Edited by Leslie Gordon

Warmth is an important sensory attribute in product design and a subtle but integral part of branding. As winter approaches, we might pile on layers of clothing and wish our offices were better insulated. On cold mornings, we probably tiptoe on the ceramic tile floor of a bathroom to reduce our contact with the floor. Of course, mats or rugs provide safe havens from the frigid substrate.

But why doesn’t the rug feel cold? After all, it is in the same ambient temperature as the floor tile. Our sense of warmth or coldness is actually related to the rate of heat transfer to or from our bodies. We perceive heat loss as a feeling of coldness and heat gain as a feeling of warmth. At roughly 98.6°F, our bodies are at a higher temperature than the bathroom floor at, say, 68°F. Therefore, heat flows from our feet to the floor. But the rate of heat loss to the rug is much slower than to the ceramic floor, so stepping on the rug feels less cold.

Determining heat transfer between contacting bodies is a common engineering problem. The rate at which heat transfers between parts in contact is governed by the physical and thermal properties of the part materials. Perceived warmth depends on the material’s thermal conductivity, density, and specific heat (or heat capacity — the amount of thermal energy required to change the material’s temperature by 1°).

Wood, for example, has relatively low values of these properties as compare to metals. Polymers also have low values and foam polymers’ are even lower. Air trapped in the materials lends them extremely low conductivity and imparts a strong sense of warmth.

Returning to the floor example, the thermal conductivity, density, and specific heat of ceramic floor tile are greater than those of a rug. Heat transfers more rapidly to the ceramic floor tile than to the rug, so we sense it is colder. If the bathroom floor were made of stainless steel it would feel even colder because the conductivity, density, and specific heat of stainless steel are much higher than those of ceramic floor tile.

The converse is true, as well. If we touch something that is hotter than our body temperature, heat transfers from the object to our body. Next time you empty the dishwasher just after the cycle is completed, compare the apparent temperatures of the silverware and ceramic mugs. A famous picture of a person holding a glowing cube of space-shuttle heatshield material shows an extreme example of this effect. The material is porous silica and its temperature is 2,700°F, yet it can be held with a bare hand for a few seconds. The material’s conductivity, density, and specific heat are extremely low. Thus, the rate of heat transfer is quite low and the silica doesn’t feel as hot as it actually is.

The rate of heat transfer is related to the square root of the product of thermal conductivity, density, and specific heat. So, if you want to remake your product with, say, twice the warmth (one-half the heat-transfer rate), the product of these properties for the new material would have to be one-fourth that of the replaced material.

Howard A. Kuhn is R&D Director of The Ex One Co. and is responsible for developing and implementing direct digital manufacturing and tooling technologies. Kuhn is also an Adjunct Professor at the Univ. of Pittsburgh, School of Engineering, where he is involved in the digital manufacturing of scaffolds for regenerative medicine.