**The Critical Radius**

**02/18/2018**

*“What is the most optimal radius for insulation?”*

It is usually thought that if one wants to provide more insulation to an object, then all they have to do is add more layers. However, if this also increases the surface area of an object, which can cause the heat loss by convection to increase as well. If the insulation becomes too large, then the convection effect actually takes over! So how can we find the most optimal radius for convection? Well, if we use our knowledge of heat transfer and calculus, then we can find out that the **critical radius **r for a cylinder is equal to *k/h and 2k/h for a sphere*, where *k *is the conductive heat transfer coefficient and *h *is the convective heat transfer coefficient.