On the Barber Boundary Conditions for Thermoelastic Contact

1979 ◽  
Vol 46 (4) ◽  
pp. 849-853 ◽  
Author(s):  
Maria Comninou ◽  
J. Dundurs
Keyword(s):  
Heat Flux ◽  
Heat Flow ◽  
Boundary Conditions ◽  
Half Space ◽  
Direct Transition ◽  
Imperfect Contact ◽  
Heat Flows ◽  
Thermoelastic Contact ◽  
Perfect Contact ◽  
Resistance To Heat

A dilemma arising from the conventional boundary conditions for thermoelastic contact was observed by Barber in treating the indentation of an elastic half space by a rigid sphere. If the sphere is colder than the half space, the interface tractions are necessarily tensile near the periphery of the contact region. In order to overcome this difficulty, Barber introduced the idea of an imperfect contact zone. An asymptotic analysis of the transitions between the different zones is carried out in this article. It is found that, if heat flows into the body with the larger distortivity, a direct transition from perfect contact (no resistance to heat flow) to separation (no heat flow) is possible, the zone of imperfect contact (vanishing contact pressure and some resistance to heat flow) is automatically excluded, and the heat flux is square-root singular at the transition. If heat flows in the opposite direction, no direct transition from perfect contact to separation is possible, there must be an intervening zone of imperfect contact, and the heat flux is logarithmically singular at the transition from perfect to imperfect contact. The transition from imperfect contact to separation is always possible, and it is smooth. These conclusions are direct consequences of the inequalities that must be enforced because of the unilateral nature of thermoelastic contact.

scholarly journals IDENTIFICATION OF MEMORY KERNELS IN HEAT FLOW MEASURING HEAT FLUX AT THE ENDS OF THE BAR

2010 ◽  
Vol 15 (4) ◽  
pp. 473-490 ◽  
Author(s):  
Enno Pais
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Flow ◽  
Boundary Conditions ◽  
Internal Energy ◽  
Existence And Uniqueness ◽  
Financial Support ◽  
Thermal Memory ◽  
Flux Measurements ◽  
Uniqueness Of A Solution

An inverse problem to determine time‐ and space‐dependent relaxation kernels of internal energy and heat flux with first kind boundary conditions by means of heat flux measurements is considered. The case when observations of the heat flux are made at the ends of the bar with thermal memory was not studied before. Existence and uniqueness of a solution to the inverse problem are proved. The financial support of Estonian Science Foundation is gratefully acknowledged (Grant nr. 7728).

scholarly journals Heat Conduction Through a Flat Punch

1981 ◽  
Vol 48 (4) ◽  
pp. 871-875 ◽  
Author(s):  
Maria Comninou ◽  
J. R. Barber ◽  
John Dundurs
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Half Plane ◽  
Contact Region ◽  
Thermal Contact ◽  
Total Heat Flux ◽  
Flat Punch ◽  
Imperfect Contact ◽  
Perfect Contact ◽  
Perfect Thermal Contact

An elastic half plane is indented by a perfectly conducting rigid flat punch, which is maintained at a different temperature from the half plane. It is found that, depending on the magnitude and direction of the total heat flux, one of the following states occurs: separation at the punch corners, perfect thermal contact throughout the punch face, or an imperfect contact region at the center with adjacent perfect contact regions.

scholarly journals Planar Hertz Contact With Heat Conduction

1981 ◽  
Vol 48 (3) ◽  
pp. 549-554 ◽  
Author(s):  
M. Comninou ◽  
J. Dundurs ◽  
J. R. Barber
Keyword(s):  
Integral Equation ◽  
Heat Conduction ◽  
Contact Problem ◽  
Boundary Conditions ◽  
Hertz Contact ◽  
Imperfect Contact ◽  
Common Boundary ◽  
Heat Flows ◽  
The Common ◽  
Hertz Contact Problem

The paper discusses the planar Hertz contact problem when the bodies are not only pressed together but also exchange heat by conduction. The nature of the problem and the results depend strongly on the direction of heat flow. If heat flows into the material with the larger distortivity, the common boundary conditions are sufficient to achieve a solution which satisfies the inequalities associated with a contact problem. For heat flowing in the opposite direction, the common boundary conditions by themselves lead to contradictions, but the difficulties can be overcome by introducing a zone of imperfect contact. The formulation is based on a suitable Green’s function, and the problem is reduced to a singular integral equation which must be solved numerically.

Thermoelastic Contact Between Bodies With Wavy Surfaces

1979 ◽  
Vol 46 (4) ◽  
pp. 854-860 ◽  
Author(s):  
Carl Panek ◽  
J. Dundurs
Keyword(s):  
Heat Flow ◽  
Boundary Conditions ◽  
Elastic Solid ◽  
Rigid Sphere ◽  
Thermal Coefficient ◽  
Elastic Solids ◽  
Contact Zones ◽  
Heat Flows ◽  
Wavy Surfaces ◽  
Separation Zones

The problem treated involves two elastic solids with wavy surfaces that are pressed together and at the same time exchange heat by conduction because of an externally imposed temperature gradient. The conventional boundary conditions of no interface resistance to heat flow in the contact zones, and no heat transmission in the separation zones are adopted. It is found that the contact tractions are compressive if heat flows into the material with the higher distortivity (essentially the thermal coefficient of expansion divided by the thermal conductivity). For heat flow in the opposite direction, however, the conventional boundary conditions lead to some tensile tractions at the ends of the contact zones. The same observation has also been made by Barber who considered the indentation of an elastic solid by a rigid sphere that is either heated or cooled. The modification of the boundary conditions proposed by Barber, and which maintains linearity, is mentioned parenthetically.

Solution of a Heat Flow Problem

1951 ◽  
Vol 4 (1) ◽  
pp. 12 ◽  
Author(s):  
JRM Radok
Keyword(s):  
Heat Flux ◽  
Heat Flow ◽  
Temperature Gradient ◽  
Heat Source ◽  
Boundary Conditions ◽  
Flow Problem ◽  
Zero Temperature ◽  
Insulating Materials ◽  
Constant Temperature Gradient ◽  
Flow Through

This paper deals with the heat flow through a rectangle subject to the following boundary conditions : One end is completely insulated (without heat flux across it) and at the opposite end a constant temperature gradient is maintained; the remaining sides radiate into a medium which is at zero temperature. Initially the rectangle is at zero temperature. The problem is converted into a homogeneous one by considering a rectangle of twice the length with a uniformly distributed heat source along the centre line. The solution of this problem is effected by using particular solutions given in Carslaw and Jaeger. The problem considered is of interest in connection with the testing of heat-insulating materials.

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

Boundary-value problems in the kinetic theory of gases. Part 2. Thermal creep

1971 ◽  
Vol 45 (4) ◽  
pp. 759-768 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Kinetic Theory ◽  
Effective Thermal Conductivity ◽  
Half Space ◽  
Thermal Creep ◽  
Kinetic Theory Of Gases ◽  
Boundary Wall ◽  
Creep Velocity

The effect of a temperature gradient in a gas inclined at an angle to a boundary wall has been investigated. For an infinite half-space of gas it is found that, in addition to the conventional temperature slip problem, the component of the temperature gradient parallel to the wall induces a net mass flow known as thermal creep. We show that the temperature slip and thermal creep effects can be decoupled and treated quite separately.Expressions are obtained for the creep velocity and heat flux, both far from and at the boundary; it is noted that thermal creep tends to reduce the effective thermal conductivity of the medium.

Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

1978 ◽  
Vol 45 (4) ◽  
pp. 812-816 ◽  
Author(s):  
B. S. Berger ◽  
B. Alabi
Keyword(s):  
Fourier Transform ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Half Space ◽  
Coordinate Transformation ◽  
Numerical Results ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Rectangular Region

A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3, is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

Calculations of Phase Transformations in Welding Simulations

2014 ◽  
Vol 611 ◽  
pp. 46-53 ◽  
Author(s):  
Ladislav Novotný ◽  
Vladimír Ivančo
Keyword(s):  
Heat Flux ◽  
Phase Transformation ◽  
Boundary Conditions ◽  
Phase Transformations ◽  
Diffusion Processes ◽  
Transient Solution ◽  
Welding Simulation

In the paper the principle of welding simulation is presented and the methods of solution of phase transformation are described. The first part characterizes elementary equations of heat transient solution, boundary conditions during welding simulation (prescribing moving heat flux, convection, radiation). The methods of phase transformations’ solution are described for diffusion processes as well as diffusionless processes.

Sign in / Sign up

Export Citation Format

Share Document