P. Bera

Bio: P. Bera is an academic researcher from Indian Institute of Technology Roorkee. The author has contributed to research in topics: Heat transfer & Combined forced and natural convection. The author has an hindex of 13, co-authored 33 publications receiving 505 citations. Previous affiliations of P. Bera include Max Planck Society.

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

Abstract: 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...

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

Abstract: 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.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions

Abstract: Previous studies of fluid convection in porous media have considered the onset of convection in isotropic systems and the steady convection in anisotropic systems. This paper bridges between these and develops new results for the onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. These results are relevant to sedimentary formations where the average vertical permeability is some fraction γ of the average horizontal permeability. Linear and global stability analyses are used to define the critical time tc at which the instability occurs as a function of γ and the dimensionless Rayleigh-Darcy number Ra* for both thermal and solute-driven convection in an infinite horizontal slab. Numerical results and approximate analytical solutions are obtained for both a slab of finite thickness and the limit of large slab thickness. For a thick slab, the increase in tc as γ decreases is approximately given by (1+γ)4∕(16γ2). One important application is to the geological storage of carbon dioxide where it is shown that the use of an effective vertical permeability in estimating the critical time is only valid for low permeabilities. The time scale for the onset of convection in geological storage can range from less than a year (for high-permeability formations) to decades or centuries (for low-permeability ones).