A mathematician from the University of the Philippines (UP) Diliman has developed a new model for understanding heat propagation through rough surfaces, potentially improving the design of cooling devices and heat-resistant infrastructures.
Jake Avila from the UP Diliman College of Science Institute of Mathematics formulated the theory in collaboration with mathematicians from Italy.
The model uses a method called homogenization to account for both microscopic and macroscopic properties of materials.
“Homogenization theory aims to describe the macroscopic or effective properties of composite materials while taking into account simultaneously the microscopic or local properties of its components,” Avila said.
The new model addresses the complexities of heat transfer in materials with uneven surfaces, where traditional flat-surface models fall short.
This breakthrough could have significant implications for various industries, including HVAC (heating, ventilation, and air conditioning) and construction.
While the current application focuses on heat propagation, Avila noted that the theory has broader potential uses.
“It can also be applied to describe acoustic wave propagation over rough walls or turbulence flow in the rough ocean surface,” he said.
Avila and his team are now working on expanding the theory for more general applications.
“The next plan is to study a more complicated and general problem wherein a sign-changing density function is involved in the eigenvalue problem in a domain through rough surfaces,” said Avila.
“The problem in the article is a special case where a unit density function is treated,” he added.