THE ASYMPTOTIC SOLUTION OF THE UNSTEADY PLANAR PARALLEL GAS FLOW FOR THE CASE TEAT THE ADIABATIC INDEX NUMBER γ IS BIG

1.Fo’·mulation of the Problem 。VVlllll山lit山llollp〔)1111匕川11h)11V111()fily山clfl!ICUOI仆O门I工ch11川p川jllilTldco\\℃\cCk h。\川VC山c cqu川11)11s()1山) Idl川pIS fills比S心phllul卜ti川*pt!ttlljll 11OW. !山C卜(小11 Ic(】l川111比八八1111,山11qtJZtllOOS()1山e心)川》u口111lildy philuI 卜11i川d卜ILllll川*】V illC‘ (J;。,口‘I,I【.、o(v丫)。4;1, 刃’I 于十N宁十叫 讣一 i)“二二二二+TX+…一1)。二W卜0(l) 山 *厂 厂坯(V 川J 口01 o川,oil。、,。。;I :一+刊十(叫十丁‘)十一上二一卜O(I…     

THE NUMERICAL SOLUTION OF THE UNSTEADY NATURAL CONVECTION FLOW IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER USING SADI METHOD

The unsteady natural convection flow in a square cavity at high Rayleigh numberRa=10~7 and 2×10~7 has been computed using cubic spline integration.The requiredsolutions to the two dimensional Navier-Stokes and energy equations have been obtainedusing two alternate numerical formulations on non-uniform grids.The main features of thetransient flow have been briefly discussed.The results obtained by using the present methodare in good agreement.with the theoretical predictions.The steady state results havebeen compared with accurate solutions presented recently for Ra=10~7.     

ASYMPTOTIC SOLUTION OF SINGULAR PERTURBATION PROBLEMS FOR THE FOURTH-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper we consider the singularly perturbed boundary value problem for thefourth-order elliptic differential equation,establish the energy estimates of the solutionandits derivatives and construct the formal asymptotic solution by Lyuternik-Vishik’s method.Finally,by means of the energy estimates we obtain the bound of the remainder of theasymptotic solution.     

THE APPROXIMATE SOLUTION OF THE SELF-SIMILAR PROBLEM FOR RADIAL FLOW OF NON-NEWTONIAN FLUIDS THROUGH POROUS MEDIA

In this paper, we study the approximate solution of the self-simikar problem for radial flow of non-Newtonian fluids through porous media. Assuming that the fluids obey the exponential function law, we obtain an exact solution for the exponent n=0 and compare it with the approximate solution in ref.[1]. For n>1 and n<1, we obtain respectively approximate solutions. Some exampls are presented.     

THE ASYMPTOTIC EXPRESSION OF THE SOLUTION OF THE CAUCHY’S PROBLEM FOR A HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION WHEN THE LIMIT EQUATION HAS SINGULARITY

ＴＨＥＡＳＹＭＰＴＯＴＩＣＥＸＰＲＥＳＳＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＯＦＴＨＥＣＡＵＣＨＹ’ＳＰＲＯＢＬＥＭＦＯＲＡＨＩＧＨＥＲＯＲＤＥＲＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＨＥＮＴＨＥＬＩＭＩＴＥＱＵＡＴＩＯＮ...     

A NEW APPROXIMATE ANALYTICAL SOLUTION OF THE IDEAL POTENTIAL FLOW AROUND A CIRCULAR CYLINDER BETWEEN TWO PARALLEL FLAT PLATES

In ref. [1], Lin obtained an approximate analytical solution of the ideal potential flow around a circular cylinder between two parallel flat flates. In this paper, the author shows that one may obtain the result coinciding with that obtained in ref. [1] by making use of the Shvez's method. Morever, we can obtain a more accurate result than that obtained in ref. [1], if we make use of the improved Shvez's method. Some calculating examples are presented.     

ASYMPTOTIC EXPERSSION OF THE SOLUTION OF GENERAL BOUNDARY VALUE PROBLEN FOR HIGHER ORDER ELLIPTIC EQUATION WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

In this paper basing on (1) and (2),we study thesingular perturbation of general boundary value problemfor higher order elliptic equation with perturbationboth in the boundary and in the operator,so as to es-tablish the asymptotic expression involving two para-meters.Thus,the iterative process of finding theasymptotic solution is derived and the estimation ofthe remainder term is given out,we extend and improvethe previously published papers.