Mridula Kanoria

Bio: Mridula Kanoria is an academic researcher from University of Calcutta. The author has contributed to research in topics: Thermoelastic damping & Laplace transform. The author has an hindex of 27, co-authored 102 publications receiving 2094 citations. Previous affiliations of Mridula Kanoria include Indian Statistical Institute & University College West.

Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect

Abstract: This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model.

Generalized thermoelastic functionally graded solid with a periodically varying heat source

Abstract: This paper deals with the problem of thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of the linear theory of generalized thermoelasticity without energy dissipation (TEWOED). The governing equations of generalized thermoelasticity without energy dissipation (GN model type II) for a functionally graded materials (FGM) (i.e. material with spatially varying material properties)are established. The governing equations are expressed in Laplace–Fourier double transform domain and solved in that domain. Now, the inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand is obtained numerically in complex domain by using Laguerre’s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic material is obtained by taking nonhomogeneity parameter suitably. Finally the results obtained are presented graphically to show the effect of nonhomogeneity on displacement, temperature, stress and strain.

Fractional order two-temperature thermoelasticity with finite wave speed

Abstract: In this paper, a new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of heat conduction with fractional orders. The two-temperature Lord–Shulman (2TLS) model and two-temperature Green–Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation using the unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by using a state-space approach. The inversions of Laplace transforms are computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter.

Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect

Abstract: This problem deals with the thermo-visco-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic isotropic spherical shell in the context of generalized theories of thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigen value approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. [R. Bellman, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Publishing Company, New York, 1966]. The stresses are computed numerically and presented graphically in a number of figures for copper material. A comparison of the results for different theories (TEWED (GN-III), three-phase-lag method) is presented. When the body is elastic and the outer radius of the shell tends to infinity, the corresponding results agree with the result of existing literature.

Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity

Abstract: The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace transformation, the fundamental equations are expressed in the form of a vector-matrix differential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the thermal loading (the thermal shock and the ramp-type heating) and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion techniques. The numerical values of the physical quantity are computed for the copper like material. Significant dissimilarities between two models (the two-temperature Green-Naghdi theory with energy dissipation (2TGN-III) and two-temperature TPL model (2T3phase)) are shown graphically. The effects of two-temperature and ramping parameters are also studied.

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 …

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Of ocean waves and sea-ice revisited

Abstract: The review of Squire et al. [Squire, V.A., Dugan, J.P., Wadhams, P., Rottier, P.J., Liu, A.K., 1995. Of ocean waves and sea-ice. Annu. Rev. Fluid Mech. 27, 115–168.] is updated to take account of the astonishing surge of activity that has occurred over the last decade or so on topics in the general area of ocean wave/sea-ice interactions, especially in relation to mathematical modelling. Models have become much more sophisticated with the most recent ones allowing the sea-ice to be heterogeneous and the ocean to have variable depth. Pressure ridges, cracks, open and refrozen leads, and gradual or abrupt changes of material property can all be accommodated, and inhomogeneous marginal ice zones can also be effectively modelled. In this paper the author distinguishes between two major sea-ice types: continuous ice, such as is normally found in the central Arctic, and the ice of marginal neighbourhoods, i.e. near the open sea, where individual ice floes and cakes are present at typically lower levels of concentration. The partition is convenient but artificial, of course, as many of the methods employed apply to any kind of sea-ice. A discussion on laboratory and field experiments conducted during the period is also included.