IMECE2002/HTD-33632 BIFURCATION ANALYSIS FOR HORIZONTAL LONGITUDINAL FINS UNDER MULTI- BOILING CONDITIONS

ABSTRACT A numerical bifurcation analysis is carried out in order to determine the solution structure of a fin subject to multi-boiling heat transfer mode. The thermal analysis can no longer performed independently of the working fluid since the heat transfer coefficient is temperature dependent and includes the nucleate, the transition and the film boiling regime where the boiling curve is obtained experimentally for a specific fluid. The heat transfer process is modeled using one-dimensional heat conduction with or without heat transfer from the fin tip. Furthermore, five fin profiles are considered: the constant thickness, the trapezoidal, the triangular, the convex parabolic and the parabolic. The multiplicity structure is obtained in order to determine the different types of bifurcation diagrams, which describe the dependence of a state variable of the system (for instance the fin temperature or the heat dissipation) on a design (CCP) or operation parameter (base TD). Specifically the effects of the base TD, of CCP and of the Biot number are analyzed and presented in several diagrams since it is important to know the behavioral features of the heat rejection mechanism such as the number of the possible steady states and the influence of a change in one or more operating variables to these states. Stability analysis is carried out using the "resonance integral" technique and the Sturm-liouville eigensystem analysis

Multiplicity Analysis of a Thermistor Problem—A Possible Explanation of Delamination Fracture

In the present study, a numerical bifurcation analysis of a PTC thermistor problem is carried out, considering a realistic heat dissipation mechanism due to conduction, nonlinear temperature-dependent natural convection, and radiation. The electric conductivity is modeled as a strongly nonlinear and smooth function of the temperature between two limiting values, based on measurements. The temperature field has been resolved for both cases were either the current or the voltage (nonlocal problem) is the controlling parameter. With the aid of an efficient continuation algorithm, multiple steady-state solutions that do not depend on the external circuit have been identified as a result of the inherent nonlinearities. The analysis reveals that the conduction–convection parameter and the type of the imposed boundary conditions have a profound effect on the solution structure and the temperature profiles. For the case of current control, depending on the boundary conditions, a complex and interesting multiplicity pattern appears either as a series of nested cusp points or as enclosed branches emanating from pitchfork bifurcation points. The stability analysis reveals that when the device edges are insulated, only the uniform solutions are stable, namely, one “cold” and one “hot”. A key feature of the “hot” state is that the corresponding temperature is proportional to the input power and its magnitude could be one or even two orders of magnitude higher than the “cold” one. Therefore, the change over from the “cold” to the “hot” state induces a thermal shock and could perhaps be the reason for the mechanical failure (delamination fracture) of PTC thermistors

Analysis of High-Temperature Superconducting Current Leads: Multiple Solutions, Thermal Runaway, and Protection

The multiple steady states of Ag/Bi2212-composite high-Tc superconducting leads modeling current delivery to a superconducting magnet have been numerically calculated. The model is based on longitudinal conduction combined with convective heat dissipation from a helium gas stream along the conductor. Because of the nonlinearities introduced by the voltage–current relationship and the temperature-dependent material properties, up to three solutions have been identified within the range of parameters considered. Linear stability analysis reveals that two of them are stable, i.e., the superconducting and the normal branches, while the remaining one is unstable. The limit points separating the stable from the unstable steady states form the blow-up threshold, beyond which any further increase in the operating current results in a thermal runway. Interesting findings are that for low filling ratios no bounded solution exists when the length of the lead exceeds the lower limit point, while very high maximum temperatures may be encountered along the normal solution branch. The effect of various parameters such as the conduction–convection parameter, the applied current, and the reduction in coolant flow (LOFA) on the bifurcation structure and their stabilization effect on the blow-up threshold are also evaluated. Apart from the steady and unsteady operating modes, the multiplicity analysis is also used to identify the range of the design and operating variables where safe operation, with a sufficient margin from the onset of instabilities, may be established, thus facilitating the protection of the leads and the device connected to it

On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup

In the present study, a numerical bifurcation analysis is carried out in order to investigate the multiplicity and the thermal runaway features of metallic and superconducting wires in a unified framework. The analysis reveals that the electrical resistance, combined with the boiling curve, are the dominant factors shaping the conditions of bistability—which result in a quenching process—and the conditions of multistability—which may lead to a temperature blowup in the wire. An interesting finding of the theoretical analysis is that, for the case of multistability, there are two ways that a thermal runaway may be triggered. One is associated with a high current value (“normal” runaway) whereas the other one is associated with a lower current value (“premature” runaway), as has been experimentally observed with certain types of superconducting magnets. Moreover, the results of the bifurcation analysis suggest that a static criterion of a warm or a cold thermal wave propagation may be established based on the limit points obtained