SOLUTION TO A PARAMETRIC EQUATION WITH GENERALIZED BOUNDARY CONDITION IN TRANSPORT THEORY

This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue delta0 is established.

A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS

In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.

Electro-osmotic chemical behavior of clayey soil under various boundary conditions

The use of electro-osmotic chemical is an effective method to improve the clayey soil foundation.Various boundary conditions can be adopted in this method.In this work,two electrode–clay contacts,three solution conditioners,and four anode solution supply times were used for clayey soil improvement.Based on the experimental data,electro-osmotic consolidation theory,and transport of ion theory,it is found that the electro-osmotic chemical effect of the separation of electrode–clay(E_S)is more beneficial for the transport of Ca^(2+),production of cementing material,and reduction of water content than that of electrode–clay(E_C)joining;through electrode–clay contact separation,the anode solution conditioner(NaPO3)6(E_SHMP)delayed the cementing reaction and then increased the transport of Ca^(2+)near the cathode,which increased the amount of cementing material and the electro-osmotic chemical effect;and when the anode conditioner(NaPO3)6 was used,two days of anode solution supply followed by three days cut off from the anode solution led to the highest undrained shear strength increase after the application of electro-osmotic chemical,which resolved the uneven electro-osmotic chemical effect in the E_SHMP.

Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition

This study deals with the stagnation point flow of ferrofluid over a flat plate with non-linear slip boundary condition in the presence of homogeneous-heterogeneous reactions.Three kinds of ferroparticles,namely,magnetite(Fe_3O_4),cobalt ferrite(CoFe_2O_4) and manganese zinc ferrite(Mn-ZnFe_2O_4) are taken into account with water and kerosene as conventional base fluids.The developed model of homogeneous-heterogeneous reactions in boundary layer flow with equal and unequal diffusivities for reactant and autocatalysis is considered.The governing partial differential equations are converted into system of non-linear ordinary differential equations by mean of similarity transformations.These ordinary differential equations are integrated numerically using shooting method.The effects of pertinent parameters on velocity and concentration profiles are presented graphically and discussed.We found that in the presence of Fe_3O_4-kerosene and CoFe_2O_4-kerosene,velocity profiles increase for large values of α and β whereas there is a decrement in concentration profiles with increasing values of if and K_s.Furthermore,the comparison between non-magnetic(A1_2O_3) and magnetic Fe_3O_4 nanoparticles is given in tabular form.

Radiation efects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition

The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder.The effects of radiation and convective boundary condition are also taken into account.The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis.The resulting nonlinear momentum,energy and nano particle equations are simplifed using similarity transformations.Numerical solutions have been obtained for the velocity,temperature and nanoparticle fraction profles.The influence of physical parameters on the velocity,temperature,nanoparticle fraction,rates of heat transfer and nanoparticle fraction are shown graphically.

BOUNDARY VXLUE PROBLEMS FOR SYSTEMS OF NONLINEAR SECOND ORDER DIFFERENTIAL DFFERENCE EQUATIONS

The author studies the boundary value problems for systems of nonlinear second order differential dmerence equstions and adopts a new-type Nagumo conditinn, in which the controlfunction is a vector-Valued function of several variables and which can guarsntee simultaneously and easily finding a priori bounds of eaCh component of the deriVatives of the solutions.Under this new-type Nagumo condition the existence results of solution are proved by meansof differential inopality technique.