摘要:

AbstractA series solution in descending powers of time is developed for heatconduction problems with initial profiles prescribed at an instant t*>0. The leading term of the series solution, the first eigensolution, represents a source with strength given by the integral of the initial profile. It is shown that the coefficients of the eigensolutions corresponding to the second eigenvalue can be equated to zero when the origin is shifted to the center of gravity of the initial profile and that the coefficient of the symmetric eigensolution of the third eigenvalue will vanish when the time shift t* is related to the second moment of the initial profile. The first eigensolution with these optimum shifts in space and time variables yields an optimum one term representation of the exact solution as time increases. The optimum solution fulfills two properties of the exact solution, the conservation of energy integral and the invariance of the center of gravity of the temperature profile. Proofs for these properties of the exact solution are presented.

ISSN:0044-2267    

DOI:10.1002/zamm.19710510101

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

摘要:

AbstractThe slow stationary motion of a uniformly flowing viscous fluid past a circular porous inhomogeneous cylinder of radius (a + b) is considered. The problem is fully described by the Darcy law, which holds good in the region inside the body, the Navier‐Stokes equations, describing the flow field outside the body, the continuity conditions and the suitable boundary conditions. The solution to the system of equations is obtained by the construction and suitable matching of four simultaneous asymptotic expansions: inner‐most expansion valid in the region 0 ≦ r' ≦ a, interior expansion valid in the region a ≦ r' ≦ (a + b) and the usual inner (Stokes) and outer (Oseen) expansions. The drag formula is expressed in terms of an equivalent permeability. The effect of permeability on the drag is that it reduces the effective radius of the cylinder by a factor exp [–∽KT'/(a + b)2]. Several special cases have

ISSN:0044-2267    

DOI:10.1002/zamm.19710510102

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

摘要:

AbstractThe present investigation is concerned with the problem of studying the effect of permeability on drag coefficient for the flow past a porous sphere placed in an otherwise uniform incident stream at low Reynolds number. The problem is formulated using the full Navier‐Stokes equations describing the flow outside the sphere while Darcy's law governs the flow inside the sphere. The solution is, then, sought by the method of matched asymptotic expansions involving three simultaneous expansions up to an order Re. It is found that the effect of porosity on the drag is that it reduces the effective radius a of the sphere by a factor (1 + k'/2a2)−1, where k' is the permeabil

ISSN:0044-2267    

DOI:10.1002/zamm.19710510103

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

摘要:

AbstractEs wird das instationäre Problem der Hyperschallströmung um rotationssymmetrische stumpfe Körper behandelt, deren Profilform von der Wandtemperatur abhängt. Auf dem Körper soll eine dünne Schicht aufgetragen sein, deren Schmelztemperatur niedriger als die für den Körper zulässige Temperatur ist. Die Temperaturverteilung im Inneren der Schicht muß numerisch errechnet werden. Zu einem Zeitpunktt=t0wird die Schmelztemperatur im Staupunkt der aufgetragenen Schicht erreicht, beit=tTim Staupunkt des eigentlichen Körpers. Fürt≦t0ist die Strömung stationär, fürt0≦t≦tTwird der Wanddruck aus dem instationären Gleichungssystem bestimmt, das bezüglich der stationären Str

ISSN:0044-2267    

DOI:10.1002/zamm.19710510104

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

摘要:

AbstractThe general quasistatic Stokes force and settling velocity acting on a spherical droplet were formulated. The droplet is submerged in an unbounded flow field, which is Stokes'ian far from the droplet. The drag force formulated here by eq. (41) includes the law of Faxên as a special case. The settling velocity formulated here by eq. (43) includes all previous solutions with similar boundary conditions. It is demonstrated that these parameters can be computed solely from a knowledge of the solution of Hadamard‐Rybczynski and the unperturbed flow fie

ISSN:0044-2267    

DOI:10.1002/zamm.19710510105

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19710510106

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19710510107

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19710510108

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19710510109

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19710510110

出版商:WILEY‐VCH Verlag    

年代:1971

数据来源: WILEY