The mathematical modelling group works at IUMPA on developing mathematical models that describe heat transfer processes. As it is known, the basic equation that rules these processes is the equation of heat, which is a differential equation with second partial derivatives of parabolic type. There are different reformulations and modifications of the same equation. For example, the addition of convective terms allows us to study the mass transfer phenomena; and the addition of a second derivative with respect to time turns the parabolic equation into a hyperbolic one which describes heat waves. 

There are two examples of models that are developed in this area and related to the analysis of geothermal heating and industrial grinding parts. The first one refers to the usual air-conditioning systems in buildings, which use refrigeration/heating units situated in roofs or terraces that operates on transferring or removing heat in the air environment. Opposite to this, there exist the geothermal systems which extract or transfer heat to the soil surrounding of the building through a buried water circuit. This technology allows huge energy savings compared to conventional air conditioning. Grinding metal parts through grinding wheel has great industrial interest. This process generates large quantities of heat by friction between the grinding wheel and the piece.

 

Mathematical modelling area at IUMPA deals with such problems by means of differential equations. This area analyses mathematical aspects such as the existence and stability of the solutions, the spectrum, and properties of the associated Cauchy problem which, from a technological point of view, leads to the optimization of air conditioning and thermal grinding techniques.

Research Groups: Interdisciplinary Modelling Group- InterTech