Design of Heating Coils Based on Space-Filling Fractal Curves for Highly Uniform Temperature Distribution

Abstract

Heating coils utilize the concept of resistive heating to convert electrical energy into thermal energy. Uniform heating of the target area is the key performance indicator for heating coil design. Highly uniform distribution of temperature can be achieved by using a dense metal distribution in the area under consideration, however, this increases the cost of production significantly. A low-cost and efficient heating coil should have excellent temperature uniformity while having minimum metal consumption. In this work, space-filling fractal curves, such as Peano curve, Hilbert curve and Moore curve of various orders, have been studied as geometries for heating coils. In order to compare them in an effective way, the area of the geometries has been held constant at 30 mm × 30 mm and a constant power of 2 W has been maintained across all the geometries. Further, the thickness of the metal coils and their widths have been kept constant for all geometries. Finite Element Analysis (FEA) results show Hilbert and Moore curves of order-4, and Peano curve of order-3 outperform the typical double-spiral heater in terms of temperature uniformity and metal coil length.