Determination of nonstationary thermal field of passenger car wheel at braking

2020 ◽  
pp. 40-44
Author(s):  
Alexander Vyacheslavovich Zyablov ◽  
◽  
Sergey Valeryevich Bespalko ◽  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Field ◽  
Thermal Emission ◽  
Euler Method ◽  
Rolling Stock ◽  
Conductivity Equation ◽  
Passenger Car ◽  
Thermal Conductivity Equation ◽  
Nonstationary Field ◽  
Curved Rod

The paper is devoted to modeling of nonstationary field of a passenger car wheel at braking. The calculation is based on formulation of thermal conductivity equation for the wheel tread as a curved rod with the application of linear approximation of thermal field. At formulation of thermal conductivity equation it is necessary to consider a balance of heat in small volume of tread with the consideration for thermal flow from braking shoe, thermal emission to the environment and thermal conductivity in circular direction. The authors have set for the initial equation of thermal conductivity a functional and have formulated conditions of stationarity that leads after integration to the system of the first order differential equations of time. The authors have applied the Euler method at integration. The developed method has been realized in the C++ program. With the use of this application the authors have conducted a research of the thermal field of the passenger car wheel. The method can be used at designing of new rolling stock and for the analysis of reasons of flaws appearance on the surface of car wheels.

The Simulation of Discrete Vessel Effects in Experimental Hyperthermia

1994 ◽  
Vol 116 (3) ◽  
pp. 256-262 ◽  
Author(s):  
R. J. Rawnsley ◽  
R. B. Roemer ◽  
A. W. Dutton
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Blood Vessel ◽  
Effective Thermal Conductivity ◽  
Blood Vessels ◽  
Temperature Data ◽  
Experimental Temperature ◽  
Conductivity Equation ◽  
Thermal Models ◽  
Thermal Conductivity Equation

The ability of two simple thermal models to predict experimentally measured in vivo temperature profiles was compared. These comparisons were done both with and without the inclusion of separate, discrete blood vessels. The two tissue models were: 1) Pennes’ Bio-Heat Transfer equation (BHTE), and 2) an effective thermal conductivity equation (ETCE). The experimental temperature data were measured (Moros, 1990; Moros et al., 1993) in the thighs of anesthetized greyhound dogs under hyperthermic conditions generated by scanned focused ultrasound. Blood vessels were added to the thermal models in counter-current pairs transiting the model domain. The blood vessels in both models were assumed to have a constant heat transfer coefficient, and an axially varying mixed mean temperature. The vessel locations were determined a posteriori, via inspection of the experimental temperature data. Least square error fits of the predicted model temperatures to the experimental temperature data were obtained by adjusting both (a) the mass flow rate within and (b) the position of each blood vessel, and (c) the value of either the perfusion parameter (W) in the BHTE or the effective thermal conductivity parameter (Keff) in the ETCE. When small numbers (3-4) of blood vessel pairs were included, both of the models showed significant improvement in their ability to predict the experimental temperatures. Although both models performed well in terms of predicting temperatures near large vessels, the BHTE had a statistically significant better ability to predict the complete set of measured temperatures at all locations.

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