برآورد مقاومت گرمایی با استفاده از تجزیه و تحلیل حساسیت و تنظیم

Characterization of the thermal contact resistance is important in modeling of multi-component thermal systems which feature mechanically mated surfaces. Thermal resistance is phenomenologically quite complex and depends on many parameters including surface characteristics of the interfacial region and contact pressure. Although most studies seek a single value as a function of these parameters, in general, the contact resistance is non-uniform over the interface. In this paper, a technique is developed for extracting non-uniform contact resistance values from experiments in two-dimensional configurations. To begin, a two-dimensional model problem is formulated for a known contact resistance between two mated surfaces. An inverse problem is devised to estimate the variation of the contact resistance by using the BEM to determine sensitivity coefficients for specific temperature measurement points in the geometry. Temperature measured at these discrete locations can be processed to yield the contact resistance between the two mating surfaces using a simple matrix inversion technique. The inversion process is sensitive to noise and requires using a regularization technique to obtain physically possible results. The regularization technique is then extended to a genetic algorithm for performing the inverse analysis. Numerical simulations are carried out to demonstrate the approach. Random noise is used to simulate the effect of input uncertainties in measured temperatures at the sensors.

Thermal systems generally feature composite regions that are mechanically mated. There exists an often significant temperature drop across the interface between such regions which may be composed of similar or different materials. The parameter characterizing this temperature drop is the thermal contact resistance, View the MathML sourceRt,c″=ΔT/q″, which is defined as the ratio of the temperature drop, ΔTΔT, to the heat flux normal to the interface, q″q″. The thermal contact resistance is due to roughness effects between mating surfaces which cause certain regions of the mating surfaces to lose contact thereby creating gaps. In these gap regions, the principal modes of heat transfer are conduction across the fluid filling the gap and radiation across the gap surfaces. Moreover, the contact resistance is a function of contact pressure as this can significantly alter the topology of the contact region. Clearly, the thermal contact resistance is a phenomenologically complex function and can significantly alter prediction of thermal models of complex multi-component structures. Accurate estimates of thermal contact resistance are thus important in engineering calculations and find application in thermal analysis ranging from relatively simple layered and composite materials to more complex biomaterials. There have been many studies devoted to the theoretical predictions of thermal contact resistance for instance [1], [2], [3] and [4] and comprehensive reviews of previous work on thermal contact resistance can be found in [5], [6], [7] and [8]. Although general theories have been somewhat successful in predicting thermal contact resistances, most reliable results have been obtained experimentally. This is due to the fact that the nature of thermal contact resistance is quite complex and depends on many parameters including types of mating materials, surface characteristics of the interfacial region such as roughness and hardness, and contact pressure distribution. In experiments, temperatures are measured at a certain number of locations, usually close to the contact surface, and these measurements are used as inputs to a parameter estimation procedure to arrive at the sought-after thermal contact resistance. Most studies seek a single value for the contact resistance, while the resistance may in fact also vary spatially. In this paper, an inverse problem [9], [10] and [11] is formulated to estimate the variation of the thermal contact resistance along an interface in a two-dimensional configuration. Temperature measured at discrete locations using embedded sensors placed in proximity to the interface provide the information required to solve the inverse problem. The contact resistance is found by using a superposition method to determine sensitivity coefficients [12] and [13] for specific temperature measurement points in the geometry. This serves to guide in the location of the measuring points. Temperature measured at these discrete locations are then used in a regularized least-squares problem to yield the contact resistance between the two mating surfaces. A boundary element method (BEM) [14], [15], [16], [17], [18] and [19] is also used to solve for the temperature under current estimates of the contact resistance during the solution of the inverse problem. The inverse problem is solved using sensitivity analysis and also via a regularized BEM/genetic algorithm (GA) [20] approach previously developed by the authors [21]. The L-curve method of Hansen [22] and [23] is used to choose the optimal regularization parameter. A series of numerical examples are provided to demonstrate the approach.

A two-dimensional inverse problem has been solved for a known contact resistance between two mated surfaces. An inverse problem is formulated to estimate the variation of the contact resistance by using a BEM to determine sensitivity coefficients for specific temperature measurement points in the geometry. Temperature measured at these discrete locations can be processed to yield the contact resistance between the two mating surfaces using a simple matrix inversion technique. The inversion process is sensitive to noise and requires using a regularization technique to obtain physically possible results. The regularization technique is then extended to a (GA) for performing the inverse analysis. Numerical simulations are carried out to demonstrate the approach. Random noise is used to simulate the effect of input uncertainties in measured temperatures at the sensors. It was demonstrated that the regularization technique for the GA consistently resulted in an improved result. Even though, for the cases presented here using the GA-based approach showed only a slight improvement over the sensitivity-based method, it is worth noting when working with real data one seeks the best method.