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1
Content available remote On the solution of a problem of extended thermoelasticity theory (ETE) by using a complete finite element approach
Shivay O.N., Mukhopadhyay S.
Computational Methods in Science and Technology
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2019
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Vol. 25, No. 2
61--70
EN
This paper attempts to apply a complete finite element approach for the solution of problems on coupled dynamical thermoelasticity theory. Presently, we employ the extended thermoelasticity theory proposed by Lord and Shulman (1969) and consider a problem of linear thermoelasticity for the hollow disk with a thermal shock applied on its inner boundary. The thermoelastic equations have been solved using the complete finite element approach, where we have used discretization in the time domain as well as space domain and applied the Galerkin’s approach of the finite element for both time and space domain. We implement our scheme for a particular case and carry out computational work to obtain the numerical solution of the problem. Further, we compare the present results with the solutions obtained by FEM with Newmark time integration method and the solutions obtained by a trans-FEM method in which Laplace transform technique is used for the time domain. We show that, there is a perfect match in solutions of complete finite element approach with trans-finite element method and Newmark method. The efficiency of the method with respect to computation time is also compared with other two methods.
2
Content available remote Thermo-Mechanical Responses of an Annular Cylinder with Temperature Dependent Material Properties under Thermoelasticity without Energy Dissipation
Kumar A., Kumari B., Mukhopadhyay S.
Computational Methods in Science and Technology
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2017
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Vol. 23, No. 4
317--329
EN
The present work is concerned with thermoelasticity without the energy dissipation theory for a problem of an infinitely long and isotropic annular cylinder of temperature dependent physical properties.We employ the thermoelasticity theory of GN-II and derive the basic governing equations with variable material properties. The formulation is then applied to solve a boundary value problem of an annular cylinder with its inner boundary assuming to be stress free and subjected to exponential decay in temperature and sinusoidal temperature distribution. The outer boundary is also assumed to be stress free and is maintained at reference temperature in both cases. We solve the non-linear coupled differential equations by applying the finite difference approach efficiently. We analyze the numerical results in a detailed way with the help of different graphs. The effects of temperature dependency of material properties on the thermo-mechanical responses for two different time dependent temperature distributions applied at the inner boundary are highlighted.
3
Content available remote Investigation on Magneto-thermoelastic Disturbances Induced by Thermal Shock in an Elastic Half Space Having Finite Conductivity under Dual Phase-lag Heat Conduction
Tiwari R., Kumar A., Mukhopadhyay S.
Computational Methods in Science and Technology
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2016
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Vol. 22, No. 4
201--215
EN
The present work seeks to investigate the propagation of magneto-thermoelastic disturbances produced by a thermal shock in a finitely conducting elastic half-space in contact with vacuum. Normal load has been applied on the boundary of the existing media that is supposed to be permeated by a primary uniform magnetic field. We employ both the parabolic type (dual phase-lag magneto-thermoelasticity of type I (MTDPL-I)) and hyperbolic type (dual phase-lag magneto-thermoelasticity of type II (MTDPL-II)) dual phase-lag heat conduction models to account for the interactions among the magnetic, elastic and thermal fields. The integral transform technique is applied to solve the present problem and the analytical results of both cases have been obtained separately. A detailed analysis of results has been made in order to understand the nature of waves propagating inside the medium and the effects of the phase-lag parameters. The effect of the presence of magnetic field has been highlighted. Numerical results have also been obtained to analyze the effect of magnetic field on the behavior of the solution more clearly and a detailed analysis of the results predicted by two models has been presented. It has been noted that in some cases there are significant differences in the solution obtained in the contexts of MTDPL-I and MTDPL-II theory of magneto-thermoelasticity.
4
Content available remote Boundary Integral Equations Formulation for Fractional Order Thermoelasticity
Tiwari R., Mukhopadhyay S.
Computational Methods in Science and Technology
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2014
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Vol. 20, No. 2
49--58
EN
The present work is concerned with the boundary integral equation formulation for the solutions of equations under fractional order thermo elasticity in a three dimensional Euclidean space. A mixed initial-boundary value problem is considered and the fundamental solutions of the corresponding coupled differential equations are obtained in the Laplace transform domain. We employ one reciprocal relation in the present context and formulate the boundary integral equations on the basis of our fundamental solutions.Then the formulation is illustrated with a suitable example.
5
Content available Slip effects on boundary layer flow and heat transfer along a stretching cylinder
Mukhopadhyay S., Gorla R. S. R.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 2
447--459
EN
An axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder is presented. Velocity slip is considered instead of the no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and heat equations into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by the shooting method. It is found that the velocity decreases with increasing the slip parameter. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to those for a flat plate.
6
Content available Dual solutions for boundary layer flow of moving fluid over a moving surface with power-law surface temperature
Mukhopadhyay S., Gorla R. S. R.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 1
113--124
EN
An analysis of heat transfer for boundary layer forced convective flow past a moving flat surface parallel to a moving stream is presented. The power-law surface temperature at the boundary is prescribed. The surface temperature varying directly (or inversely) with power-law exponent is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with known results from the open literature for some particular cases of the present study. When the surface and the fluid move in the opposite directions, dual solutions exist.
7
Content available remote Propagation of Harmonic Plane Waves in a Rotating Elastic Medium under Two-Temperature Thermoelasticity with Relaxation Parameter
Prasad R., Mukhopadhyay S.
Computational Methods in Science and Technology
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2012
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Vol. 18, No. 1
25-37
EN
The present work investigates the propagation of harmonic plane waves in an isotropic and homogeneous elastic medium that is rotating with uniform angular velocity by employing the two-temperature generalized thermoelasticity, recently introduced by Youssef (IMA Journal of Applied Mathematics, 71, 383-390, 2006). Dispersion relation solutions for longitudinal as well as transverse plane waves are obtained analytically. Asymptotic expressions of several important characterizations of the wave fields, such as phase velocity, specific loss, penetration depth, amplitude coefficient factor and phase shift of thermodynamic temperature are obtained for high frequency as well as low frequency values. A critical value of the two-temperature parameter for the low frequency case is obtained. Using Mathematica, numerical values of the wave fields at intermediate values of frequency and for various values of the twotemperature parameter are computed. A detailed analysis of the effects of rotation on the plane wave is presented on the basis of analytical and numerical results. An in-depth comparative analysis of our results with the corresponding results of the special cases of absence of rotation of the body and with the case of generalized thermoelasticity is also presented. The most significant points are highlighted.
8
Content available remote Analysis of the Effects of Phase-lags on Propagation of Harmonic Plane Waves in Thermoelastic Media
Kumar R., Mukhopadhyay S.
Computational Methods in Science and Technology
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2010
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Vol. 16, No. 1
19-28
EN
The present paper attempts to investigate the propagation of harmonic plane waves of assigned frequency by employing the thermoelasticity theory with three phase-lags, recently proposed by Roychoudhuri (2007). The solutions of dispersion relation for the longitudinal plane waves are determined analytically and asymptotic expansions of several characterizations of the wave fields- phase velocity, specific loss and penetration depth of the dilatational waves are obtained for both the high frequency and low frequency values. Computational work for numerical values of the above quantities is also carried out with the help of Mathematica. A detailed analysis of the effects of phase-lags on the plane wave is presented by contrasting the theoretical as well as numerical results of the present work with the corresponding results of the theory of thermoelasticity type III (Green and Naghdi, 1993) as reported earlier.
9
Content available remote Solution of a Problem of Generalized Thermoelasticity of an Annular Cylinder with Variable Material Properties by Finite Difference Method
Mukhopadhyay S., Kumar R.
Computational Methods in Science and Technology
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2009
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Vol. 15, nr 2
169-176
EN
The present work deals with a new problem of generalized thermoelasticity with one relaxation time for an infinitely long and isotropic annular cylinder of temperature dependent physical properties. The inner and outer curved surfaces of the cylinder are subjected to both the mechanical and thermal boundary conditions. A finite difference model is developed to derive the solution of the problem in which the governing equations are coupled non linear partial differential equations. The transient solution at any time can be evaluated directly from the model. In order to demonstrate the efficiency of the present model we consider a suitable material and obtain the numerical solution of displacement, temperature, and stresses inside the annulus for both the temperature-dependent and temperature-independent material properties of the medium. The results are analyzed with the help of different graphical plots.
10
Content available remote Flow characteristics in a vascular tube with an overIapping constriction
Pramanik S., Mukhopadhyay S., Layek G. C., Samad S. A.
International Journal of Applied Mechanics and Engineering
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2007
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Vol. 12, no 1
153-167
EN
A numerical solution to the unsteady blood flow in the neighbourhood of an overlapping constriction is obtained under laminar flow conditions. Blood is modelled as a viscous, incompressible and of Newtonian type fluid. A finite-difference staggered grid has been used to solve the unsteady incompressible Navier-Stokes equations in cylindrical polar co-ordinates under the axi-symmetric conditions. A co-ordinate transformation has been employed to map the constricted tube into a straight tube. The effect of flow characteristics in this type of constriction and its consequences in arterial diseases are investigated. Flow features such as velocity, pressure and wall shear stress distributions are presented graphically. The secondary separation has been noted in the downstream of the overlapping constriction when the Reynolds number of the flow is about 205.
11
Content available remote Effect of drawing different MFI polypropylene filaments on a gradient heater
Mukhopadhyay S., Deopura B. L., Alagirusamy R.
Autex Research Journal
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2006
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Vol. 6, no. 3
136--141
EN
High-modulus and high-tenacity polypropylene fibres were prepared by drawing as-spun filaments on a heater with a temperature gradient. The results on two different MFI PP show that the fibre properties are significantly affected by the temperature profiles at the final stage of drawing on a gradient heater. High crystal perfection and crystallinity at very high draw ratios have been obtained for the gradient drawn fibres. The gradient drawn filaments showed superior mechanical properties when compared to filaments drawn over a constant temperature heater. Fibres with an initial modulus of 16.4 GPa and tenacity of 875 MPa were obtained in the process. The molecular weight of the parent material significantly influenced the mechanical properties of the material. High molecular-weight (low MFI - Melt Flow Index) materials are characterised by comparatively lower modulus but higher tenacity values. High draw ratios were possible for the higher MFI samples, leading to more orientation and modulus.
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