Free and forced convection boundary layer flow through a porous medium with large suction

An analytical study is made of the free and forced convection boundary layer flow past a porous medium bounded by a semi-infinite vertical porous plate. Locally similar solutions are then obtained by a perturbation method for large suction. Solutions for the velocity and temperature distributions are shown graphically for various suction velocities and values of the driving parameter G_r/R, where G_r is the Grashof number and R_e is the Reynolds number. The corresponding values of the skin friction coefficient and the Nusselt number are finally shown in tabular form.     

Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

Numerical techniques are used to study the receptivity to small-amplitude thermal disturbances of the boundary layer flow of air which is induced by a heated vertical flat plate. The fully elliptic nonlinear, time-dependent Navier–Stokes and energy equations are first solved to determine the steady state boundary-layer flow, while a linearised version of the same code is used to determine the stability characteristics. In particular we investigate (i) the ultimate fate of a localised thermal disturbance placed in the region near the leading edge and (ii) the effect of small-scale surface temperature oscillations as means of understanding the stability characteristics of the boundary layer. We show that there is a favoured frequency of excitation for the time-periodic disturbance which maximises the local response in terms of the local rate of heat transfer. However the magnitude of the favoured frequency depends on precisely how far from the leading edge the local response is measured. We also find that the instability is advective in nature and that the response of the boundary layer consists of a starting transient which eventually leaves the computational domain, leaving behind the large-time time-periodic asymptotic state. Our detailed numerical results are compared with those obtained using parallel flow theory.     

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.     

Soret and Dufour effects on free convection boundary layer over a vertical cylinder in a saturated porous medium

This paper deals with an analysis of the Soret and Dufour effects on the boundary layer flow due to free convection heat and mass transfer over a vertical cylinder in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A suitable coordination transformation is used to derive the similar governing boundary-layer equations, and the cubic spline collocation method is then employed to solve the similar governing boundary-layer equations. The variation of the Nusselt number and the Sherwood number with the Dufour parameter and the Soret parameter for various Lewis numbers and buoyancy ratios have been presented in this work. Results show that an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number. The local Nusselt number tends to decrease as the Dufour parameter is increased. Moreover, an increase in the Lewis number enhances the effect of the Dufour parameter on the local Nusselt number.     

Effect of convection on boundary layer structures in finite thermoelasticity

Abstract

Till now, all of the research on boundary layer structures in thermoelasticity has focused on conduction as the primary mode of heat transfer. In this article, we investigate the additional effect of convection on the deformation field boundary layer structures formed within a thin infinite slab made of a neo-Hookean material. We find that additionally introducing convection in finite thermos-elasticity shifts the boundary layer vertically, while retaining its shape.     

Effect of variable viscosity on mixed convection boundary layer flow over a vertical surface embedded in a porous medium

The steady mixed convection boundary layer flow over a vertical impermeable surface embedded in a porous medium when the viscosity of the fluid varies inversely as a linear function of the temperature is studied. Both cases of assisting and opposing flows are considered. The transformed boundary layer equations are solved numerically by a finite difference method. Numerical results for the flow and heat transfer characteristics are obtained for various values of the mixed convection parameter ε and the variable viscosity parameter θ_e. It has been found that in the opposing flow case, dual solutions exist and boundary separation occurs.     

Natural convection boundary layer flow over a truncated cone in a porous medium saturated by a nanofluid

This work studies the natural convection boundary layer flow over a truncated cone embedded in a porous medium saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A suitable coordinate transformation is performed, and the obtained nonsimilar equations are solved by the cubic spline collocation method. The effect of the Brownian motion parameter and thermophoresis parameter on the temperature, nanoparticle volume fraction and velocity profiles are discussed. The effects of the thermophoresis parameter, Brownian parameter, Lewis number, and buoyancy ratio on the local Nusselt number have been studied. Results show that an increase in the thermophoresis parameter or the Brownian parameter tends to decrease the local Nusselt number. Moreover, the local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased.     

Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids

The steady mixed convection boundary layer flow past a vertical flat plate embedded in a porous medium filled with nanofluids is studied using different types of nanoparticles as Cu (cuprom), Al₂O₃ (aluminium) and TiO₂ (titanium). The model used for the nanofluid is the one which incorporates only the nanoparticle volume fraction parameter. The basic partial equations are reduced to an ordinary differential equation which is solved numerically for some values of the volume fraction and mixed convection parameters. It is shown that the solution has two branches in a certain range of the parameters. The effects of these parameters on the velocity distribution are presented graphically.     

Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet

The effect of radiation on the boundary layer flow and heat transfer of a viscous fluid over an exponentially stretching sheet is studied. The homotopy analysis method (HAM) is employed to determine the convergent series expressions of velocity and temperature. The physical interpretation to these expressions is assigned through graphs. It is found that the effects of Prandtl and radiation numbers on the temperature are opposite.     

Soret and Dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a vertical cone in a fluid-saturated porous medium with constant wall heat and mass fluxes. A similarity analysis is performed, and the obtained similar equations are solved by the cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local surface temperature tends to increase as the Dufour parameter is increased. The effect of the Dufour parameter on the local surface temperature becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret parameter leads to an increase in the local surface concentration and a decrease in the local surface temperature.     

Stabilization of thermocapillary instability in a fluid layer with internal heat source

The onset of steady thermocapillary (surface-tension-driven Marangoni) instability in a horizontal fluid layer in the presence of a uniform heat generation is considered theoretically using stability theory. The fluid layer, heated from below, is bounded above by a deformable free upper surface and below by a rigid plane boundary. The stability of the fluid layer is investigated and subjected to a feedback control on the temperatures of the boundaries. An exact solution for marginal stability owing to an exchange of stabilities has been obtained. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points.     

Numerical study of thermal instability in mixed convection flow over horizontal and inclined surfaces

This paper presents numerical study of thermal instability in mixed convection flow over horizontal and inclined plates. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, wave number, and the inclined angle φ from the horizontal. The flow is found to become more stable to the vortex mode of instability as the value of inclined angle increases, owing to a decrease in buoyancy force in the normal direction. However, the Prandtl number has a destabilizing effect on the flow. The results of the present numerical prediction show reasonable agreement with the experimental data in the literature.     

CFD analysis on the influence of helical carving in a vortex flow solar reactor

Solar thermal cracking of natural gas is a promising technology, which has attracted researchers in recent years for its potential to lead to the development of CO₂ free hydrogen production process. However, experimental access to the reaction chamber of solar cracking reactors is a challenge due to the high temperature process as the instruments capable of measuring fluid flow cannot survive the medium inside the reactor. However, computational fluid dynamics (CFD) can provide an insight into the flow, where experimental access is limited or not possible. This paper presents a CFD analysis for directly irradiated solar thermochemical reactor to characterize the influence of flow behavior on the heat transfer and solar cracking process. The heat transfer by radiation from carbon particles is considered by providing global absorption and scattering coefficients in the computational domain obtained from Mie code. The flow field is based on RNG k–? model derived using renormalization group theory. This technique accounts for the effect of swirl on turbulence thereby enhancing accuracy for the swirl flows. Validation of the numerical results is carried out by making a comparison with the experimental results. Highlighting the effects of carving on the solar reactor walls, this study presents numerical analyses of solar reactor geometry for two cases; namely, when there is no vortex forming carving in the cavity, and when there is vortex forming helical carving. The results show that carving has significant influence on the flow behavior, however, it has very little effect on the outlet temperature. The numerical results also show that the radiative heat transfer mechanism is the dominant means of heat transfer compared to the effects of conduction and convection.     

Effect of catch cup geometry on 3D boundary layer flow over the wafer surface in a spin coating

Recently, development of high technology has been required for the formation of thin uniform film in manufacturing processes of semiconductor as the semiconductor instruments become more sophisticated. Spin coating is usually used for spreading photoresist on a wafer surface. However, since rotating speed of the disk is very high in spin coating, the dropped photoresist scarers outward and reattaches on the film surface. A catch cup is set up outside the wafer in spin coating, and scattered photoresist mist is removed from the wafer edge by the exhaust flow generated at the gap between the wafer edge and the catch cup. In the dry process of a spin coating, it is a serious concern that the film thickness increases near the wafer edge in the case of low rotating speed. The purpose of this study is to make clear the effect of the catch cup geometry on the 3D boundary layer flow over the wafer surface and the drying rate of liquid film.     

Unsteady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface

The unsteady mixed convection boundary-layer flow of a micropolar fluid near the region of the stagnation point on a double-infinite vertical flat plate is studied. It is assumed that the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase or sudden decrease in the surface temperature from the uniform ambient temperature. The problem is reduced to a system of non-dimensional partial differential equations, which is solved numerically using the Keller-box method. This method may present well-behaved solutions for the transient (small time) solution and those of the steady-state flow (large time) solution. It was found that there is a smooth transition from the small-time solution (initial unsteady-state flow) to the large-time solution (final steady-state flow). Further, it is shown that for both assisting and opposing cases and a fixed value of the Prandtl number, the reduced steady-state skin friction and the steady-state heat transfer from the wall (or Nusselt number) decrease with the increase of the material parameter. On the other hand, it is shown that with the increase of the Prandtl number and a fixed value of the material parameter, the reduced steady-state skin friction decreases when the flow is assisting and it increases when the flow is opposing.     

Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below

Natural convection in air-filled 2D square enclosure heated with a constant source from below and cooled from above is studied numerically for a variety of thermal boundary conditions at the top and sidewalls. Simulations are performed for two kinds of lengths of the heated source, i.e., a small and a large source corresponding to 20% and 80% of the total length of the bottom wall, respectively. The Rayleigh number varied from 10³ to 10⁷. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface. Comparisons among the different thermal configurations considered are reported.     

Natural convection heat transfer of non-Newtonian fluids in porous media from a vertical cone under mixed thermal boundary conditions

This work studies the problem of the steady natural convection boundary layer flow over a downward-pointing vertical cone in porous media saturated with non-Newtonian power-law fluids under mixed thermal boundary conditions. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the power-law viscosity index and the similarity exponent on the heat transfer characteristics under mixed thermal boundary conditions have been studied. Under mixed thermal boundary conditions, both the surface heat flux and the surface temperature are found to decrease when the power-law viscosity index of the non-Newtonian power-law fluid in porous media is increased. Moreover, an increase in the similarity exponent tends to increase the boundary layer thickness and thus decreases the surface heat flux under mixed thermal conditions. The generalized governing equations derived in this work can be applied to the cases of prescribed surface temperature and prescribed heat flux.     

Characteristics of transient vortices in the boundary layer on a rotating disk under orbital motion

The objective of this study is to experimentally examine the characteristics of transient vortices in the boundary layer on a disk undergoing both rotation and orbital motion. The velocity fluctuations on a rotating, orbiting disk （disk radius equal to orbital radius） are measured by the hot-wire method, and the effects of orbital motion on the transient vortices in the boundary layer are examined. When the ratio of the orbital speed to the speed of rotation is i-0.025, the interval of transient vortices depends on only the orbital radius, regardless of the directions of rota- tion and orbital motion. The rate of low-frequency disturbances increases as the orbital speed increases, and the vortices induced by these low-frequency disturbances travel over the disk and then develop in the region of in- creased velocity. Consequently, no vortices generated on a rotating disk under orbital motion are stationary rela- tive to the disk.     

Experimental investigation of dimensionless velocity and shearing stress in boundary layer flow on continuous moving surface in power law fluids

An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.     

Mixed convection in laminar film flow of a micropolar fluid

In this paper, the steady mixed convection boundary layer in laminar film flow of a micropolar fluid is considered. The resulting nonlinear coupled ordinary differential equations are solved numerically using an efficient implicit finite-difference scheme. The numerical results obtained for the skin friction coefficient and the local Nusselt number, as well as the velocity, angular velocity or microrotation and temperature profiles are presented in tables and figures for different values of the material parameter K and the Richardson number Ri when the Prandtl number Pr = 0.7 and Pr = 1.