Vertical Wavy Surface Research Articles

Double diffusive natural convection in a doubly stratified wavy porous enclosure

Combined heat and mass transfer process by natural convection along a vertical wavy surface in a thermal and mass stratified fluid saturated porous enclosure has been numerically analysed. Finite element method has been used and the influence of varying flow, heat and mass transfer governing parameters has been reported. Presence of thermal and mass stratification terms reduces the Nusselt number and Sherwood number values in all the cases. The flow circulation pattern which is anti-clockwise when the species buoyancy forces are opposing the thermal buoyancy forces, gets clockwise when the forces are aiding. When the two buoyancy forces are equal and opposing, a multi-cellular pattern with alternating circulation orientation manifests. Several other interesting features such as thermal and mass boundary layers, thermal plumes, secondary circulation zones, flow intensification etc. are noticed in the flow, temperature and concentration fields with varying flow, heat and mass transfer governing parameters.

Transient analysis of heat and mass transfer by natural convection over a vertical wavy surface

The transient behaviors of natural convection heat and mass transfer along a vertical wavy surface subjected to step changes of wall temperature and wall concentration have been investigated numerically by using a simple coordinate transformation to transform the complex wavy surface into a flat plate. An implicit marching finite-difference scheme is employed for the analysis. It is well know that the buoyancy ratio N and Schmidt number Sc are the parameters of importance for heat and mass transfer. The wavy geometry is also an important factor for this problem. Numerical results show that the flow field takes more time to reach steady condition for a high amplitude-wavelength ratio α, small buoyancy ratio N, and large Schmidt number Sc. The effects of wavy geometry, buoyancy ratio N and Schmidt number Sc on the transient local skin-friction, local Nusselt number and local Sherwood number have been discussed in detail.

Natural convection flow along a vertical wavy surface with uniform surface temperature in presence of heat generation/absorption

The effect of internal heat generation/absorption on a steady two-dimensional natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The equations are mapped into the domain of flat vertical plate, and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. Effects of the pertinent parameters, such as the heat generation/absorption parameter ( Q), the amplitude of the waviness ( α) of the surface and Prandtl number Pr on the rate of heat transfer in terms of the local Nusselt number ( Nu x ), isotherms and the streamlines are discussed.

Non-Darcy free convection induced by a vertical wavy surface in a thermally stratified porous medium

The partial differential equations governing the natural convection heat transfer from a vertical wavy surface in a thermally stratified fluid saturated porous medium are analysed under Forchheimer based non-Darcian assumptions. Based on non-similarity transformation deduced by scale analysis the governing equations are reduced to boundary layer equations. These simplified partial differential equations are solved numerically by a finite difference scheme following the Keller Box approach. Extensive numerical simulations are carried out for various values of wavelength-to-amplitude ratio of wavy vertical surface at different thermal stratification levels of porous medium both under Darcian and non-Darcian assumptions. Results from the current study are compared with those available in literature. In Darcian case local heat fluxes along the wavy vertical surface are periodic with an oscillatory pattern of period, which is exactly half of the period of vertical wavy surface. In the non-Darcian case local heat fluxes continue to be periodic but with a complex oscillatory pattern of period exactly same as that of the vertical wavy surface. Increasing S or Gr ∗ or a leads to a fall in local Nusselt number.

Mixed convection heat and mass transfer along a vertical wavy surface

A numerical study of mixed convection heat and mass transfer along a vertical wavy surface has been carried out numerically. The wavy surface is maintained at uniform wall temperature and constant wall concentration that is higher than that of the ambient. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for present analysis. The buoyancy ratio N, amplitude–wavelength ratio α, and Richardson number ( Gr/ Re 2) are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surface are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.

Natural convection heat and mass transfer along a vertical wavy surface

A numerical study of natural convection heat and mass transfer along a vertical wavy surface has been performed. The wavy surface is maintained at uniform wall temperature and constant wall concentration. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for the analysis. The buoyancy ratio N, amplitude–wavelength ratio α, and Schmidt number Sc are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surfaces are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.

MIXED CONVECTION OF MICROPOLAR FLUIDS ALONG A VERTICAL WAVY SURFACE WITH A DISCONTINUOUS TEMPERATURE PROFILE

This article presents numerical solutions for solving the problem of a mixed convective micropolar fluid flow and heat transfer along a vertical wavy surface with a discontinuous temperature profile. The overall surface is equally divided into a heated section succeeded by an unheated section alternately. The problems in the present study have been formulated by using a simple transposition theorem and the cubic spline collocation method. Eringen has applied the spline alternating direction implicit (SADI) procedure to solve the governing momentum, angular momentum, and energy equations those formulated. Along the wavy surface, the velocity, temperature, and microrotation profiles are presented. The influences of micropolar parameters R, u , geometry, and Gr/Re 2 number on the skin friction coefficient and Nusselt number have been studied in this work. The results demonstrate that the skin friction coefficient consists of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases, but the skin friction increases. In addition, when the spin gradient viscosity parameter ( u ) increases, the skin friction decreases. Comparisons between a Newtonian fluid and a micropolar fluid are also discussed.

Natural Convection from a Vertical Wavy Surface Embedded in Saturated Porous Media

The mass-transfer coefficients have been obtained experimentally for natural convection from vertical wavy surfaces of varying amplitude-to-wavelength ratio (a/λ) when embedded in saturated porous media. The porous media were formed by randomly packing glass spheres of 3-, 4-, and 6-mm diameters. A limiting diffusion current technique based on cathodic reduction of cupric ions in acidic solution was used. The obtained data correspond to high Rayleigh numbers and exhibit non-Darcian effects. The mass-transfer coefficients from the wavy surfaces in porous media can be estimated as = [3.3284 − 2.4068(a/λ)]( /DaL)0.26 in the studied range of [(1.31 × 106) − (5.56 × 107)], where and DaL are the modified Rayleigh and Darcy numbers, respectively.

Natural convection of fluid with variable viscosity from a heated vertical wavy surface

In the present paper, the effect of a temperature dependent viscosity on natural convection flow of viscous incompressible fluid from a vertical wavy surface has been investigated using an implicit finite difference method. Here we have focused our attention on the evaluation of the local skin-friction and the local Nusselt number. The governing parameters are the Prandtl number, Pr, ranging from 1 to 100, the amplitude of the waviness of the surface, α, ranging from 0.0 to 0.4 and the viscosity variation parameter, e, ranging from 0.0 to 6.

Transient force and free convection along a vertical wavy surface in micropolar fluids

This work studies the transient behavior of the laminar mixed convection in micropolar fluid flow over a vertical wavy surface. Effects of micropolar parameters and wavy geometry on the transient skin friction coefficient and Nusselt number are examined. Results show that the transient skin-friction coefficient and heat transfer rate show a mixture of two harmonics. Forced convection dominates the first harmonic at smaller time or near the leading edge, while free convection dominates the second harmonic as the time increases and fluid moves downstream. As the vortex viscosity increases the Nusselt number decreases, thus micropolar fluids have smaller heat transfer rates.

Natural convection heat and mass transfer near a vertical wavy surface with constant wall temperature and concentration in a porous medium

This paper reports a study of the phenomenon of natural convection heat and mass transfer near a vertical wavy surface embedded in a fluid-saturated porous medium. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate, and the obtained boundary layer equations is then solved by the local nonsimilarity method and the cubic spline collocation method. Effects of the Lewis number, the buoyancy ratio, and the wavy geometry on the local Sherwood number and the local Nusselt number are studied. The harmonic curves for the local Sherwood number and the local Nusselt number have a frequency twice the frequency of the wavy surface. Moreover, increasing the amplitude-wavelength ratio tends to increase the amplitude of the local Sherwood number and the local Nusselt number. Further, the average Sherwood number and the average Nusselt number for a sinusoidal wavy surface are found to be constantly smaller than that of the corresponding flat plate.

Mixed convection of micropolar fluids along a vertical wavy surface

This paper presents numerical results for the steady-state mixed convection in micropolar fluids along a vertical wavy surface. The problem has been formulated by a simple trnasposition theorem, and the spline alternating-direction implicit method has been applied to solve the governing momentum, angular momentum and energy equations. The influence of the micropolar parameters (R and λ), the amplitude-wave length ratio and the Gr/Re2 number on the skin-friction coefficient and Nusselt number have been studied. Results demonstrate that the skin friction coefficient and local Nusselt number consist of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases but the skin friction increases. In addition, when the spin gradient viscosity parameter (λ) increases, the heat transfer rate and the skin friction decreases. However, the heat transfer rate of a micropolar fluid is smaller than a Newtonian fluid, but the skin friction of a micropolar fluid is larger than a Newtonian fluid under all circumstances.

A Study of Free Convection Induced by a Vertical Wavy Surface with Heat Flux in a Porous Enclosure

Free convection induced by a vertical wavy surface with uniform heat flux in a porous enclosure has been analyzed numerically using the finite element method (FEM). The flow and the convection process in the cavity is found to be sensitive to the flow parameter Rayleigh number (Ra), and geometrical parameters like wave amplitude (a), wave phase (φ), and number of waves (N) in the vertical dimension of the cavity. The study reveals that small sinusoidal drifts from the smoothness of a vertical wall with a phase angle of 60o and high frequency enhances the free convection from a vertical wall with uniform heat flux.

Combined heat and mass transfer in natural convection flow from a vertical wavy surface

In the present paper, effects of combined buoyancy forces from mass and thermal diffusion by natural convection flow from a vertical wavy surface have been investigated using the implicit finite difference method. Here we have focused our attention on the evolution of the surface shear stress,f″(0), rate of heat transfer,g′(0), and surface concentration gradient,h′(0) with effect of different values of the governing parameters, such as the Schmidt number Sc ranging from 7 to 1500 which are appropriate for different species concentration in water (Pr=7.0), the amplitude of the waviness of the surface ranging from 0.0 to 0.4 and the buoyancy parameter,w, ranging from 0.0 to 1.

Free-convection boundary-layer flow of a non-Newtonian fluid along a vertical wavy surface

A theoretical analysis of laminar free-convection flow over a vertical isothermal wavy surface in a non-Newtonian power-law fluid is considered. The governing equations are first cast into a nondimensional form by using suitable boundary-layer variables that substract out the effect of the wavy surface from the boundary conditions. The boundary-layer equations are then solved numerically by a very efficient implicit finite-difference method known as the Kelter-Box method. A sinusoidal surface is used to elucidate the effects of the power-law index, amplitude wavelength, and Prandtl number on the velocity and temperature fields, as well as on the local Nusselt number. It is shown that the local Nusselt number varies periodically along the wavy surface. The wavelength of the local Nusselt number variation is half that of the wavy surface, irrespective of whether the fluid is a Newtonian fluid or a non-Newtonian fluid. Comparisons with earlier works are also made, and the agreement is found to be very good.

A study of natural convection in non-Newtonian fluids induced by a vertical wavy surface

A numerical investigation of natural convection flow along irregular vertical surfaces is reported. A transformation method is applied to the problem of natural convection under the assumption of a large Grashof number. A vertical wavy surface is used as an example to demonstrate the advantages of the transformation method, and to show the heat transfer mechanism near such surfaces. Surface non-uniformities on the boundary layer flow induced by a constant was temperature, semi-infinite surface are investigated. Also the effects of Prandtl number, flow index, and surface amplitude in Non-Newtonian fluids are discussed. When possible, the comparison of the numerical results shows a good agreement. The amplitude is proportional to the amplitude of a wavy surface. The results demonstrate that the local heat flux along a wavy surface is smaller than that of a flat surface. The frequency of the wavy surface is half that of the local heat transfer rate. The amplitude of the local Nusselt number gradually decreases downstream where the natural convection boundary layer grows thick.

Free Convection of a Non‐Newtonian Power‐Law Fluid from a Vertical Wavy Surface with Uniform Surface Heat Flux

AbstractThe steady laminar free convection in the flow of a non‐Newtonian power‐law fluid along a vertical wavy surface with constant heat flux has been investigated in this paper. The transformed boundary layer equations are solved by using a very efficient implicit finite‐difference method. A sinusoidal surface is used to elucidate the amplitude of the wavy surface effects. Along with the wall temperature, representative velocity and temperature profiles are presented. Numerical results show that the wall temperature decreases as the power‐law index increases, while it increases with the amplitude of the wavy surface. Comparisons with earlier work are also made for a flat plate immersed in a Newtonian fluid. The results are found to compare very well.

Non-Darcy natural convection from a vertical wavy surface in a porous medium

We examine the combined effect of spatially stationary surface waves and the presence of fluid inertia on the free convection induced by a vertical heated surface embedded in a fluid-saturated porous medium. We consider the boundary-layer regime where the Darcy-Rayleigh number, Ra, is very large, and assume that the surface waves have O(1) amplitude and wavelength. The resulting boundary-layer equations are found to be nonsimilar only when the surface is nonuniform and inertia effects are present; self-similarity results when either or both effects are absent. Detailed results for the local and global rates of heat transfer are presented for a range of values of the inertia parameter and the surface wave amplitude.

Free Convection Induced by a Vertical Wavy Surface With Uniform Heat Flux in a Porous Medium

Free Convection Induced by a Vertical Wavy Surface With Uniform Heat Flux in a Porous Medium

A Note on Free Convection Along a Vertical Wavy Surface in a Porous Medium

A Note on Free Convection Along a Vertical Wavy Surface in a Porous Medium