Radiation-conduction interaction on mixed convection from a horizontal circular cylinder

A mixed convection flow of an optically dense viscous incompressible fluid along a horizontal circular cylinder has been studied with the effect of radiation when the surface temperature is uniform. Using appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity form. Solutions of the governing equations are obtained employing the implicit finite difference method. Effects of varying the pertinent parameters, such as, the Planck number, R _w the surface temperature parameter, θ_w and the buoyancy parameter, α on the local skin-friction and local heat transfer coefficients are shown graphically as well as in tabular form against the curvature parameter ξ, while taking Prandtl number Pr = 1.0. It is found that an increase of R _d,θ_w or α leads to increases in the values of the local skin-friction and the local rate of heat transfer coefficients. At the stagnation point asymptotic solutions for large value of α are also obtained and the effect of the other pertinent parameters on the formation of the flow separation are studied. Received on 28 July 1998     

Natural convection-radiation interaction on boundary layer flow along a thin vertical cylinder

A free convertion flow of an optically dense viscous incompressible fluid along a vertical thin circular cylinder has been studied with effect of radiation when the surface temperature is uniform. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations. Solutions of the governing equations are obtained employing the implicit finite difference methods together with Keller box scheme as well the local nonsimilarity method with second order truncation for all ξ (nondimensional transverse curvature parameter) in the interval [0,10] and are expressed in terms of local Nusselt number for a range of values of the pertinent parameters. Effects of pertinent parameters, such as, the radiation parameter, R _d , the surface temperature parameter, θ _w , taking Prandtl number, Pr, equals 0.7 on the velocity and temperature field are also presented graphically. From the solution it is seen that increase of R _d , or θ _w leads to increase in the local rate of heat transfer coefficients. Results obtained by both the methods are obtained in excellent agreement between each other upto ξ = 10.     

Thermal radiation effects on the natural convection flow over an isothermal horizontal plate

The natural convection boundary layer flow with conduction-radiation interaction of a viscous incompressible fluid along an isothermal horizontal surface has been studied. The equations valid in the upstream, downstream as well as in the entire regime are obtained. Solutions of the non-similar equations governing the flow for the entire regime and the downstream regime are obtained by employing an efficient implicit finite difference approximation together with the Keller box method, for a Prandtl number of 0.73. Also, the effects of the pertinent parameters, R _d, the radiation-conduction parameter and θ_w, the surface heating parameter are shown graphically in terms of the local skin-friction and the local rate of heat transfer. Comparison of the results obtained for the upstream and the downstream regimes shows good agreement over the entire regime. Effects of R _d and θ_w are also shown on the streamlines and the isotherms. Received on 15 December 1998     

Radiation effect on mixed convection along a vertical plate with uniform surface temperature

This paper investigates the effect of radiation on the forced and free convection flow of an optically dense viscous incompressible fluid along a heated vertical flat plate with uniform free stream and uniform surface temperature with Rosseland diffusion approximation. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations valid in the forced convection regime as well as in the free convection regime. A group of transformation is, also, introduced to reduce the boundary layer equations to a set of local nonsimilarity equations valid in both the forced and free convection regimes. Solutions of the governing equations are obtained by employing the implicit finite difference methods together with Keller box scheme and are expressed in terms of local shear stress and local rate of heat transfer for a range of values of the pertinent parameters.     

MHD mixed convective heat transfer flow about an inclined plate

Mixed convection heat transfer about a semi-infinite inclined plate in the presence of magneto and thermal radiation effects is studied. The fluid is assumed to be incompressible and dense. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the non-similar boundary layer equations, which are then solved numerically using the Keller box method. The effects of the mixed convection parameter R _i, the angle of inclination α, the magnetic parameter M and the radiation–conduction parameter R _d on the velocity and temperature profiles as well as on the local skin friction and local heat transfer parameters. For some specific values of the governing parameters, the results are compared with those available in the literature and a fairly good agreement is obtained.     

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF). The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method. Moreover, the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method, for the whole range of the local transpiration parameter ζ. Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough. However, in these particular regions, solutions are acquired with the aid of a regular perturbation method. The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (= 0.005, 0.01, 0.05). Furthermore, the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.     

Thermal radiation effects on MHD flow past a semi-infinite inclined plate in the presence of mass diffusion

MHD mixed free-forced heat and mass convective steady incompressible laminar boundary layer flow of a gray optically thick electrically conducting viscous fluid past a semi-infinite inclined plate for high temperature and concentration differences is studied. A uniform magnetic field is applied perpendicular to the plate. The density of the fluid is assumed to reduce exponentially with temperature and concentration. The usual Boussinesq approximation is neglected due to the high temperature and concentration differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying an efficient technique. The effects of the density/temperature parameter n, the density/concentration parameter m, the local magnetic parameter M_x and the radiation parameter R are examined on the velocity, temperature and concentration distributions as well as the coefficients of skin-friction, heat flux and mass flux.     

COUPLING BETWEEN LAMINAR FILM CONDENSATION AND NATURAL CONVECTION ON OPPOSITE SIDES OF A VERTICAL PLATE

Theoretical analyses which incorporate one-dimensional heat conduction along a plate and transverse heat conduction approximations are presented to predict the net heat transfer between laminar film condensation of a saturated vapour on one side of a vertical plate and boundary layer natural convection on the other side. It is assumed that countercurrent boundary layer flows are formed on the two sides. The governing boundary layer equations of this problem and their corresponding boundary conditions are all cast into dimensionless forms by using a non-similarity transformation. Thus the resulting system of equations can be solved by using the local non-similarity method for the boundary layer equations and a finite difference method for the heat conduction equation of the plate. The plate temperature and the heat flux through the plate are repetitively determined until the solutions for each side of the plate match. The predicted results show that the effect of Pr_c is not negligible for larger values of A* (thermal resistance ratio between natural convecti on side and condensing film side) and the approximation of transverse heat conduction overpredicts the plate temperature for lower values of R_t (thermal resistance ratio between plate and condensing film). However, no significant differences are observed between the two different approximations for higher values of R_t. © by 1997 John Wiley & Sons, Ltd.     

Radiative and Thermal Dispersion Effects on Non-Darcy Natural Convection with Lateral Mass Flux for Non-Newtonian Fluid from a Vertical Flat Plate in a Saturated Porous Medium

The problem of natural convective heat transfer for a non-Newtonian fluid from an impermeable vertical plate embedded in a fluid-saturated porous medium has been analyzed. Non-Darcian, radiative and thermal dispersion effects have been considered in the present analysis. The governing boundary layer equations and boundary conditions are cast into a dimensionless form and simplified by using a similarity transformation. The resulting system of equations is solved by using a double shooting Runge–Kutta method. The effect of viscosity index n, the conduction–radiation parameter R, the non-Darcy parameter Gr*, the thermal dispersion parameter Ds and the suction/injection parameter f_w on the fluid velocities, temperatures and the local Nusselt number are discussed.     

Thermofluiddynamic experiments with a heated and rotating circular cylinder in crossflow

Two-dimensional flow fields and temperature boundary layer profiles around a heated and rotating circular cylinder in crossflow were experimentally investigated for a subcritical freestream-Reynolds-number 5.6 · 10⁴ corresponding to a flow velocity of 7 m/s. Test parameter was the ratio of free stream velocity to peripheral speed, which encompasses the range between zero and 2.5. An electronically-controlled hot wire measurement technique, practicable for the requirements of 1–2 mm boundary layer thickness, was used. The numerous reliable test results confirm previous reported experiments. Characteristic features in heat transfer are discussed.List of symbols C _b correction factor for blockage - n rotation rate in rpm - r radial coordinate - R cylinder radius - Re Reynolds-number = U 2R/v - Re _R circumferential Reynolds-number = U _R 2R/v - T local temperature - U velocity - = U · C _b/U _R velocity ratio of air flow and cylinder surface, corrected for blockage - v kinematic viscosity - = T — T /T _w — T non-dimensional temperature Indices undisturbed flow conditions - w wall - R circumferential - c critical Dedicated to Alfred Walz on the occasion of his 80th birthday     

Variable permeability effect on buoyancy-induced inclined boundary layer flow in a saturated porous medium with variable wall temperature

The analysis is carried out for buoyancy-induced boundary layer flow adjacent to an inclined heated surface in a saturated porous medium incorporating the variation of permeability and thermal conductivity due to paking particles with non-uniform temperature. The surface temperature is assumed to vary as a power function of the axial coordinate measured from the leading edge of the surface. Both the streamwise and normal component of the buoyancy force are retained in the momentum equations. Numerical solutions are obtained in the cases of uniform and nonuniform permeability and various values of the inclination parameter ξ (x) = (Ra _x cos ϕ)^1/3 tan ϕ by using finite difference method. The problem is solved using nonsimilarity solutions for the case of variable wall temperature. Results for the details of the velocity and temperature fields as well as local Nusselt number have been presented.     

Effect of different sized transverse square grooves on a turbulent boundary layer

The effect of three different sized transverse square grooves (5, 10, and 20 mm) on a turbulent boundary layer was investigated at two values of momentum thickness Reynolds numbers (R _θ =1,000 and 3,000) using hot-wire anemometry. The ratios of the groove depth to the boundary layer thickness (d/δ ₀) are approximately 0.07, 0.13, and 0.27. Wall shear stress (τ _w), mean velocity (U), and turbulence intensity downstream of the grooves are compared to those on a corresponding smooth wall The effects of the grooves are more significant at the higher R _θ , with the most pronounced effects caused by the largest size groove. There is an increase in mean velocity (U), streamwise (u′/U ₀), and wall-normal (ν′/U ₀) turbulence intensities in the near-wall region immediately downstream of the grooves. The increase propagates outwards in the layer as the streamwise distance increases downstream of the grooves. The increase in ν′/U ₀ is much more significant than that of u′/U ₀, which is also evident in the spectra of u′ and ν′. There is an increase in τ _w over the smooth wall value immediately downstream of the grooves at R _θ =1,000, with the increase being more pronounced as the groove size increases. The growth of the internal layer downstream of the grooves is found to scale with the groove size, and is more rapid at R _θ =3,000. Published online: 23 November 2002     

Mixed convection boundary layer flow over a horizontal circular cylinder with Newtonian heating

The steady mixed convection boundary layer flow over a horizontal circular cylinder, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered in this study. The governing boundary layer equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into non-similar equations before they are solved numerically using a numerical scheme known as the Keller-box method. Numerical solutions are obtained for the skin friction coefficient Re ^1/2 C _f and the local wall temperature θ _w (x) as well as the velocity and temperature profiles with two parameters, namely the mixed convection parameter λ and the Prandtl number Pr.     

On thermal boundary layer of a non-Newtonian fluid on a power-law stretched surface of variable temperature with suction or injection

 Heat transfer characteristics of a non-Newtonian fluid on a power-law stretched surface of variable temperature with suction or injection were investigated. Similarity solutions of the laminar boundary layer equations describing heat transfer and fluid flow in a quiescent fluid were obtained and solved numerically. Velocity and temperature profiles as well as the Nusselt number, Nu, were studied for two thermal boundary conditions; uniform surface temperature and variable surface temperature, for different parameters; Prandtl number Pr, temperature exponent b, velocity exponent m, injection parameter d and power-law index n. It was found that decreasing injection parameter d, and power-law index n and increasing Prandtl number Pr and surface temperature exponent b enhance the heat transfer coefficient. Received on 27 April 2000     

Flow and heat transfer from a continuous surface in a parallel free stream of viscoelastic second-order fluid

Boundary layer solutions are presented to investigate the steady flow and heat transfer characteristics from a continuous flat surface moving in a parallel free stream of viscoelastic fluid. Numerical results are presented for the distribution of velocity and temperature profiles within the boundary layer. The effects of the viscoelastic parameter of the fluid on the shear stress at the wall and rate of heat transfer are studied. For the same Reynolds (based on the larger of the free stream and wall velocities) and Prandtl numbers and the same velocity difference |U _w >|, larger skin-friction and heat transfer coefficient result for U _w > than for U _w <.     

Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium

In this study, laminar boundary layer flow over a flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation, inertia effect and suction/injection is analyzed using the Keller box finite difference method. The flat plate is assumed to be held at constant temperature. The non-Darcian effects of convection, boundary and inertia are considered. Results for the local heat transfer parameter and the local skin friction parameter as well as the velocity and temperature profiles are presented for various values of the governing parameters. The non-Darcian effects are shown to decrease the velocity and to increase the temperature. It is also shown that the local heat transfer parameter and the local skin friction parameter increase due to suction of fluid while injection reverses this trend. It is disclosed that the effect of the viscous dissipation for negative values of Ec (T _w < T _∞) is to enhance the heat transfer coefficient while the opposite is true for positive values of Ec (T _w > T _∞). The results are compared with those available in the existing literature and an excellent agreement is obtained.     

Transient compressible boundary layer on a wedge impulsively set into motion

Summary The development of a compressible boundary layer over a wedge impulsively set into motion is studied in this paper. The initial motion is independent of the leading edge effect and the solutions are those of a Rayleigh-type problem. The motion tends to an ultimate steady state of Falkner-Skan type. The equations governing the transient boundary layer from the initial steady state to the terminal steady-state change their character after certain time due to the leading edge effect and thereafter solution depends on both the end conditions. Numerical solutions are obtained through the second-order accuracy upwind scheme. The effects of the Falkner-Skan parameter and the surface temperature on the transient flow and heat transfer are also studied. It has been found that the flow separation does not occur form–0.0707 when _w = 1.5 (hot wall), andm–0.118 when _0.5 (cold wall).     

Combined heat and mass transfer along a vertical moving cylinder with a free stream

The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u _w/(u _w + u _∞), where u _w and u _∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1 it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution. For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction decreases as the relative velocity between the surface and free stream decreases. Received on 17 May 1999     

Auto-correlation measurements and integral time scales in three-dimensional turbulent boundary layers

Auto-correlation, time and length scales of the three components of turbulence and power spectra in a three-dimensional turbulent boundary layer developing on a yawed flat plate have been obtained. The measurements indicate that close to the wall, in the region of turbulence production, there is a marked disparity among the time scales but as the outer edge of the boundary layer is approached, the scales become comparable to one another. Also, the behaviour of the length scales and the power spectra across the boundary layer is presented.Nomenclature Boundary layer thickness where Q/Q _e=0.995 - E _u(f) one dimensional frequency spectra - f frequency in Hz - k ₁ wave number defined as k ₁=2f/Q - L length scale defined as: time scale times local mean velocity - Q local mean velocity - Q _e free stream velocity - R _u, R _v, R _w Auto-correlation coefficients of u, v and w respectively as defined in equation (1) - T _u, T _v, T _w the time scales of u, v and w fluctuations as defined in equation (2) - delay time - u fluctuating velocity component in x-direction - v fluctuation velocity component in y-direction - w fluctuation velocity component in z-direction - x coordinate axis in the streamwise direction - y coordinate axis normal to the surface - z coordinate axis normal to the x-direction and parallel to the wall     

Asymptotic Solutions of Problems of One-Dimensional Time-Dependent Combustible Gas Flows in the Presence of Thermal Action

In a development of studies [1, 2], asymptotic solutions of the Navier-Stokes equations are found for one-dimensional combustible gas flows in the presence of various forms of thermal action on a moving surface (x=x _w(t)). In the problems considered, the temperature or the heat flux q _w(t) is specified on the surface or the surface is the interface between a combustible gas and a moving heated piston or another gas (for example, in a shock tube). Use is made of the fact that, as t , in many cases the values of v _w=(dx/dt)_w and q _w are bounded. This leads to a steady-state flow in the flame zone in the coordinate system moving with its front and homogeneous uniform flow ahead of and behind it. Solutions of all these problems are given for the burnt-gas boundary layer region adjacent to the surface. The numerical calculations performed confirm the results obtained. A velocity law leading to time invariability of the flow pattern obtained with allowance for the interaction between the boundary layer and the burnt-gas homogeneous flow is found, including in the problem of the breakdown of an arbitrary discontinuity. The results are generalized to include the case of motion at an angle of incidence with an additional velocity component aligned with the surface.