial variable, while its programming does not involve manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The technique is always stable and convergent. Velocity, temperature and concentration profiles, local skin-friction, local Nusselt and local Sherwood numbers are plotted for air. The influence of the viscous dissipation, buoyancy ratio parameter, Schmidt number and magnetic parameter on heat and mass transfer and on the time needed to reach the steady-state are discussed.     

Stability of free convection with uniform suction or injection from a vertical flat plate subjected to a constant wall heat flux

Summary A theoretical study is presented for the stability characteristics of the laminar free convection boundary layer flow along a vertical porous (permeable) flat plate subjected to a constant heat flux. The disturbance equations are solved numerically on the basis of the linear stability theory for a wide range of values of the modified Grashof number,G, and some values of the suction or injection parameterX when the Prandtl number, Pr, is 0.73 (air). These solutions indicate the important role of the parametersG andX on the flow and heat transfer characteristics. It is found that the present results are in very good agreement with those from the open literature.     

Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction

An exact solution to the flow due to impulsive motion of an infinite vertical plate in its own plane in the presence of i) species concentration ii) constant heat flux at the plate iii) chemical reaction of first order, has been derived by the Laplace-transform technique. Velocity and concentration profiles are shown on graphs. It is observed that due to the presence of first order chemical reaction, the velocity decreases but the skin-friction being positive at large values of the chemical reaction parameter, there may not occur separation of the flow near the plate.     

Free convective heat exchange of a cylinder with an exponentially decaying heat flux on the surface

Results of a numerical calculation of heat liberation from a vertical cylinder to the surrounding medium are presented. The data obtained are generalized to a wide range of problem parameters.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 3, pp. 508–512, September, 1979.     

Mixed convection near a non-orthogonal stagnation point flow on a vertical plate with uniform surface heat flux

Summary The interaction of a buoyancy induced mixed convection flow and a free stream impinging at some angle of incidence on a vertical flat plate with a prescribed surface heat flux is studied in this paper. The similarity equations are numerically solved for some values of the governing parameters. It is found that the buoyancy force and non-orthogonal mechanisms act to either reinforce or oppose one another. The stagnation point (separation point) is shifted at the left or at the right of the origin and it depends upon the balance between obliqueness and thermal effects.     

Boundary of the wave regime in film condensation with constant heat flux on a vertical surface

An expression for the boundary of the origin of the laminar-wave section of condensation was obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 6, pp. 958–962, June, 1985.     

On the free convection boundary layer on a vertical plate with prescribed surface heat flux

The free convection boundary layer on a vertical plate with a prescribed surface heat flux proportional to (1 +x ²)^µ (µ a constant) is discussed. For µ > –12 the boundary-layer solution develops from a similarity solution valid forx small to the one valid forx large. However, with µ –12 the similarity equations forx large are not solvable and the behaviour for largex in this case is discussed. It is found that there are two cases to consider, namely µ < –12 and µ = –12. In both cases the leading-order problem is homogeneous involving an arbitrary constant which is determined from an integral property of the full boundary-layer problem. However, in the former case the asymptotic behaviour is algebraic, with the perturbation to the leading-order solution, arising from the heat flux boundary condition, being ofO[x ^1+2µ]. The latter case also involves logarithmic terms, with the perturbation to be leading-order solution now being ofO[(logx)^–1].     

First-order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux

Summary A finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with uniform heat and mass flux is presented here, taking into account the homogeneous chemical reaction of first order. The velocity profiles are compared with the available theoretical solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.List of symbols C concentration - C species concentration in the fluid far away from the plate - C _w species concentration near the plate - C dimensionless concentration - D mass diffusion coefficient - Gc mass Grashof number - Gr thermal Grashof number - g acceleration due to gravity - j mass flux per unit area at the plate - K dimensionless chemical reaction parameter - K _l chemical reaction parameter - k thermal conductivity - Nu_x dimensionless local Nusselt number - dimensionless average Nusselt number - Pr Prandtl number - q heat flux per unit area at the plate - Sc Schmidt number - Sh_x dimensionless local Sherwood number - dimensionless average Sherwood number - T temperature - T temperature of the fluid far away from the plate - T _w temperature of the plate - T dimensionless temperature - t time - t dimensionless time - u ₀ velocity of the plate - U, V dimensionless velocity components inX,Y-directions, respectively - u, v velocity components inx, y-directions, respectively - X dimensionless spatial coordinate along the plate - x spatial coordinate along the plate - Y dimensionless spatial coordinate normal to the plate - y spatial coordinate normal to the plate - thermal diffusivity - volumetric coefficient of thermal expansion - * volumetric coefficient of expansion with concentration - coefficient of viscosity - kinematic viscosity - _x dimensionless local skin-friction - dimensionless average skin-friction     

Magnetohydrodynamic natural convection flow on a sphere with uniform heat flux in presence of heat generation

Summary Magnetohydrodynamic natural convection boundary layer flow on a sphere with uniform heat flux in presence of heat generation has been investigated in this paper. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is then solved numerically by two distinct efficient methods, namely (i) implicit finite difference method together with the Keller box scheme and (ii) perturbation or series solution technique. The results of the surface shear stress in terms of local skin friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution as well as temperature distribution are shown graphically for a selection of parameter sets consisting of the heat generation parameter and the magnetic parameter.     

Free convection heat transfer to steady radiating non-Newtonian MHD flow past a vertical porous plate

Non-Newtonian fluid motion generated by a vertical porous hot plate in the presence of a transverse magnetic field is studied when viscous and ohmic dissipations are significant. When the temperature of the plate is very large, a general differential approximation for the radiative flux enables the asymptotic flow, valid far away from the tips of the plate, to reduce to a set of nonlinear and coupled ordinary differential equations. The solutions of these differential equations are studied for both small and large values of the absorption coefficient. The temperature, velocity and magnetic field distributions are discussed quantitatively. A primary conclusion of the analysis is that the distributions of temperature, velocity and magnetic field are much larger for a fluid with a large absorption coefficient than for a fluid with a small absorption coefficient.     

Heat transfer by natural convection and hydrodynamics on a vertical plate with a discontinuity in the heat flux

It is observed that the temperature distribution in the boundary layer changes qualitatively and the heat transfer in the upper part of a plate intensifies substantially in comparison with a surface with a continuous heat flux. For the case of substantial heat flux density in the initial stage of formation of a free convective flow a two-dimensional vortex is found to appear.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 2, pp. 179–183, March–April, 1995.     

Mixed convective flow and heat transfer in a vertical helicoidal pipe with finite pitch

Fully developed laminar mixed convective flow and heat transfer in a vertical helicoidal pipe with finite pitch is studied numerically in this paper. The centrifugal, buoyancy, and torsion forces created by the pitch of the helix are considered. The thermal boundary conditions are uniform heat flux axially and uniform wall temperature peripherally. The velocity, the temperature profiles, the friction factor, and the Nusselt number are obtained. The results indicate that torsion can significantly change the axial and secondary flow patterns and temperature distributions in the helicoidal pipe with a fixed pressure gradient. Torsion can also remarkably affect the flow rate, the friction factor, and the Nusselt number. However, at a fixed Dean number, there is only slight difference in the Nusselt numbers of the upward and downward flow.The results presented in this paper were obtained in the course of research sponsored by the National Science Foundation (NSF) under Grant No. CTS-9017732     

Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing fluid along a semi-infinite vertical permeable moving plate in the presence of a uniform transverse magnetic field and thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The obtained analytical results reduce to previously published results on a special case of the problem. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and the Sherwood number are presented and discussed.     

Heat transfer response of free convection flow from a vertical heated plate to an oscillating surface heat flux

Summary 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.