P. Bera

Double-diffusive natural convection in an anisotropic porous cavity with opposing buoyancy forces: multi-solutions and oscillations

Abstract Natural convection by combined heat and mass transfer with opposing horizontal heat and solute gradients has been investigated in an anisotropic porous cavity using the Darcy model. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. The principal directions of the permeability tensor are taken oblique to the gravity vector, while those of thermal and solutal diffusivity coincide with horizontal and vertical coordinate axes. Special attention is given to understand the effect of anisotropic parameters on the existence of unsteady permanent oscillations and multiple steady-state solutions. From the study of analytical solutions, which can be regarded as a verification of the numerical results, simultaneously, it is found that there exists an interval of buoyancy ratio, I NM , depending on the parametric values, in which multiple solutions exist. For the unsteady case a similar interval, I NO , for the buoyancy ratio has been observed numerically, in which permanent oscillations exist. Periodicity of the oscillation changes drastically by changing the permeability of the medium. The results indicate that the maximum I NM and I NO interval are attained at an orientation angle of θ =45°. The local direction of the flow changes because of the variation in the extent of the thermal and concentration layers, the opposite buoyant mechanism, and anisotropic parameters.

NUMERICAL STUDY OF HEAT AND MASS TRANSFER IN AN ANISOTROPIC POROUS ENCLOSURE DUE TO CONSTANT HEATING AND COOLING

Double-diffusive natural connective flow within a rectangular enclosure has been studied for an anisotropic porous medium using a non-Darcy extension. The principal direction of the permeability tensor has been taken oblique to the gravity vector. The spectral element method has been used to solve the problem numerically. The method has been validated using existing analytical and numerical results. Parametric studies are presented for isotropic and anisotropic cases for different fundamental parameters, e.g., buoyancy ratio, Lewis number, Rayleigh number, Darcy number. The results show that anisotropy causes significant changes in the Nusselt and Sherwood numbers. In particular, the present analysis shows that permeability orientation angle has a significant effect on the flow rate and, consequently, on the heat and mass transfer.

An efficient C0 FE model for the analysis of composites and sandwich laminates with general layup

A C0 continuous finite element model is developed to model the refined higher order shear deformation theory. The proposed element is an upgraded version of an element based on higher order shear deformation theory. The C0 continuity of the present element is compensated in the stiffness matrix calculations. The computational efficiency is achieved by the C0 continuous finite element model by satisfying the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. The performance of the upgraded element is illustrated with many numerical examples.

Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium

Buoyancy opposed mixed convection is considered in a vertical channel filled with an isotropic, porous medium, in which the motion of an incompressible fluid is induced by external pressure gradients and buoyancy forces. The Brinkman-Wooding-extended Darcy model has been used to study the instability mechanisms of the basic flow and its dependence on the Prandtl number (Pr) of the fluid. The stability analysis indicated that for the same Reynolds number (Re), the fully developed base flow was highly unstable for a fluid with high Pr. For a porous medium with a Darcy number (Da) of 10−6 and Pr⩾0.7, two different types of instability, Rayleigh-Taylor (R-T) and buoyant instability, are observed. The R-T instability mode is observed for relatively small values of Re. Further, the results show that for Da=10−5 and Pr<1, the spectrum of the energy profile is abrupt and sudden, whereas the same is smooth when Da=10−6. In the case of R-T instability, the critical value of Ra at low Re is given by −2.47∕Da. Though...

Stability of mixed convection in an anisotropic vertical porous channel

This paper addresses the stability of mixed convective buoyancy assisted flow due to external pressure gradient and buoyancy force in a vertical fluid saturated porous channel with linearly varying wall temperature. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. Two different types of temperature perturbations, (i) zero temperature and (ii) zero heat flux, have been considered to study the effect of anisotropic permeability and thermal diffusivity on the flow stability. The stability analysis indicated that the least stable mode is two-dimensional. Furthermore, the results show that for the same Reynolds number, the fully developed base flow is highly unstable (stable) for high (low) permeable porous media as well as for a porous medium with small (large) thermal diffusivity ratio. Depending on the magnitude of all parameters studied, three types of instabilities (shear, thermal, and mixed instability) occurred. The transition of instability from one type to another took place smoothly, except when the permeability ratio exceeded 6. Based on the value of the permeability ratio, the flow in an anisotropic medium for a specific Reynolds number may be either more or less stable than the flow in an isotropic medium. In addition, the fully developed flow is more stable for relatively small values of the modified Darcy number than for larger values. The effect of Brinkman as well as Forchheimer terms are negligible for the set of other parameters studied here. In contrast to a pure viscous fluid or an isotropic porous medium, which are characterized by unicellular convective cells, in anisotropic porous media convective cells may be unicellular or bicellular. The stability analysis of mixed convection in channels filled either with a viscous fluid or with an isotropic saturated porous medium may be obtained as special cases of the general study presented here.

Natural Convection in an Anisotropic Porous Enclosure Due to Nonuniform Heating From the Bottom Wall

A comprehensive numerical investigation on the natural convection in a hydrodynamically anisotropic porous enclosure is presented. The flow is due to nonuniformly heated bottom wall and maintenance of constant temperature at cold vertical walls along with adiabatic top wall. Brinkman-extended non-Darcy model, including material derivative, is considered. The principal direction of the permeability tensor has been taken oblique to the gravity vector. The spectral element method has been adopted to solve numerically the governing conservative equations of mass, momentum, and energy by using a stream-function vorticity formulation. Special attention is given to understand the effect of anisotropic parameters on the heat transfer rate as well as flow configurations. The numerical experiments show that in the case of isotropic porous enclosure, the maximum rates of bottom as well as side heat transfers (Nu b and Nu s ) take place at the aspect ratio, A, of the enclosure equal to 1, which is, in general, not true in the case of anisotropic porous enclosures. The flow in the enclosure is governed by two different types of convective cells: rotating (i) clockwise and (ii) anticlockwise. Based on the value of media permeability as well as orientation angle, in the anisotropic case, one of the cells will dominate the other. In contrast to isotropic porous media, enhancement of flow convection in the anisotropic porous enclosure does not mean increasing the side heat transfer rate always. Furthermore, the results show that anisotropy causes significant changes in the bottom as well as side average Nusselt numbers. In particular, the present analysis shows that permeability orientation angle has a significant effect on the flow dynamics and temperature profile and consequently on the heat transfer rates.

Weakly nonlinear stability analysis of non-isothermal Poiseuille flow in a vertical channel

A weakly nonlinear stability theory in terms of Landau equation is developed to analyze the nonlinear saturation of stably stratified non-isothermal Poiseuille flow in a vertical channel. The results are presented with respect to fluids: mercury, gases, liquids, and heavy oils. The weakly nonlinear stability results predict only the supercritical instability, in agreement with the published result [Y. C. Chen and J. N. Chung, “A direct numerical simulation of K and H-type flow transition in heated vertical channel,” Comput. Fluids 32, 795–822 (2003)] based on direct numerical simulation. Apart from this, the influence of nonlinear interaction among different superimposed waves on the heat transfer rate, real part of wavespeed, and friction coefficient on the wall is also investigated. A substantial enhancement (reduction) in heat transfer rate (friction coefficient) is found for liquids and heavy oils from the basic state beyond the critical Rayleigh number. The amplitude analysis indicates that the equil...

Effect of Periodicity of Non-Uniform Sinusoidal Side Heating on Natural Convection in an Anisotropic Porous-Enclosure

A comprehensive numerical study on the natural convection in a hydrodynamically anisotropic as well as isotropic porous enclosure is presented, flow is induced by non uniform sinusoidal heating of the right wall of the enclosure. The principal directions of the permeability tensor has been taken oblique to the gravity vector. The spectral Element method has been adopted to solve numerically the governing differential equations by using the vorticity-stream-function approach. The results are presented in terms of stream function, temperature profile and Nusselt number. The result show that the maximum heat transfer takes place at y = 1.5 when N is odd.. Also, increasing media permeability, by changing K* = 1 to K* = 0.2, increases heat transfer rate at below and above right corner of the enclosure. Furthermore, for the all values of N, profiles of local Nusselt number (Nuy) in isotropic as well as anisotropic media are similar, but for even values of N differ slightly at N = 2.. In particular the present analysis shows that, different periodicity (N) of temperature boundary condition has the significant effect on the flow pattern and consequently on the local heat transfer phenomena.

Influence of Non-Uniform Sinusoidal Periodic Bottom Boundary Condition on Natural Convection in an Isotropic Porous Enclosure

A comprehensive numerical investigation on the natural convection in an isotropic porous enclosure is presented. All the walls of the enclosure are adiabatic except the bottom wall which is partially heated and cooled by sinusoidal temperature profile. The governing equations were written under assumption of Brinkman-extended non-Darcy model, including material derivative, and then solved by numerically using spectral element method (SEM). The heat transfer and fluid flow mechanisms in isotropic case are governed by periodicity parameter (N) Rayleigh Number (Ra), Darcy number (Da), aspect ratio (A), Prandtl number (Pr) and media permeability (K). The main emphasize is given on effect of N on local heat transfer as well as mechanism of heat transfer and fluid flow in enclosure. The results shows that, as the periodicity is decreased on increasing N the absolute value of Nux at the bottom left corner point increases. For odd values of N, the local heat transfer profile is symmetric about the line x=0.5, which is consequence of symmetric boundary condition at the bottom wall of the enclosure. The entire flow is governed by two type convective cells: (i) rotating clockwise (ii) rotating anticlockwise. Furthermore for even values of N cells rotating anticlockwise are dominated and covered the entire domain. In particular the present analysis shows that, different periodicity of temperature boundary condition has the significant effect on the flow mechanism and consequently on the heat transfer rate.