Archive issue - vol.10, No.2



   No.   Author(s) - Title
Pages

   1.
 

 P.D. Ariel -- Fluid dynamics of the elliptic porous slider at high crossflow Reynolds numbers
 

193-206
 

   2.
 

 I.E. Esparragoza -- Plastic stresses at the tip of a crack impinging perpendicularly the interface of two different elastic-plastic materials
 

207-216
 

   3.
 

 A.K. Haghi -- Experimental survey on heat and moisture transport through fabrics
 

217-226
 

   4.
 

 R. Kumar and R. Singh -- Elastodynamics of an axisymmetric problem in microstretch viscoelastic solid
 

227-244
 

   5.
 

 R. Kandasamy and K. Periasamy -- Nonlinear hydromagnetic flow, heat and mass transfer over an accelerating vertical surface in the presence of internal heat generation and chemical reaction
 

245-252
 

   6.
 

 R. Kumar and G. Partap -- Reflection of plane waves in a heat flux dependent microstretch thermoelastic solid half space
 

253-266
 

   7.
 

 S.K. Khan -- Boundary layer MHD flow of a viscoelastic fluid over a porous quadratic stretching sheet
 

267-279
 

   8.
 

 R. Kumar and L. Rani -- Response of thermoelastic half-space with voids due to inclined load
 

281-294
 

   9.
 

 Liu Ren-Huai and Wang Fan -- Nonlinear stability of corrugated shallow spherical shell
 

295-309
 

   10.
 

 S. Sharidan, N. Amin and I. Pop -- G-jitter induced free convection near a two-dimensional stagnation point in micropolar fluids
 

311-328
 

   11.
 

 Sunil, Y.D. Sharma, P.K. Bharti and R.C. Sharma -- Thermosolutal instability of compressible Rivlin-Ericksen fluid with Hall currents
 

329-343
 

   12.
 

 S.K. Tomar and B. Singh -- Propagation of SH-wave through an elastic slab sandwiched between two half-spaces
 

329-343
 

   13.
 

 A.K. Haghi -- A theoretical approach to the solutions of surface irregularities parameters
 

359-364
 

 



1.

FLUID DYNAMICS OF THE ELLIPTIC POROUS SLIDER AT HIGH CROSSFLOW REYNOLDS NUMBERS

P.D. ARIEL

Department of Mathematical Sciences
Trinity Western University, Langley, V2Y 1Y1, CANADA
e-mail: dariel@twu.ca

     The numerical and asymptotic solutions for high crossflow Reynolds numbers in the flow of an incompressible, Newtonian fluid through an elliptical porous slider are developed. An efficient numerical scheme is presented which allows the flow to be computed practically for arbitrarily large values of the Reynold's number. A comparison is made of the results obtained by the two techniques and the domain of the physical parameters for which the asymptotic solution can be used reasonably has been demarcated.

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2.

PLASTIC STRESSES AT THE TIP OF A CRACK IMPINGING PERPENDICULARLY THE INTERFACE OF TWO DIFFERENT ELASTIC-PLASTIC MATERIALS

I.E. ESPARRAGOZA

School of Engineering Design, Technology and Professional Programs
The Pennsylvania State University
25 Yearsley Mill Rd., Media, PA. 19063, U.S.A.
e-mail: iee1@psu.edu

     The problem of stresses at the tip of a crack impinging the interface of two different elastic-perfectly plastic materials is considered. The mathematical model is based on the assumption that both solids are incompressible elastic-perfectly plastic materials obeying the Huber-Von Misses yielding criterion under conditions of plane strain. It is shown that the problem of local stresses near the crack tip has two possible solutions, one of which is continuous and the other discontinuous. For the inhomogeneous case it was found that the discontinuous solution is the only feasible. In the limiting case of a homogeneous elastic-perfectly plastic material, the continuous solution coincides with that of Prandtl (1920), and the discontinuous solution with that of Cherepanov (1997). Some reasons for preferring the discontinuous solutions are provided since it is evident that both solutions cannot exist simultaneously.

Key words:

crack tip, plasticity, elastic-perfectly plastic materials, Huber-Von Mises yielding condition.

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3.

EXPERIMENTAL SURVEY ON HEAT AND MOISTURE TRANSPORT THROUGH FABRICS

A.K. HAGHI

University of Guilan, P.O. Box 3756, Rasht, IRAN
e-mail: haghi@guilan.ac.ir

     Heat and moisture transport processes occurring within the solid matrix and in the voids are complicated even for a regularly shaped matrix and impossible for the irregular shaped configurations that exist in general, in porous media. The aim of this article is to contribute to the understanding of the behavior of fabric during dynamic moisture and heat transfer with particular reference to clothing comfort and to review the latest developments.

Key words:

heat transport, moisture transport, fabrics.

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4.

ELASTODYNAMICS OF AN AXISYMMETRIC PROBLEM IN MICROSTRETCH VISCOELASTIC SOLID

R. KUMAR

Department of Mathematics
K.U., Kurukshetra, Haryana 136119, INDIA
e-mail: rajneesh_kuk@rediffmail.com

R. SINGH
Department of Mathematics, S.G.A.D. Govt. College
Tarn Taran, Amritsar
e-mail: kalsi_ranjit@yahoo.com

     An eigen value approach, following Laplace and Hankel transforms, has been employed to find the general solution to the field equations in a microstretch viscoelastic medium for an axisymmetric problem. An application of an infinite space with a concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inverted by using a numerical inversion technique to get the results in the physical domain. The results in the form of normal displacement, normal force stress, tangential force stress, tangential couple stress and microstress components have been obtained numerically and illustrated graphically to depict the effects of stretch and viscosity. Special cases of microstretch elastic solid and micropolar elastic solid have also been deduced.

Key words:

microstretch viscoelastic solid, Laplace-Hankel transforms, eigen value, concentrated force, korrecture method.

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5.

NONLINEAR HYDROMAGNETIC FLOW, HEAT AND MASS TRANSFER OVER AN ACCELERATING VERTICAL SURFACE IN THE PRESENCE OF INTERNAL HEAT GENERATION AND CHEMICAL REACTION

R. KANDASAMY

Department of Mathematics, Institute of Road and Transport Technology
Erode-638 316, INDIA
e-mail: kandan_kkk@yahoo.co.in

K. PERIASAMY
Institute of Road and Transport Technology
Erode-638 316, INDIA

     An analysis is carried out to study a nonlinear hydromagnetic flow, heat and mass transfer over an accelerating vertical surface with internal heat generation and chemical reaction. The fluid is assumed to be incompressible, viscous, electrically conducting and Boussinesq. A magnetic field is applied transversely to the direction of the flow. The similarity transformation has been utilized to convert the governing partial differential equations into ordinary differential equations and then the numerical solution of the problem is drawn using Runge Kutta Gill method. Numerical calculations for different values of dimensionless parameters entering the problem under consideration are carried out for the purpose of illustrating the results graphically. Examinations of such flow models reveal the influence of the chemical reaction, Prandtl number and strength of the magnetic field.

Key words:

chemical reaction, magnetic field, Runge Kutta Gill method, internal heat generation and nonlinear hydromagnetic flow.

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6.

REFLECTION OF PLANE WAVES IN A HEAT FLUX DEPENDENT MICROSTRETCH THERMOELASTIC SOLID HALF SPACE

R. KUMAR

Department of Mathematics, Kurukshetra University
Kurukshetra, Haryana, INDIA
e-mail: rajneesh_kuk@rediffmail.com

G. PARTAP
Department of Applied Mathematics
Dr. B.R. Ambedkar National Institute of Technology
Jalandhar, Punjab, INDIA
e-mail: partap_geeta@rediffmail.com

     The present investigation is concerned with the reflection of plane waves in a heat flux dependent microstretch thermoelastic solid half space. The reflection coefficients of various reflected waves with the angle of incidence for Green-Lindsay theory for stress free and rigidly fixed boundaries have been obtained. The variations of various reflected waves showing thermal and stretch effects have been shown graphically. Special cases have been deduced.

Key words:

reflection, microstretch, thermoelastic, amplitude ratios.

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7.

BOUNDARY LAYER MHD FLOW OF A VISCOELASTIC FLUID OVER A POROUS QUADRATIC STRETCHING SHEET

S.K. KHAN

Department of Mathematics Gulbarga University
Gulbarga-585 106 Karnataka, INDIA
e-mail: sujit_kumar@hotmail.com

     A mathematical analysis on the boundary layer MHD flow of a viscoelastic fluid over a porous stretching sheet has been presented in this paper. A typical choice of quadratic stretching of the boundary, which generates a quadratic part in velocity parallel to the boundary sheet and a linear mass flux part in the velocity normal to the stretching sheet, has been assumed. Streamline patterns and skin friction coefficients are discussed for various values of nondimensional physical parameters. The result of the analysis reveals that the combined effect of the non-dimensional viscoelastic parameter and Hartmann number is to increase significantly the values of skin friction coefficient, whereas, the combined effect of the nondimensional constant mass flux parameter and modified linear mass flux parameter is to reduce largely the values of skin friction coefficient. For positive values of the linear mass flux parameter the stream functions attain a positive slope away from the origin while they attain a negative slope everywhere for zero value. The limiting cases of our results yield the results of Andersson (1992) and Kumaran and Ramanaiah (1996).

Key words:

viscoelastic fluid, quadratic stretching, MHD flow, stream function, skin friction.

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8.

RESPONSE OF THERMOELASTIC HALF-SPACE WITH VOIDS DUE TO INCLINED LOAD

R. KUMAR

Mathematics Department, Kurukshetra University
Kurukshetra 136119 Haryana, INDIA
e-mail: rajneesh_kuk@rediffmail.com

L. RANI
Doon Valley Institute of Engineering and Technology
Outside Jundla Gate, KARNAL
e-mail: leena_1973@rediffmail.com

     A two-dimensional deformation of a homogeneous, isotropic, thermoelastic half-space with voids as a result of an inclined line load is investigated by applying the Laplace and Fourier transforms. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The displacements, stresses, temperature distribution and change in the volume fraction field so obtained in the physical domain are computed numerically. The variations of these quantities have been depicted graphically in the coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) for an insulated boundary.

Key words:

thermoelastic, voids, inclined load, Laplace and Fourier transforms.

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9.

NONLINEAR STABILITY OF CORRUGATED SHALLOW SPHERICAL SHELL

LIU Ren-Huai and WANG Fan

Institute of Applied Mechanics, Jinan University
Guangzhou 510632, P.R.CHINA
e-mail: twfan@jnu.edu.cn

     In this paper, a nonlinear bending theory for a corrugated shallow spherical shell is constructed. By means of this theory and the modified iteration method, the analytical solution of the critical buckling pressure for a corrugated shallow spherical shell with a rigidly clamped edge under the action of uniform pressure is obtained.

Key words:

corrugated shallow spherical shell, modified iteration method, nonlinear stability.

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10.

G-JITTER INDUCED FREE CONVECTION NEAR A TWO-DIMENSIONAL STAGNATION POINT IN MICROPOLAR FLUIDS

S. SHARIDAN and N. AMIN

Department of Mathematics, University of Technology
81310 Johor Bahru, Johor, MALAYSIA

I. POP
Faculty of Mathematics, University of Cluj
R-3400 Cluj, CP 253, ROMANIA
e-mail: popi@math.ubbcluj.ro

     A numerical solution for the effect of a small but fluctuating gravitational field, characteristic of g-jitter, on the free convection boundary layer flow near the forward stagnation point of a two-dimensional symmetric body resulting from a step change in its surface temperature and immersed in a micropolar fluid is presented in this paper. Both the cases when the spin gradient on the wall is zero and non-zero are considered. The transformed non-similar boundary layer equations are solved numerically by a very efficient implicit finite-difference scheme known as the Keller-box method to investigate the effects on the skin friction and on the rate of heat transfer of variations in the forcing amplitude, a, forcing frequency, 'omega', and micropolar parameter, K. The results are given for a value of the Prandt number Pr=0.7. It has been found that these parameters affect considerably the considered flow characteristics. A comparison with earlier results for a Newtonian fluid (K=0) shows a good agreement.

Key words:

g-jitter, boundary layer, stagnation point, numerical results.

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11.

THERMOSOLUTAL INSTABILITY OF COMPRESSIBLE RIVLIN-ERICKSEN FLUID WITH HALL CURRENTS

SUNIL, Y.D. SHARMA, P.K. BHARTI

Department of Applied Sciences, National Institute of Technology, Deemed University
Hamirpur (H.P.)-177 005, INDIA
e-mail: sunil@nitham.ac.in

R.C. SHARMA
Department of Mathematics, Himachal Pradesh University
Summer Hill, Shimla-171 005, INDIA

     The thermosolutal instability of a compressible Rivlin-Ericksen viscoelastic fluid is predicted for a layer heated and soluted from below in the presence of the vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like a Newtonian viscous fluid. The Hall currents found to hasten the onset of thermosolutal instability whereas the compressibility, stable solute gradient and magnetic field postpone the onset of thermosolutal instability. Also, the dispersion relation is analyzed numerically and results are depicted graphically. The stable solute gradient and magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system, which were nonexistent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

Key words:

Hall effect, thermosolutal instability, Rivlin-Ericksen fluid, magnetic field, compressibility.

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12.

PROPAGATION OF SH-WAVE THROUGH AN ELASTIC SLAB SANDWICHED BETWEEN TWO HALF-SPACES

S.K. TOMAR

Department of Mathematics, Panjab University, Chandigarh-1600 14, INDIA
e-mail: sktomar@yahoo.com

B. SINGH
Department of Mathematics, Government College, Sector-11, Chandigarh-1600 11, INDIA
e-mail: baljeet_gill@hotmail.com

     Two boundary value problems are investigated in this paper: first, a plane SH-wave incident upon a slab of monoclinic crystal which is interposed between two uniform elastic solid half-spaces; second, a plane SH-wave incident upon a linear homogeneous isotropic elastic slab interposed between two monoclinic elastic half-spaces. The expressions of reflection and transmission coefficients are derived in a closed form and several particular cases are discussed. Elastic constants for rock gypsum (CaSO4.2H2O) are used in numerical computations to describe the effect of monoclinic properties on reflection and transmission coefficients. It is found that there is a significant effect of the interposed layer on reflection and transmission coefficients.

Key words:

monoclinic elastic, SH-wave reflection and transmission, sandwiched layer, anisotropy.

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13.

A THEORETICAL APPROACH TO THE SOLUTIONS OF SURFACE IRREGULARITIES PARAMETERS

A.K. HAGHI

University of Guilan
P.O. Box 3756, Rasht, IRAN
e-mail: Haghi@Guilan.ac.ir

     In this paper, the probability characteristics of surface irregularities parameters described by the composition of the deterministic component and the homogeneous random normal field were analysed. Formulae for the calculation of the mathematical expectation of the Ras parameter and the evaluation of its variance are given.

Key words:

mathematical approach, surface irregularities, deterministic component.

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