Transient spreading resistance of arbitrary isoflux contact areas - Development of a universal time function

Dimensionless spreading resistances of iso ux planar contact areas are presented for two families of geometries: regular polygons and the hyperellipse. The spreading resistance is based on the transient centroid temperature rise. Closed-form expressions are presented for the steadystate spreading resistance of regular polygons as a function of the number of sides, and the hyperellipse as a function of the shape parameter and the aspect ratio. Expressions are presented for the centroid based and area-average based spreading resistances which are valid for all dimensionless time for the circular contact area. A closed-form relationship based on the solution for the circular contact area is used to develop a universal time function which is recommended for the accurate calculation of the spreading resistance for all polygons and hyperellipse contact areas having a wide range of aspect ratios. An alternate simpler expression is also presented for quick calculation of the spreading resistance.

[1]  James V. Beck,et al.  On the Nondimensionalization of Constriction Resistance for Semi-infinite Heat Flux Tubes , 1989 .

[2]  P. Greene.  A Useful Approximation to the Error Function: Applications to Mass, Momentum, and Energy Transport in Shear Layers , 1989 .

[3]  M. Yovanovich,et al.  TRANSIENT TEMPERATURE RISE AT SURFACE DUE TO ARBITRARY CONTACTS ON HALF-SPACES , 1989 .

[4]  M. Yovanovich,et al.  Transient constriction resistance for elemental flux channels heated by uniform flux sources , 1984 .

[5]  M. Yovanovich,et al.  Transient temperature rise of arbitrary contacts with uniform flux by surface element methods , 1984 .

[6]  J. Beck,et al.  Unsteady Surface Element Method , 1981 .

[7]  M. Yovanovich,et al.  Thermal constriction resistance of contacts on a half-space - Integral formulation , 1975 .

[8]  N. Keltner,et al.  Transient Heat Flow in Half-Space Due to an Isothermal Disk on the Surface , 1973 .

[9]  J. Blackwell.  Transient heat flow from a thin circular disk — small-time solution , 1972, Journal of the Australian Mathematical Society.

[10]  E. J. Norminton,et al.  TRANSIENT HEAT FLOW FROM CONSTANT TEMPERATURE SPHEROIDS AND THE THIN CIRCULAR DISK , 1964 .

[11]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[12]  W. J. Oosterkamp.  Calculation of the Temperature Development in a Contact Heated in the Contact Surface, and Application to the Problem of the Temperature in a Sliding Contact , 1948 .

[13]  Ragnar Holm,et al.  Calculation of the Temperature Development in a Contact Heated in the Contact Surface, and Application to the Problem of the Temperature Rise in a Sliding Contact , 1948 .

[14]  Allie M. Smith.  Transient Heat Flow from a Thin Circular Disk , 1976 .