Volume 92, Issue 1
September 1983, pages 1-65
pp 1-6 September 1983
In this paper, we have developed an algorithm to determine the trade-off solution pairs in a special type of transportation problem considering two objectives,viz., cost and time. It is assumed that the time of transportation from an origin to a destination depends on the quantity transported. This results in a time objective, which is a piecewise constant increasing function. The cost objective function is taken to be linear. A potential physical situation of this model is given and a numerical example is worked out to illustrate the algorithm.
pp 7-17 September 1983
The velocity and temperature distribution in a system consisting of a fluid layer overlying a layer of porous medium is investigated in the presence of buoyancy and surface tension forces. The analysis indicates that buoyancy and surface tension forces are additive and aid the flow by counteracting the effect of permeability. The temperature distribution is sensitive to the variation of the aspect ratio, and conductivities of the media. Further, the inclusion of the viscous dissipation term markedly affects the temperature distribution.
pp 19-27 September 1983
Approximate analytical solutions are obtained for self-similar flows behind strong shocks with variable energy deposition or withdrawal at the wavefront in a perfect gas at rest with constant initial density. Numerical solutions are also obtained and the approximate solutions agree with these solutions. The effect of the adiabatic index on the solutions is investigated. The dependence of shock density ratio on the parameter characterizing the energy of the flow is studied. It is observed that the rate of deposition of energy at the wavefront decreases with increase of the parameter that specifies the total energy of the flow.
pp 29-39 September 1983
The flow of an incompressible viscous fluid between two torsionally oscillating noncoaxial cylinders has been investigated. Closed form solutions for symmetric and first order asymmetric flow are obtained for the cases when the gap between the cylinders is finite. Solutions of the governing equations under the geometrical restriction of narrow gap are also presented. These solutions coincide with the solutions of the finite gap by incorporating in them the condition of narrow gap. The components of the force acting on the inner cylinder are calculated.
pp 41-47 September 1983
The diffraction of SH-waves by an infinite periodic system of cuts in an infinite medium possessing nonhomogeneity has been studied. Assuming that shear modulus and density vary, the problem of diffraction of SH-waves by the periodic system of cuts depends on the solution of dual series equations which ultimately reduces to the solution of an infinite system of algebraic equations.
pp 49-52 September 1983
Formulae for computing thenth prime, twinprime, the number of primes smaller than a given integer, and the number of twinprimes smaller than a given integer are presented. Proofs for the development are also furnished.
pp 53-59 September 1983
The problem of combined, natural and forced convection for the laminar flow in a vertical channel of equilateral triangular cross-section is discussed. Internal heat generation is assumed to be uniform. The coupled equations in velocity and temperature are solved using equitriangular transform. Expressions for pressure drop parameter and Nusselt number are obtained and their behaviour for different values of Rayleigh number and heat generation function, is studied.
pp 61-65 September 1983
An approximate solvability scheme for equations of the typeu+Ku(u)=w, in a closed convex subsetA of a Hilbert spaceX is given. Here, for eachu ∈ A, Ku: X → X is a bounded linear operator.