Exact solution of constriction resistance and temperature field within a homogeneous cylindrical body heated by an isothermal circular contact spot

1985 ◽  
Vol 12 (6) ◽  
pp. 677-686 ◽  
Author(s):  
C. Faltin
Keyword(s):  
Exact Solution ◽  
Temperature Field ◽  
Cylindrical Body ◽  
Contact Spot ◽  
Constriction Resistance ◽  
Circular Contact

scholarly journals Cylindrical body temperature field simulation which made in the transitional thermal process conditions out of polymer material

2020 ◽  
Vol 7 (3) ◽  
Author(s):  
Liliya Petrova ◽  
Tatyana Gavrilova
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Body Temperature ◽  
Polymer Composite ◽  
Thermal Process ◽  
Cylindrical Body ◽  
Phase Delay ◽  
Process Conditions ◽  
Two Phase ◽  
Transient Thermal

The advancing requirements for strength, relaxation, thermophysical, electrical, and other structural elements characteristics actualizes the polymer composite material use for the soft part and node point manufacture, which improves performance index. This paper reported the need to take into account relaxation phenomena in predicting the body’s thermal field development that is made of polymeric materials, and the thermal relaxation time and the thermal damping time proportional to the duration of transient thermal process certain periods. In this article three-period thermal process in a cylindrical body mathematical model is presented. cylindrical body made of a low-heat-conducting material by using a heat conduction hyperbolic equation that is reflecting the heat flow relaxation and thermal damping phenomenon. A numerical solution to the problem of unsteady heat conduction in a circular disk for a two-phase delay equation is presented, which is based on the grid method implementation by using a three-layer implicit difference scheme and the finite difference method use. Calculation formulas for the run-through coefficients as well as the temperature values at the outer boundaries are concluded using the boundary conditions approximation for the intermediate and upper time layers, taking into account the multi-period of the process. The implementation of the modified run-through method when solving the non-stationary heat conduction problem in a cylindrical body, taking into account the finite heat propagation speed and thermal damping is described. The calculation results for the cylindrical body temperature field are obtained by using the polymethyl methacrylate example upon sudden heating based on a model with a two-phase delay. The results presented in this paper aid in an increase in predicting temperature field accuracy in polymer composite materials in the transient thermal processes study.

Effect of Surface Curvature on Contact Resistance Between Cylinders

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Michael Mayer ◽  
Marc Hodes ◽  
Toby Kirk ◽  
Darren Crowdy
Keyword(s):  
Boundary Condition ◽  
Contact Resistance ◽  
Full Range ◽  
Constant Heat Flux ◽  
Contact Spot ◽  
Outer Radius ◽  
Spreading Resistance ◽  
Single Cylinder ◽  
Flat Base ◽  
Circular Contact

Due to the microscopic roughness of contacting materials, an additional thermal resistance arises from the constriction and spreading of heat near contact spots. Predictive models for contact resistance typically consider abutting semi-infinite cylinders subjected to an adiabatic boundary condition along their outer radius. At the nominal plane of contact, an isothermal and circular contact spot is surrounded by an adiabatic annulus and the far-field boundary condition is one of constant heat flux. However, cylinders with flat bases do not mimic the geometry of contacts. To remedy this, we perturb the geometry of the problem such that, in cross section, the circular contact is surrounded by an adiabatic arc. When the curvature of this arc is small, we employ a series solution for the leading-order (flat base) problem. Then, Green's second identity is used to compute the increase in spreading resistance in a single cylinder, and thus the contact resistance for abutting ones, without fully resolving the temperature field. Complementary numerical results for contact resistance span the full range of contact fraction and protrusion angle of the arc. The results suggest as much as a 10–15% increase in contact resistance for realistic contact fraction and asperity slopes. When the protrusion angle is negative, the decrease in spreading resistance for a single cylinder is also provided.

scholarly journals Exact Solution for the Time-Dependent Temperature Field in Dry Grinding: Application to Segmental Wheels

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
J. L. González-Santander ◽  
J. M. Valdés Placeres ◽  
J. M. Isidro
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Temperature Field ◽  
Analytical Solution ◽  
Time Evolution ◽  
Time Dependent ◽  
Temperature Fields ◽  
Grinding Wheel ◽  
Workpiece Surface ◽  
Dry Grinding

We present a closed analytical solution for the time evolution of the temperature field in dry grinding for any time-dependent friction profile between the grinding wheel and the workpiece. We base our solution in the framework of the Samara-Valencia model Skuratov et al., 2007, solving the integral equation posed for the case of dry grinding. We apply our solution to segmental wheels that produce an intermittent friction over the workpiece surface. For the same grinding parameters, we plot the temperature fields of up- and downgrinding, showing that they are quite different from each other.

The Effect of Coatings on the Steady-State and Short Time Constriction Resistance for an Arbitrary Axisymmetric Flux

1985 ◽  
Vol 107 (1) ◽  
pp. 33-38 ◽  
Author(s):  
J. R. Dryden ◽  
M. M. Yovanovich ◽  
A. S. Deakin
Keyword(s):  
Thermal Properties ◽  
Steady State ◽  
Heat Flow ◽  
Contact Spot ◽  
One Dimensional ◽  
Constriction Resistance ◽  
Transient Heat Flow ◽  
Flow Through ◽  
Short Time ◽  
Short Times

The effect of a coating upon the short-time and steady-state constriction resistance is analyzed for an arbitrary axisymmetric contact spot flux. At very short times the expression obtained for R is identical to the expression for one-dimensional transient heat flow through a two-layer wall. At steady-state, the results of the analysis predict that the effect of the coating are mainly dependent on the relative thermal properties of the coating and substrate. The limiting cases, where the coating thickness approaches either zero or infinity, are discussed.

scholarly journals Studying the stratification of hydrodynamic fields for laminar flows of vertically swirling fluid

2020 ◽  
pp. 62-78
Author(s):  
N. V. Burmasheva ◽  
◽  
E. Yu. Prosviryakov ◽  
Keyword(s):  
Exact Solution ◽  
Temperature Field ◽  
Fluid Layer ◽  
Reference Value ◽  
Horizontal Layer ◽  
Laminar Flows ◽  
Degree Polynomial ◽  
Thermocapillary Forces ◽  
Hydrodynamic Fields ◽  
Zero Points

The article proposes an approach to estimating the number of stratification points in hydrodynamic fields. The article provides a method allowing one to estimate from above the number of zero points of hydrodynamic fields (points and stratification zones). The application of the proposed methodology is illustrated by several examples of the analysis of the exact solution to the problem of describing steady laminar flows of a viscous incompressible fluid in an infinite horizontal layer. In example 1, convection is induced by setting the shear stress field at one of the layer boundaries. The features of the background temperature profile, which is a seventh-degree polynomial, are discussed. It is shown that this component of the temperature field is a nonmonotonic function and that the obtained exact solution for the temperature field can describe the stratification of the considered fluid layer into one, two or three zones relative to the reference value. Example 2 illustrates evaluating the number of the zero points of the velocity field components in a vertically swirling fluid, in which convective flows are initiated by thermocapillary forces at the upper boundary of the layer. The exact solution studied in this example is a sixth-degree polynomial, which can have at most two zeros inside the region under consideration. This means that this exact solution is able to describe the stratification of the fluid layer into three zones, in each of which the test speed takes values of the same sign.

The thermal constriction resistance of a strip contact spot on a thin film

1999 ◽  
Vol 32 (8) ◽  
pp. 930-936
Author(s):  
Fuqian Yang ◽  
Vish Prasad ◽  
Imin Kao
Keyword(s):  
Thin Film ◽  
Contact Spot ◽  
Constriction Resistance

scholarly journals Identities for droplets with circular footprint on tilted surfaces

2020 ◽  
Vol 7 (11) ◽  
pp. 201534
Author(s):  
François Dunlop ◽  
Amir H. Fatollahi ◽  
Maryam Hajirahimi ◽  
Thierry Huillet
Keyword(s):  
Exact Solution ◽  
Linear Response ◽  
Numerical Solutions ◽  
Full Range ◽  
Vertical Surface ◽  
Force Balance ◽  
Contact Boundary ◽  
Surface Evolver ◽  
Mathematical Identities ◽  
Circular Contact

Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface). The identities are put under test both by the available solutions of a linear response approximation at small Bond numbers as well as the ones obtained from numerical solutions, making use of the Surface Evolver software. The subtleties to obtain certain angle-averages appearing in identities by the numerical solutions are discussed in detail. It is argued how the identities are useful in two respects. First is to replace some unknown values in the Young–Laplace equation by their expressions obtained from the identities. Second is to use the identities to estimate the error for approximate analytical or numerical solutions without any reference to an exact solution.

Distorted constriction contact resistance between clamped slabs

2014 ◽  
Vol 33 (4) ◽  
pp. 1366-1378 ◽  
Author(s):  
Grigore A. Cividjian
Keyword(s):  
Contact Resistance ◽  
Alternate Current ◽  
Electrical Equipment ◽  
Contact Spot ◽  
Mems Devices ◽  
Element Analysis ◽  
Content Type ◽  
Constriction Resistance ◽  
Macro Scale ◽  
Exact Evaluation

Purpose – The purpose of this paper is the more exact evaluation of distorted constriction contact resistance between two clamped slabs or thin films, having a bi-dimensional current lines structure. Design/methodology/approach – Mathematical modeling using conformal mappings. Findings – The influence of the tarnish film on the distorted constriction resistance is clarified and three new exact formulas are proposed for the distorted constriction resistance between clamped slabs with rectangular contact spot. Comparisons with early proposed formula for constriction resistance of slab narrowing and with finite element analysis results are presented. Research limitations/implications – The research is limited to direct current and homogeneous and isotropic media and the results can be extended at alternate current when the skin effect is negligible. Practical implications – Exact evaluation of 2D constriction contact resistance which appears in macro-scale contacts electrical equipment and in MEMS devices, particularly in crimp contacts. Originality/value – The proposed formulas are new, original, simple and exact.

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