An exact solution for non-darcy free convection from a horizontal line source of heat

1988 ◽  
Vol 22 (3-4) ◽  
pp. 125-127 ◽  
Author(s):  
D. B. Ingham
Keyword(s):  
Exact Solution ◽  
Free Convection ◽  
Line Source ◽  
Horizontal Line

Diffraction of impulsive elastic waves by a fluid cylinder

1974 ◽  
Vol 75 (3) ◽  
pp. 391-404 ◽  
Author(s):  
Ramanand Jha
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Elastic Medium ◽  
Elastic Waves ◽  
Line Source ◽  
Inviscid Fluid ◽  
Geometrical Theory ◽  
Shadow Zone ◽  
Integral Transformations ◽  
Geometrical Theory Of Diffraction

AbstractIn this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

scholarly journals Laminar free convection induced by a line heat source, and heat transfer from wires at small Grashof numbers

1998 ◽  
Vol 362 ◽  
pp. 199-227 ◽  
Author(s):  
AMABLE LIÑÁN ◽  
VADIM N. KURDYUMOV
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Line Source ◽  
Outer Region ◽  
Analytical Description ◽  
Temperature Fields ◽  
Thermal Plume ◽  
Line Heat Source ◽  
First Approximation ◽  
Wide Range

The buoyancy-induced laminar flow and temperature fields associated with a line source of heat in an unbounded environment are described by numerically solving the non-dimensional Boussinesq equations with the appropriate boundary conditions. The solution is given for values of the Prandtl number, the single parameter, ranging from zero to infinity. The far-field form of the solution is well known, including a self-similar thermal plume above the source. The analytical description close to the source involves constants that must be evaluated with the numerical solution.These constants are used when calculating the free convection heat transfer from wires (or cylinders of non-circular shape) at small Grashof numbers. We find two regions in the flow field: an inner region, scaled with the radius of the wire, where the effects of convection can be neglected in first approximation, and an outer region where, also in first approximation, the flow and temperature fields are those due to a line source of heat. The cases of large and small Prandtl numbers are considered separately. There is good agreement between the Nusselt numbers given by the asymptotic analysis and by the numerical analysis, which we carry out for a wide range of Grashof numbers, extending to very small values the range of existing numerical results; there is also agreement with the existing correlations of the experimental results. A correlation expression is proposed for the relation between the Nusselt and Grashof numbers, based on the asymptotic forms of the relation for small and large Grashof numbers.

Vertex generated waves outside metallic wedges

1961 ◽  
Vol 57 (2) ◽  
pp. 393-400 ◽  
Author(s):  
W. E. Williams ◽  
L. Rosenhead
Keyword(s):  
Exact Solution ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Surface Impedance ◽  
Line Source ◽  
Complete Agreement ◽  
Magnetic Line ◽  
Arbitrary Angle ◽  
Surface Reactance ◽  
The Waves

ABSTRACTA study is made of the waves generated by a magnetic line source placed at the vertex of a wedge of high conductivity and arbitrary angle. The boundary-value problem is reduced to the solution of a difference equation and an exact solution obtained. The method is also applied to the case of dielectric coated wedges where the surface reactance and resistance are arbitrary, and the propagation of surface waves along such surfaces is considered briefly. The forms of the solution for large and small values of the surface impedance are obtained and show complete agreement with the known results available for a right-angled wedge and a plane.

Mixed convection from a horizontal line source of heat

1986 ◽  
Vol 29 (2) ◽  
pp. 344-347 ◽  
Author(s):  
Ramesh Krishnamurthy ◽  
Benjamin Gebhart
Keyword(s):  
Mixed Convection ◽  
Line Source ◽  
Horizontal Line

On cylindrical waves in stratified media: high frequency refraction and diffraction at a plane interface

1970 ◽  
Vol 67 (1) ◽  
pp. 133-161 ◽  
Author(s):  
I. Roebuck
Keyword(s):  
Exact Solution ◽  
Wave Equation ◽  
High Frequency ◽  
Line Source ◽  
Dielectric Medium ◽  
Plane Interface ◽  
Stratified Media ◽  
Cylindrical Waves ◽  
Cylindrical Obstacle ◽  
High Frequency Waves

Introduction. The problem of the scattering of high-frequency waves, which emanate from a line source in a homogeneous isotropic dielectric medium and impinge upon a cylindrical obstacle, has been attacked in a variety of ways. In certain cases, where both the shape of the obstacle and the conditions to be satisfied on its boundary are particularly convenient, an exact solution may be found by separation of the wave equation (see, for example, Marcuvitz (l)), but in general some form of approximation is necessary to obtain an explicit answer.

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