The Onset of Convection in a Heterogeneous Porous Medium with Transient Temperature Profile

The effect of vertical heterogeneity of permeability, on the onset of convection in a horizontal layer of a saturated porous medium, uniformly heated from below but with a non-uniform basic temperature gradient resulting from transient heating or otherwise, is studied analytically using linear stability theory. Two particular situations, corresponding to instantaneous bottom heating and constant-rate bottom heating, are studied. Estimates of the timescale for the development of convection instability are obtained.     

Similarity conditions for heat transfer in incompressible two-dimensional laminar boundary layer flow

Summary Similarity conditions are presented for the solution of some problems of heat transfer in incompressible two-dimensional boundary layer flow. The treatment holds for forced convection as well as for free convection. For free convection no a priori restriction is made with respect to geometry or temperature distribution of the solid surface. For forced convection the treatment is restricted to uniform bulk flow parallel to a flat surface of non-uniform temperature or heat flux. The results are summarized in some tables that facilitate comparison with older work.     

Investigation of thermocapillary convective patterns and their role in the enhancement of evaporation from pores

The present work investigates the evaporation process from a liquid meniscus formed in capillary tubes of various sizes. A very strong convection within the liquid phase is observed; it is proposed that the non-uniform evaporation from the meniscus leads to a temperature gradient along the interface causing a surface tension gradient, which is the driving mechanism for the convection. The observed convection is shown to be clearly correlated to the evaporation rate and the volatility of the liquid. Unlike Marangoni convection observed by imposing a temperature gradient, this is a self-induced driving gradient caused by evaporative cooling effect.The Marangoni roll in the liquid phase has been visualized and characterized using seeding particles. It is shown in the present study that the observed convection contribute in enhancing the heat–mass transfer from the pore. The experimental results show that when the meniscus recedes inside the pore, the convection slows down and eventually stops. A theoretical model is developed to describe the temperature gradient, which establishes due to the evaporative cooling effect between the centre and the wedge of the meniscus. The results of the model show a good qualitative agreement with the experimental observations.     

A steady conjugate heat transfer problem with conduction and free convection

Summary A steady conjugate heat transfer problem dealing with conduction in a heat-generating slab and free convection in the surrounding fluid is studied analytically. Free convection is analyzed by a Görtler-type series solution to the boundary-layer equations for non-uniform surface-temperature variations, while conduction is treated by the standard technique of Fourier transforms. Interfacial temperature and heat flux variations from both solutions in series forms are then formally matched to yield algebraic relations for the coefficients in the series. These coefficients can then be simply evaluated in a given problem in terms of three physical parameters. A numerical example is shown.     

Numerical solution of natural convection flow past a non-isothermal vertical flat plate

The problem of natural convection over a semi-infinite flat plate with non-uniform wall temperature is studied by using a numerical method. The local rates of heat transfer as a function of the distance along the plate are tabulated for a range of Prandtl numbers (0.01 to 100) and for a few cases of wall temperature distributions. Such tabulations serve as a reference against which other approximate solutions can be compared in the future.     

Mixed convection film condensation from downward flowing vapors onto a sphere with variable wall temperature

A model is developed for the study of mixed- convection film condensation from downward flowing vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, concerning effects of pressure gradient (P), interfacial vapor shear drag and non-uniform wall temperature variation (A), has been investigated and solved numerically. The effect of pressure gradient on the dimensionless mean heat transfer, NuˉRe^−1/2 will remain almost uniform with increasing P until for various corresponding available values of F. Meanwhile, the dimensionless mean heat transfer, NuˉRe^−1/2 is increasing significantly with F for its corresponding available values of P. Although the non-uniform wall temperature variation has an appreciable influence on the local film flow and heat transfer; however, the dependence of mean heat transfer on A can be almost negligible. Received on 10 October 1996     

Non-uniform slot suction/injection into mixed convection boundary layer flow over vertical cone

The aim of this work is to study the effect of non-uniform single and double slot suction/injection into a steady mixed convection boundary layer flow over a vertical cone, while the axis of the cone is inline with the flow. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar trans- formations. The resulting coupled non-linear partial differential equations are solved nu- merically by employing the quasi-linearization technique and an implicit finite-difference scheme. Numerical computations are performed for different values of the dimensionless parameters to display the velocity and temperature profiles graphically. Also, numerical results are presented for the skin friction and heat transfer coefficients. Results indicate that the skin friction and heat transfer coefficients increase with non-uniform slot suction, but the effect of non-uniform slot injection is just opposite.     

Natural Convection on a Horizontal Cone in a Porous Medium with Non-Uniform Wall Temperature/Concentration or Heat/Mass Flux and Suction/Injection

The steady natural convection flow on a horizontal cone embedded in a saturated porous medium with non-uniform wall temperature/concentration or heat/mass flux and suction/injection has been investigated. Non-similar solutions have been obtained. The nonlinear coupled differential equations under boundary layer approximations governing the flow have been numerically solved. The Nusselt and Sherwood numbers are found to depend on the buoyancy forces, suction/injection rates, variation of wall temperature/concentration or heat/mass flux, Lewis number and the non-Darcy parameter.     

On the Hydrodynamics and Heat Convection of an Impinging External Flow Upon a Cylinder with Transpiration and Embedded in a Porous Medium

This paper extends the existing studies of heat convection by an external flow impinging upon a flat porous insert to that on a circular cylinder inside a porous medium. The surface of the cylinder is subject to constant temperature and can include uniform or non-uniform transpiration. These cylindrical configurations are introduced in the analyses of stagnation-point flows in porous media for the first time. The equations governing steady transport of momentum and thermal energy in porous media are reduced to simpler nonlinear differential equations and subsequently solved numerically. This reveals the dimensionless velocity and temperature fields of the stagnation-point flow, as well as the Nusselt number and shear stress on the surface of the cylinder. The results show that transpiration on the surface of the cylinder and Reynolds number of the external flow dominate the fluid dynamics and heat transfer problems. In particular, non-uniform transpiration is shown to significantly affect the thermal and hydrodynamic responses of the system in the circumferential direction. However, the permeability and porosity of the porous medium are found to have relatively smaller influences.     

Effects of non-uniform heating on a variable viscosity Rayleigh�CB��nard problem

This study presents a natural convection problem with a temperature-dependent viscosity fluid, driven by buoyancy and influenced by horizontal temperature gradients. A numerical linear stability analysis of the stationary solutions is studied. The horizontal temperature gradients tend to localize motion near the warmer zones and favour pattern formation in the direction perpendicular to the gradient. In fact, the problem is almost 2D in the uniform heating case, but becomes totally 3D in the non-uniform heating case.     

Unsteady mixed convection boundary layer flow over a vertical cone with non-uniform slot suction (injection)

The non-similar solution of an unsteady mixed convection laminar boundary layer flow over a vertical cone in the presence of non-uniform surface mass transfer through slot has been obtained while the axis of cone is inline with the flow. The unsteadiness is caused by the time dependent free stream velocity. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting coupled non-linear partial differential equations have been solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity and temperature profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are reported to display the effects of non-uniform single and double slot suction (injection) on skin friction and heat transfer coefficients at the wall. Further, the effects of Prandtl number, buoyancy and mass transfer (suction or injection) parameters at different stream-wise locations for various times on velocity and temperature profiles, and on skin friction and heat transfer coefficients are also presented in this paper.     

Unsteady numerical simulation of double diffusive convection heat transfer in a pulsating horizontal heating annulus

A numerical study is conducted on time-dependent double-diffusive natural convection heat transfer in a horizontal annulus. The inner cylinder is heated with sinusoidally-varying temperature while the outer cylinder is maintained at a cold constant temperature. The numerical procedure used in the present work is based on the Galerkin weighted residual method of finite-element formulation by incorporating a non-uniform mesh size. Comparisons with previous studies are performed and the results show excellent agreement. In addition, the effects of pertinent dimensionless parameters such as the thermal Rayleigh number, Buoyancy ratio, Lewis number, and the amplitude of the thermal forcing on the flow and heat transfer characteristics are considered in the present study. Furthermore, the amplitude and frequency of the heated inner cylinder is found to cause significant augmentation in heat transfer rate. The predictions of the temporal variation of Nusselt and Sherwood numbers are obtained and discussed.     

Effect of Time Periodic Boundary Conditions on Convective Flows in a Porous Square Enclosure with Non-Uniform Internal Heating

The problem of unsteady natural convection in a square region filled with a fluid-saturated porous medium having non-uniform internal heating and heated laterally is considered. The heated wall surface temperature varies sinusoidally with the time about fixed mean temperature. The opposite cold wall is maintained at a constant temperature. The top and bottom horizontal walls are kept adiabatic. The flow field is modelled with the Darcy model and is solved numerically using a finite difference method. The transient solutions obtained are all periodic in time. The effect of Rayleigh number, internal heating parameters, heating amplitude and oscillating frequency on the flow and temperature field as well as the total heat generated within the convective region are presented. It was found that strong internal heating can generate significant maximum fluid temperatures above the heated wall. The location of the maximum fluid temperature moves with time according to the periodically changing heated wall temperature. The augmentation of the space-averaged temperature in the cavity strongly depends on the heating amplitude and rather insensitive to the oscillating frequency.     

The Onset of Convection in a Heterogeneous Porous Medium with Vertical Throughflow

The effect of vertical heterogeneity of permeability, on the onset of convection in a horizontal layer of a saturated porous medium, uniformly heated from below but with a non-uniform basic temperature gradient resulting from vertical throughflow, is studied analytically using linear stability theory. It is found that, to first order, a linear variation of the reciprocal of permeability with depth has no effect on the critical value of the Rayleigh number Ra _c based on the harmonic mean of the permeability, but a quadratic variation increasing in the upwards direction leads to a reduction in Ra _c.     

Full-field Measurement of Topography and Curvature by Coherent Gradient Sensing Method at High Temperature

Coherent gradient sensing (CGS) method, a real time, full-field optical technique, is insensitive to vibrations and able to provide slope and curvature maps and surface topographies, to investigate non-uniform deformations. In this paper, we analyze the thermal effects on the optical path in CGS due to air convection, and the influence of grating thickness and refractive index on the measurement accuracy. A modified governing equation is derived considering the grating thickness, which is demonstrated by testing a standard sample. Finally, we apply CGS method to measure the full-field deformation of a specimen at high temperature.     

Conjugate mixed convection heat and mass transfer in brick drying

 In this study, a numerical methodology for the solution of conjugate heat and mass transfer problem is presented. Fluid flow, heat and mass transfer over a rectangular brick due to transient laminar mixed convection has been numerically simulated. The coupled non-linear partial differential equations, for both gas phase and solid are solved using finite element procedure. Flow is assumed to be incompressible, two-dimensional, laminar. Analysis has been carried out at a Reynolds number of 200 with Pr = 0.71. The effect of buoyancy on the brick drying has been investigated. Velocity vectors, streamlines in the flow field and temperature and moisture contours and temperature distribution along the solid surface are presented. It is observed that there is considerable effect of buoyancy during drying. The results indicate a non-uniform drying of the brick with the leading edge drying faster than the rest of the brick. Received on 9 December 1998     

Unsteady mixed convection flow over stretching sheet in presence of chemical reaction and heat generation or absorption with non-uniform slot suction or injection

The article examines the unsteady mixed convection flow over a vertical stretching sheet in the presence of chemical reaction and heat generation or absorption with non-uniform mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Non-similar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasilinearization technique in combination with an implicit finite difference scheme. To reveal the tendency of the solutions, typical results for the local skin friction coefficient and the local Nusselt and Sherwood numbers are presented for different values of parameters. The effects of various parameters on the velocity, temperature, and concentration distributions are discussed here. The present numerical results are compared with the previously published work, and the results are found to be in excellent agreement.     

Natural convection with evaporation in a vertical cylindrical cavity under the effect of temperature-dependent surface tension

The effect of surface tension on laminar natural convection in a vertical cylindrical cavity filled with a weak evaporating liquid has been analyzed numerically. The cylindrical enclosure is insulated at the bottom, heated by a constant heat flux from the side, and cooled by a non-uniform evaporative heat flux from the top free surface having temperature-dependent surface tension. Governing equations with corresponding boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The influence of Rayleigh number, Marangoni number, and aspect ratio on the liquid flow and heat transfer has been studied. Obtained results have revealed that the heat transfer rate at free surface decreases with Marangoni number and increases with Rayleigh number, while the average temperature inside the cavity has an opposite behavior; namely, it growths with Marangoni number and reduces with Rayleigh number.     

Convection in a low prandtl number fluid with internal heating

This paper studies the problem of non-linear thermal convection in a horizontal layer of a low Prandtl number fluid with nearly insulating boundaries and in the presence of horizontally uniform internal heat sources. Two-dimensional rolls and hexagonal cells are found to be the only possible stable convection cells. Subcritical instability associated with the hexagons can occur for a range of the amplitude of convection. It is found that non-uniform internal heating can affect various flow features and the stability of the convective motion. A new subcritical instability which exists even in a symmetric layer with arbitrary Prandtl number is also found for the case where the variations of the internal heating with respect to the vertical variable is sufficiently high.     

Non-linear convection in a porous medium with internal heat sources

The paper studies non-linear thermal convection in a horizontal porous layer of fluid with nearly insulating boundaries and in the presence of internal heat sources. Square and hexagonal cells are found to be the only possible stable convection cells. Finite amplitude instability could exist for some particular forms of an internal heat source Q. For a uniform Q, the preferred flow pattern is that of hexagons for amplitude ε smaller than some critical value ε_c, while both squares and hexagonal cells are stable for ε ? ε_c. The convective motion is downward at the hexagonal cell's centers. For a non-uniform Q, the qualitative features of thermal convection depend on the actual form Q. In particular, a non-uniform Q can increase or decrease the cell's size and the critical Rayleigh number at the onset of convection, and stabilize or destabilize the convective motion in the form of hexagonal cells with either upward or downward motion at the cell's centers.