Archive issue - vol.2 No.2



   No.   Author(s) - Title
Pages

   1.
 

 Padhy S. and Pattnaik H.B. -- An implicit stable difference scheme for unsteady viscoelastic flow and heat transfer between two parallel plates
 

157-170
 

   2.
 

 Zheng Q.S. and Betten J. -- The formulation of elastic and plastic responses for cubic crystals
 

171-186
 

   3.
 

 Mohammadein A., El-Hakiem M.A., Mansour M.A. and El-Kabeir S.M.M. -- Natural convective flow of micropolar fluids in a porous medium
 

187-204
 

   4.
 

 Takhar H.S. and Jha B.K. -- Stokes problem for an infinte vertical plate for water at 4°C with constant heat flux
 

205-212
 

   5.
 

 Liu R.H. and Zhu J.F. -- Nonlinear theory of sandwich shells. Part I. Exact kinematics of moderately thick shells
 

213-240
 

   6.
 

 Liu R.H. and Zhu J.F. -- Nonlinear theory of sandwich shells. Part II. Approximate theories
 

241-269
 

   7.
 

 Mansour M.A. -- Free convection-radiation interaction in boundary layer flow on a nonisothermal flat plate uder nonuniform gravity
 

271-284
 

   8.
 

 Banerjea S., Dolai D.P. and Mandal B.N. -- On waves due to rolling of a plate submerged in finite-depth water
 

285-297
 

 



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 Oldroyd-B 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 At1/2 is considered. An implicit finite-difference method which has been shown to be stable is employed to obtain the solution of the velocity field. Then a 4th order Runge-Kutta 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, Oldroyd-B liquid, implicit finite difference method, Runge-Kutta method.

TOP OF PAGE


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, D-52056 Aachen, GERMANY

     Many matters are cubic crystals. In this paper, we derive the complete and irreducible representations for scalar-valued and second-order symmetric tensor-valued functions (not only polynomials) of a single second-order 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.

TOP OF PAGE


3.

NATURAL CONVECTIVE FLOW OF MICROPOLAR FLUIDS IN A POROUS MEDIUM

A. MOHAMMADEIN, M. A. EL-HAKIEM, S.M.M. EL-KABEIR

Mathematics Department, Faculty of Science
South Valley University, Aswan-EGYPT

M.A. MANSOUR
Mathematics Department, Faculty of Science
Assuit University, Assuit-EGYPT

     A regular perturbation analysis is presented to study the effect of both first and second-order resistances due to the solid matrix on natural convection flow of micropolar fluid-saturated 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.

TOP OF PAGE


4.

STOKES PROBLEM FOR AN INFINITE VERTICAL PLATE
FOR WATER AT 4oC 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
Varanasi-221005, 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 skin-friction 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 skin-friction is extensively discussed.

Key words:

free convection, Stokes problem.

TOP OF PAGE


5.

NONLINEAR THEORY OF SANDWICH SHELLS
PART I
EXACT KINEMATICS OF MODERATELY THICK SHELLS

Ren-Huai LIU

Jinan University
Guang Zhou 510632, P.R.CHINA
Jin-Fu 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.

TOP OF PAGE


6.

NONLINEAR THEORY OF SANDWICH SHELLS
PART II
APPROXIMATE THEORIES

Ren-Huai LIU

Jinan University
Guang Zhou 510632, PR.CHINA

Jin-Fu 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.

TOP OF PAGE


7.

FREE CONVECTION-RADIATION 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, absorbing-emitting 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.

TOP OF PAGE


8.

ON WAVES DUE TO ROLLING OF A PLATE
SUBMERGED IN FINITE-DEPTH 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

     Two-dimensional 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 finite-depth 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 one-tenth of the bottom-depth, 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, finite-depth water, wave amplitude, eigenfunction expansion, hypersingular integral equation.

TOP OF PAGE