Characteristic length and cooling circle
Modular design, outsourcing and open innovation create a complex network of possible end product embodiments in product design for the consumer market. Analyzing each and every possibility in detail is out of the question as resources are limited and module details are often proprietary information. To meet this challenge the thermal engineer needs a feeling about what will and what will not work out, without getting bogged down in too much detail. This paper presents the concepts of characteristic length and cooling circle as an approximate measure for the extent of heat spreading in beam and in flat thin plate geometries. Beam and flat thin plate geometries are widely used by mechanical designers, and being able to assess how much of the geometry is actually thermally affected by a heat source is of great value in thermal decision making and communication. For both geometries an application is discussed and compared to CFD simulations to assess the validity of the approach.
Heat spreading in a thin longitudinal fin
In view of the trend towards higher power densities in ever shrinking geometries, understanding heat spreading fundamentals is gaining in importance. In this paper heat spreading in thin longitudinal geometries is considered. This geometry is of practical interest in one-dimensional Cartesian geometries. A characteristic length is derived and it is shown that this is has physical significance for the distance that heat spreads, and for the total amount of heat cooled away. Furthermore, it is investigated when “thin” is a viable assumption. The use of the characteristic length is illustrated for the case of a line source cooling to a plate. The results are compared to numerical simulations. The work is an extension of the authors' earlier work on heat spreading in infinite longitudinal geometries and heat spreading in infite and finite circular geometries.
APPLICATION OF THE FINITE ELEMENT METHOD TO ROTARY-WING AEROELASTICITY.
Recent research in rotary-wing aeroelasticity has indicated that all fundamental problems in this area are inherently nonlinear. The non-linearities in this problem are due to the inclusion of finite slopes, due to moderate deflections, in the structural, inertia and aerodynamic operators associated with this aeroelastic problem. In this paper the equations of motion, which are both time and space dependent, for the aeroelastic problem are first formulated in P.D.E. form. Next the equations are linearized about a suitable equilibrium position. The spatial dependence in these equations is discretized using a local Galerkin method of weighted residuals resulting in a finite element formulation of the aeroelastic problem. As an illustration the method is applied to the coupled flap-lag problem of a helicopter rotor blade in hover. Comparison of the solutions with previously published solutions establishes the convergence properties of the method. It is concluded that this formulation is a practical tool for solving rotary-wing aeroelastic stability or response problems.