RADIAL-AXIAL HEAT FLOW IN REGIONS BOUNDED INTERNALLY BY CIRCULAR CYLINDERS

1953 ◽  
Vol 31 (4) ◽  
pp. 472-479 ◽  
Author(s):  
J. H. Blackwell
Keyword(s):  
Heat Flow ◽  
Integral Transform ◽  
Circular Cylinders ◽  
Flow Problems ◽  
Solution Type ◽  
Transient Heat Flow ◽  
Different Types ◽  
Axial Heat ◽  
Simple Product ◽  
Product Solution

Two radial–axial transient heat flow problems have been solved for regions bounded internally by circular cylinders. They are not of the simple "product-solution" type and it is considered that they may have application in other fields of physics where the Diffusion Equation applies. The problems arose during investigation into "end-effect" in cylindrical thermal-conductivity probes. The solutions are obtained by integral-transform methods, two different types of transform being used in each solution.

Boundary Integral Methods for Thermoelasticity Problems

1986 ◽  
Vol 53 (2) ◽  
pp. 298-302 ◽  
Author(s):  
S. Sharp ◽  
S. L. Crouch
Keyword(s):  
Heat Flow ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Thermally Induced ◽  
Flow Problems ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Transient Heat Flow ◽  
Induced Stresses

The boundary integral method for solving transient heat flow problems is extended to calculate thermally induced stresses and displacements. These results are then corrected by means of an elastostatic solution to satisfy the boundary conditions.

Numerical Solution to Transient Heat Flow Problems

1973 ◽  
Vol 41 (4) ◽  
pp. 517-525 ◽  
Author(s):  
Ronald A. Kobiske ◽  
Jeffrey L. Hock
Keyword(s):  
Heat Flow ◽  
Numerical Solution ◽  
Flow Problems ◽  
Transient Heat Flow

The Solution of Transient Heat-flow Problems by Analogous Electrical Networks

1953 ◽  
Vol 167 (1) ◽  
pp. 275-290 ◽  
Author(s):  
D. I. Lawson ◽  
J. H. McGuire
Keyword(s):  
Heat Conduction ◽  
Heat Flow ◽  
Series Resistance ◽  
Electrical Networks ◽  
Detailed Design ◽  
Flow Problems ◽  
Transient Heat Flow ◽  
Electrical Analogy ◽  
In Series

The design of a machine for solving heat-conduction problems by their electrical analogy with the flow of current in series-resistance, shunt-capacity, networks, is described in this paper. Consideration is given to the representation of cooling by radiation and convection, and the detailed design of the circuits is discussed.

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

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