Sub Mach-1 sound due to an arbitrary time dependent source near an absorbing half plane

2005 ◽  
Vol 163 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Bashir Ahmad
Keyword(s):  
Half Plane ◽  
Time Dependent ◽  
Arbitrary Time

scholarly journals The Diffraction of Transient Electro-Magnetic Waves by a Wedge

1958 ◽  
Vol 11 (2) ◽  
pp. 95-103 ◽  
Author(s):  
A. C. Butcher ◽  
J. S. Lowndes
Keyword(s):  
Wave Equation ◽  
Time Dependence ◽  
Half Plane ◽  
Line Source ◽  
Time Dependent ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Electro Magnetic ◽  
Infinite Wedge ◽  
Magnetic Waves

Much of the work on the theory of diffraction by an infinite wedge has been for cases of harmonic time-dependence. Oberhettinger (1) obtained an expression for the Green's function of the wave equation in the two dimensional case of a line source of oscillating current parallel to the edge of a wedge with perfectly conducting walls. Solutions of the time-dependent wave equation have been obtained by Keller and Blank (2), Kay (3) and more recently by Turner (4) who considered the diffraction of a cylindrical pulse by a half plane.

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

A CLOSED-FORM SOLUTION OF THE EVOLUTION OPERATOR IN TWO-LEVEL SYSTEMS

1994 ◽  
Vol 08 (08n09) ◽  
pp. 505-508 ◽  
Author(s):  
XIAN-GENG ZHAO
Keyword(s):  
Closed Form ◽  
Lie Algebra ◽  
Evolution Operator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Two Level Systems ◽  
Special Case

It is demonstrated by using the technique of Lie algebra SU(2) that the problem of two-level systems described by arbitrary time-dependent Hamiltonians can be solved exactly. A closed-form solution of the evolution operator is presented, from which the results for any special case can be deduced.

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