Final answer:
The design of heat transfer gloves and hand warmers relies on thermodynamics principles, specifically concerning heat transfer methods such as conduction, convection, and radiation.
Step-by-step explanation:
The mathematical concept primarily utilized in designing heat transfer gloves and hand warmers is thermodynamics. This area of physics deals with the principles governing the conversion between heat and other forms of energy, such as work. Thermodynamics involves understanding and applying the concepts of heat transfer which include conduction, convection, and radiation. Specifically, for heat transfer gloves, the idea is to minimize heat loss through conduction, while hand warmers generate heat usually through a chemical reaction, which is then transferred by conduction to the hands.