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 modeled as a body of revolution generated by a smooth curve, constructed from a material with negligible thermal resistance, but insulated at the base. 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 here is analytic, and the resulting function describing the relation between height ans radius of the glass, is in closed form, providing a family of optimal glass shapes that can be manufactured by conventional methods. Special attention is payed to the dimensions and the capacity of the resulting shapes.

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 modeled as a body of revolution generated by a smooth curve, constructed from a material with negligible thermal resistance, but insulated at the base. 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 here is analytic, and the resulting function describing the relation between height ans radius of the glass, is in closed form, providing a family of optimal glass shapes that can be manufactured by conventional methods. Special attention is payed to the dimensions and the capacity of the resulting shapes.

  • akwd169
    3·
    2 days ago

    Disappointing, yes I agree. Apparently, the point was to excite an audience of young beer drinkers and future scientists, rather than solve the problem though

    The problem addressed here is far from fully solved, and further studies are needed.

    Future investigations should consider heat transfer through the base of the glass, account for radiative heat transfer, and include the presence of foam.

    Additionally, developing a criterion to obtain the global optimum for glasses across various categories is an ongoing line of research

    The primary goal of this paper is to enhance the interest of students in exact sciences, particularly in Physics and Mathematics