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1.
A new analytical solution is introduced for the effect of viscous dissipation on mixed convection flow and heat transfer about an isothermal vertical wall embedded in Darcy and non-Darcy porous media with uniform free stream velocity. The effect of viscous dissipation on mixed convection in both regimes has been analyzed for both the aiding and opposing flows using Gebhart number, Ge x =gx/c p. The governing parameters are Re, Ra, Pe and Ge x . The case of Re=0 corresponds to Darcy mixed convection region and Re/Pe is identified as the mixed convection governing parameter, Ra=0 leading to pure forced convection. A good agreement was found between the numerical and analytical solutions. It was found from the Nusselt number results that viscous dissipation lowers the heat transfer rate in both Darcy and Forchheimer flow regimes for aiding as well as opposing flows.  相似文献   

2.
Lombardi  Ariel L.  Tarzia  Domingo A. 《Meccanica》2001,36(3):251-264
Similarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type is imposed on the fixed face x=0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q 0 is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x=0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo viene imposta sulla faccia fissa x=0. Si analizzano differenti casi dipendenti da parametri fisici e la soluzione esplicita viene ottenuta se e solo se risulta verificata una diseguaglianzo per il coefficiente termico q 0. Si ottiene altresi un miglioramento della condizione di esistenza di una soluzione di similarità per lo stesso problema al contorno libero con temperatura costante sulla faccia fissa x=0.  相似文献   

3.
Nonequilibrium air–water mass transfer experiments using a laboratoryscale singleair channel setup were conducted to investigate the influence of porous media and air velocity on the fate of nonaqueous phase liquids (NAPLs) under air sparging conditions. Benzene was used as a NAPL while silica sand 30/50 (dp50=0.305mm, uniformity coefficient, UC=1.41) and silica sand 70/100 (dp50=0.168mm, UC=1.64) were used as porous media. Air velocities ranged from 0 to 1.4cm/s. Mass transfer coefficients for the dissolution of NAPLs were estimated by numerical methods using a twodimensional dissolution–diffusion–volatilization model. The study showed that the presence of advective airflow in air channels controlled the spreading of the dissolved phase but the overall removal efficiency was independent of airflow rate. Removal efficiencies and dissolution rates of the NAPL were found to be strongly affected by the mean particle size of the porous media during air sparging. More than 50% reduction in the removal rate of benzene was found when silica sand 70/100 was used instead of silica sand 30/50. Mass transfer coefficients for the dissolution of benzene NAPL were estimated to be 0.0041cm/min for silica sand 70/100 and 0.227cm/min for silica sand 30/50. Increasing the air velocity from 0.6 to 1.4cm/s for silica sand 30/50 did not result in a higher removal rate. Quantitative estimation of the dissolution rates of benzene NAPL indicated that the dissolution rates (between 0.227 and 0.265cm/min) were similar in magnitude for the same porous media but different air flow rates. Based on the visualization study, air sparging may be used to control the spreading of the dissolved phase even when the glob of NAPL is several centimeters away from the air–water interface of the air channels.  相似文献   

4.
Given a time T>0 and a region on a compact Riemannian manifold M, we consider the best constant, denoted CT,, in the observation inequality for the Schrödinger evolution group of the Laplacian with Dirichlet boundary condition: We investigate the influence of the geometry of on the growth of CT, as T tends to 0.By duality, CT, is also the controllability cost of the free Schrödinger equation on M with Dirichlet boundary condition in time T by interior controls on . It relates to hinged vibrating plates as well. We analyze separately the effects of wavelengths which are greater and lower than the order of the control time T. We emphasize a tool of wider scope: the control transmutation method.We prove that CT, grows at least like exp(d2/4T), where d is the largest distance of a point in M from , and at most like exp(*L2/T), where L is the length of the longest generalized geodesic in M which does not intersect , and * ]0,4[ is the best constant in the following inequality for the Schrödinger equation on the segment [0,L] observed from the left end: where A is the operator x2 with domain D(A)={fH2(0,L),|,Bf(0)=0=f(L)} and the inequality holds with B=1 and with B=x. We also deduce such upper bounds on product manifolds for some control regions which are not intersected by all geodesics.  相似文献   

5.
On laminar flow through a uniformly porous pipe   总被引:2,自引:0,他引:2  
Numerous investigations ([1] and [4–9]) have been made of laminar flow in a uniformly porous circular pipe with constant suction or injection applied at the wall. The object of this paper is to give a complete analysis of the numerical and theoretical solutions of this problem. It is shown that two solutions exist for all values of injection as well as the dual solutions for suction which had been noted by previous investigators. Analytical solutions are derived for large suction and injection; for large suction a viscous layer occurs at the wall while for large injection one solution has a viscous layer at the centre of the channel and the other has no viscous layer anywhere. Approximate analytic solutions are also given for small values of suction and injection.

Nomenclature

General r distance measured radially - z distance measured along axis of pipe - u velocity component in direction of z increasing - v velocity component in direction of r increasing - p pressure - density - coefficient of kinematic viscosity - a radius of pipe - V velocity of suction at the wall - r 2/a 2 - R wall or suction Reynolds number, Va/ - f() similarity function defined in (6) - u 0() eigensolution - U(0) a velocity at z=0 - K an arbitrary constant - B K Bernoulli numbers Particular Section 5 perturbation parameter, –2/R - 2 a constant, –K - x / - g(x) f()/ Section 6 perturbation parameter, –R/2 - 2 a constant, –K - g() f() - g c ()=g() near centre of pipe - * point where g()=0 Section 7 2/R - 2 K - t (1–)/ - w(t, ) [1–f(t)]/ - 0, 1 constants - g() f()– 0 - 0/ - 0 a constant - * point where f()=0  相似文献   

6.
Zusammenfassung Die Stabilität der ebenen Couette- und der ebenen Poiseuille-Strömung nicht-newtonscher Fluide wird für kleine Störungen in der viskometrischen Ebene untersucht. Der Einfluß der Relaxationszeit der Störungen wird vernachlässigt. Es wird gezeigt, daß die ebene Couette-Strömung unabhängig von der ReZahl instabil wird, fallsd(N)/d > 4 >d gilt. Hier bedeuten die Schergeschwindigkeit,N den ersten Normalspannungskoeffizienten, die Viskosität und d die differentielle Viskosität ( d =d/d). Das gleiche Kriterium gilt mit den Daten an der Kanalwand auch für die Poiseuille-Strömung. In diesem Fall oszillieren die Eigenfunktionen in einer sehr dünnen, wandnahen Schicht und klingen im Flüssigkeitsinnern sehr rasch ab.
Summary The stability of plane Couette and plane Poiseuille flow of a non-Newtonian fluid is investigated for small perturbations in the viscometric plane. The influence of the relaxation time of the perturbations is neglected. It is shown that plane Couette flow will become unstable independently of Reynolds number ifd(N)/d > 4 d holds. Here are the rate of shear velocity,N the first normal stress coefficient, the viscosity and d the differential viscosity ( d =d/d). The same criterion holds also for plane Poiseuille flow with the data taken at the wall. In this case the eigenfunctions are oscillating in a very thin layer near the wall and decaying very rapidly in the inner region of the flow field.
Mit 11 Abbildungen  相似文献   

7.
The effect of Hall currents on magneto hydrodynamic (MHD) flow of an incompressible viscous electrically conducting fluid between two non-conducting porous plates in the presence of a strong uniform magnetic field is studied. The flow is generated by a small uniform suction at the plates. Solutions are obtained for suction Reynolds number R1, considering two cases for the imposed magnetic field, viz. (i) when the magnetic field is perpendicular to the plates (parallel to y-axis), and (ii) when the magnetic field is parallel to the plates and perpendicular to the primary flow direction (parallel to z-axis). The effect of the Hall currents on the flow as well as on the heat transfer is studied. It is observed that in the absence of Hall currents, the change of the direction of the applied magnetic field does not affect the primary flow.Nomenclature B total magnetic induction vector - V velocity vector - E electric field vector - J current density vector - U 0 suction velocity - T temperature of the fluid at any point - B 0 imposed magnetic field - u x-component of fluid velocity - v y-component of fluid velocity - w z-component of fluid velocity - density of the fluid - kinematic viscosity of the fluid - c p specific heat at constant pressure - p fluid pressure - electrical conductivity of the fluid - K coefficient of thermal conductivity - e magnetic permeability - n e number density of electrons - e electric charge - dimensionless distance (=y/h) - f(), g(), Q(), () dimensionless functions defined in (14) - R suction Reynolds number (=U 0 h/) - M Hartmann number (=B 0 h(/)1/2) - m Hall parameter (=B 0/en e) - Pr Prandtl number of the fluid (=c p/K) - s dimensionless quantity defined as s=(T 1T 0)/[vU 0/(hc p)]  相似文献   

8.
We study the Cauchy problem for a strictly hyperbolic n×n system of conservation laws in one space dimension assuming that the initial data has bounded but possibly large total variation. Under a linearized stability condition on the Riemann problems generated by the jumps in we prove existence and uniqueness of a (local in time) BV solution, depending continuously on the initial data in L1loc. The last section contains an application to the 3×3 system of gas dynamics.  相似文献   

9.
In the hypersonic thin shock layer approximation for a small ratio k of the densities before and after the normal shock wave the solution of [1] for the vicinity of the stagnation point of a smooth blunt body is extended to the case of nonuniform outer flow. It is shown that the effect of this nonuniformity can be taken into account with the aid of the effective shock wave radius of curvature R*, whose introduction makes it possible to reduce to universal relations the data for different nonuniform outer flows with practically the same similarity criterion k. The results of the study are compared with numerical calculations of highly underexpanded jet flow past a sphere.Notations x, y a curvilinear coordinate system with axes directed respectively along and normal to the body surface with origin at the forward stagnation point - R radius of curvature of the meridional plane of the body surface - uV, vV., , p V 2 respectively the velocity projections on the x, y axes, density, and pressure - and V freestream density and velocity The indices =0 and=1 apply to plane and axisymmetric flows Izv. AN SSSR, Mekhanika Zhidkosti i Gaza, Vol. 5, No. 3, pp. 102–105, 1970.  相似文献   

10.
S. Kase 《Rheologica Acta》1982,21(2):210-211
The general integral of the very simple equation 21/n/() was found to describe the cross sectional area of filaments of isothermal power law fluids while in transient stretching where is time and is the initial location of fluid molecules at time = 0 given as the distance from a reference point fixed in space. Any such stretching transient given as a solution of the above equation is physically realizable subject to the restrictions > 0 and/ < 0.  相似文献   

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