A potato’s thermal processing model is solved analytically. The model is formulated using the equation of heat diffusion
in the case of a spherical potato processed in a furnace, and assuming that the potato’s thermal conductivity is radially
modulated. The model is solved using the method of the Laplace transform, applying Bromwich Integral and Residue
Theorem. The temperatures’ profile in the potato is presented as an infinite series of Heun functions. All computations
are performed with computer algebra software, specifically Maple. Using the numerical values of the thermal parameters
of the potato and geometric and thermal parameters of the processing furnace, the time evolution of the temperatures in
different regions inside the potato are presented analytically and graphically. The duration of thermal processing in order
to achieve a specified effect on the potato is computed. It is expected that the obtained analytical results will be
important in food engineering and cooking engineering.
Transient electronic devices are a new technology development whose main characteristic is that its components can
disappear in a programmed and controlled way, which means such devices have a pre-engineered service life.
Nowadays, transient electronics have a large application field, involving from the reduction of e-waste in the planet until
the development of medical instruments and implants that can be discarded when the patients do not need it anymore,
avoiding the trouble of having an extra procedure for them. These devices must be made from biocompatible materials
avoiding long-term adverse effects in the environment and patients.
It is fundamental to develop an analytical model that allows describing the behavior of these materials considering cases
which its porosity may be constant or not, in presence of water or any other biofluid. In order to accomplish this analysis
was solve the reactive diffusion equation based on Bromwich’s integral and the Residue theorem for two material cases,
those whose porosity is constant, and those whose porosity increases linearly in terms of its thickness, where was found
a general expression. This allows to the analysis of the relation of the electric resistance (per unit length) and the rate of
dissolution of the material.
A heat transfer model on a microfluidic is resolved analytically. The model describes a fluid at rest between two parallel
plates where each plate is maintained at a differentially specified temperature and the thermal conductivity of the
microfluidic is spatially modulated. The heat transfer model in such micro-hydrostatic configuration is analytically
resolved using the technique of the Laplace transform applying the Bromwich Integral and the Residue theorem. The
temperature outline in the microfluidic is presented as an infinite series of Bessel functions. It is shown that the result for
the thermal conductivity spatially modulated has as a particular case the solution when the thermal conductivity is
spatially constant. All computations were performed using the computer algebra software Maple. It is claimed that the
analytical obtained results are important for the design of nanoscale devices with applications in biotechnology.
Furthermore, it is suggested some future research lines such as the study of the heat transfer model in a microfluidic
resting between coaxial cylinders with radially modulated thermal conductivity in order to achieve future developments
in this area.
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