Effect of Material Properties on the Stability of Static Thermoelastic Contact

Abstract

When heat is conducted across an interface between two different materials, the interaction between thermoelastic distortion and thermal contact resistance can cause the system to be unstable. This paper investigates the influence of material properties on the stability criterion for an interface between two half planes. It is found that most material combinations exhibit one or other of two kinds of stability behavior. In one of these, the stability criterion is closely related to that for uniqueness of the steady-state solution and instability is only possible for one direction of heat flow. In the other, instability can occur for either direction of heat flow and in one case is characterized by the oscillatory growth of a pressure perturbation.

Interaction of thermal contact resistance and frictional heating in thermoelastic instability

“…In such cases, disturbance of the system from an unstable steady-state will cause it to gravitate towards an alternative stable state. However, for some material combinations, instability can occur for sufficiently high heat fluxes in both directions (Zhang and Barber, 1990) and unique steady states can be unstable (Zhang and Barber, 1993). A different category of thermoelastic contact instability can occur if there is sliding between the contacting bodies, in which case the work done against frictional tractions leads to localized heating proportional to the local contact pressure.…”

Thermoelastic stability of duplex heat exchanger tubes

“…We next consider a tube in which the inner and outer cylinders are of nickel alloy and magnesium alloy, respectively, which defines a Type 2 interface in the classification of Zhang and Barber [7]. Figure 5 shows the dimensionless heat flux at which a zero crosses into the right half-plane as a function of wavenumber n for the case 1 -71 = ?z -1 = 0.05, R* = 1.…”

“…For dissimilar materials, Zhang and Barber [7] showed that qualitatively distinct kinds of thermoelastic stability behaviour are obtained for the contact of two half-planes, depending on the relative values of the material property ratios defined in Eqn (38). The finite geometry of the duplex tube can be expected to modify this behaviour [17], but Zhang and Barber's classification of material pairs provides a useful starting point in exploring the behaviour of this more complex system.…”

“…We first consider the copper/aluminum alloy system, which defines a Type 1 interface in the classification of Zhang and Barber [7]. The relevant properties of these materials and others discussed in subsequent examples are listed in Table 1.…”

“…Ref. [7]) show that more complex behaviour is obtained when the contacting bodies have different thermal properties. In some circumstances, unique steady states can be unstable, leading to permanent oscillatory behaviour of the system [8].…”