  This paper addresses the problem of determining the optimum shape for a beer
glass that minimizes the heat transfer while the liquid is consumed, thereby
keeping it cold for as long as possible. The proposed solution avoids the use
of insulating materials. The glass is modelled as a body of revolution
generated by a smooth curve S, constructed from a material with negligible
thermal resistance at the revolution surface but insulated at the bottom. The
ordinary differential equation describing the problem is derived from the first
law of Thermodynamics applied to a control volume encompassing the liquid. This
is an inverse optimization problem, aiming to find the shape of the glass
(represented by curve S) that minimizes the heat transfer rate. In contrast,
the direct problem aims to determine the heat transfer rate for a given
geometry. The solution obtained is analytic, and the resulting expression for S
is in closed form, providing a family of optimal glass shapes that can be
manufactured using conventional methods.
