
Archive issue  vol.2 No.2
1.
AN IMPLICIT STABLE DIFFERENCE SCHEME FOR
UNSTEADY VISCOELASTIC FLOW AND HEAT
TRANSFER BETWEEN TWO PARALLEL PLATES
S.PADHY anf H.B.PATTNAIK
Department of Mathematics, Utkal University
Vani Vihar, Bhubaneswar  751 004, INDIA
The unsteady flow and heat transfer of OldroydB liquid between two parallel
plates when one plate is stationary and the other starts moving suddenly in its
own plane with a velocity of the form At^{1/2} is considered. An implicit
finitedifference method which has been shown to be stable is employed to obtain
the solution of the velocity field. Then a 4th order RungeKutta method is used
for obtaining the temperature field and skin friction at the plates. The
solutions for the two cases n=0 (lower plate moving with constant velocity) and
n=1 (lower plate moving with constant acceleration) are computed and the effect
of elastic parameters a and b , time t, Eckert number E and Prandtl number Pr on
velocity and temperature, skin friction and the rate of heat transfer have been
studied through graphs and tables.
 Key words: 
unsteady flow, OldroydB liquid, implicit finite difference method, RungeKutta method. 
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2.
THE FORMULATION OF ELASTIC AND PLASTIC
RESPONSES FOR CUBIC CRYSTALS
Q.S. ZHENG
Department of Engineering Mechanics, Tsinghua University
Beijing 100084, P.R.CHINA
J. BETTEN
Department of Mathematical Models in Materials Science
Technical University Aachen
Templergraben 55, D52056 Aachen, GERMANY
Many matters are cubic crystals. In this paper, we derive the complete and
irreducible representations for scalarvalued and secondorder symmetric
tensorvalued functions (not only polynomials) of a single secondorder
symmetric tensor for each of the five crystal classes in the cubic system. These
results are applied to formulate the constitutive equations of cubic crystals in
elasticity and plasticity.
 Key words: 
cubic crystals, plasticity, elasticity, tensor function representations.

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3.
NATURAL CONVECTIVE FLOW OF MICROPOLAR FLUIDS IN A POROUS MEDIUM
A. MOHAMMADEIN, M. A. ELHAKIEM, S.M.M. ELKABEIR
Mathematics Department, Faculty of Science
South Valley University, AswanEGYPT
M.A. MANSOUR
Mathematics Department, Faculty of Science
Assuit University, AssuitEGYPT
A regular perturbation analysis is presented to study the effect of both first and secondorder resistances due to the solid matrix on natural convection flow of micropolar fluidsaturated porous media. The goveming equations have been solved numerically using an expansion technique. Results for velocity, angular velocity and thermal functions are displayed graphically for a range values of the micropolar parameters. It is observed that micropolar fluids display drag reduction as well as heat transfer rate reduction when compared to Newtonian fluids.
 Key words: 
boundary layers, micropolar fluids, porous medium. 
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4.
STOKES PROBLEM FOR AN INFINITE VERTICAL PLATE
FOR WATER AT 4^{o}C WITH CONSTANT HEAT FLUX
H.S. TAKHAR
Manchester School of Engineering
University of Manchester
Manchester, M13 9PL, U.K.
B.K. JHA
Department of Mathematics
Banaras Hindu University
Varanasi221005, INDIA
An exact analysis of Stoke's problem (also Rayleigh's problem) for the flow
of water at 4oC past an infinite vertical plate is presented taking into account
constant heat flux at the plate. Expressions for the velocity field and
skinfriction for both cases of impulsive as well as uniformly accelerated
motion of the plate are obtained by using the Laplace transform technique. The
influence of the various parameters, entering into the problem, on the velocity
field and skinfriction is extensively discussed.
 Key words: 
free convection, Stokes problem. 
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5.
NONLINEAR THEORY OF SANDWICH SHELLS
PART I
EXACT KINEMATICS OF MODERATELY THICK SHELLS
RenHuai LIU
Jinan University
Guang Zhou 510632, P.R.CHINA
JinFu ZHU
Department of Aircraft Engineering
Nanjing University of Aeronautics and Astronautics
Nanjing 210016, P.R.CHINA
In order to develop a nonlinear theory of sandwich shells, the exact
kinematics of moderately thick shells is derived and discussed in detail as the
first part of the series papers. The kinematics includes displacements, strains
and compatibility conditions.
 Key words: 
sandwich shells, nonlinear theory, kinematics, compatibility conditions. 
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6.
NONLINEAR THEORY OF SANDWICH SHELLS
PART II
APPROXIMATE THEORIES
RenHuai LIU
Jinan University
Guang Zhou 510632, PR.CHINA
JinFu ZHU
Department of Aircraft Engineering
Nanjing University of Aeronautics and Astronautics
Nanjing 210016,PR.CHINA
The equations obtained in Part I of this series paper (Liu and Zhu,1996) are
simplified under the condition of small strain associated with moderate rotation
and in accordance with the structural features of sandwich shells. The
approximate geometric theories of sandwich shells are first obtained, including
second order and first order approximations. Then the associated physical
equations, including the constitutive equations, the strain energy expressions
and the equilibrium equations, etc., are developed.
 Key words: 
order analysis of magnitude, principle of energy error consistency, moderate rotation, approximate theory. 
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7.
FREE CONVECTIONRADIATION INTERACTION IN
BOUNDARY LAYER FLOW ON A NONISOTHERMAL
FLAT PLATE UDER NONUNIFORM GRAVITY
M.A. MANSOUR
Mathematics Department, Faculty of Science
Assiut University, Assiut, EGYPT
The interaction of free convection with thermal radiation in a laminar
boundary flow along a rotating nonisothermal plate subject to a nonuniform
gravity field is studied. The fluid considered is a gray, absorbingemitting but
nonscattering medium, and the Rosseland approximation is used to describe the
radiative heat flux in the energy equation. Several specific forms for the
temperature distributions of the plate are considered. Also; both the cases of
the cold and hot plates are considered.
 Key words: 
free convection, radiation, boundary layer, non uniform gravity. 
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8.
ON WAVES DUE TO ROLLING OF A PLATE
SUBMERGED IN FINITEDEPTH WATER
S. BANERJEA
Department of Mathematics
Jadavpur University
Calcutta 700 032, INDIA
D. P. DOLAI, B.N MANDAL
Physics and Applied Mathematics Unit
Indian Statistical Institute
203 B.T. Road, Calcutta 700 035, INDIA
Twodimensional problems of water wave generation due to small oscillations
of vertical plates in deep water, possess explicit solutions. However, for water
of uniform finite depth, the same problems cannot be solved exactly and some
approximate methods have to be used. Here two methods have been utilized to
compute the amplitude at infinity of the waves generated by small rolling
oscillations of a thin vertical plate submerged in finitedepth water. One
method involves eigenfunction expansion of the velocity potential describing the
ensuing motion in water while the other involves a hypersingular integral
equation formulation. The two methods produce almost the same numerical results
for the wave amplitude at infinity. This wave amplitude is depicted graphically
against wave number and compared with deep water results. It is observed that
the deep water results carry through if the lower end of the plate is submerged
to onetenth of the bottomdepth, and further, in the moderate wave number range,
the wave amplitude exhibits an oscillation, which may be attributed due to some
sort of interaction between the water bottom and the plate.
 Key words: 
submerged rolling plate, finitedepth water, wave amplitude, eigenfunction expansion, hypersingular integral equation. 
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