Mathematical Modeling of Architecture in Relation to Heat Flow

by Adele Howard

Submitted : Spring 2020

When designing and constructing a building, architects and engineers must account for environmental strains, including climate. In a cold climate, residents want to keep their houses warm in the most inexpensive way. To effectively reduce heat loss, architects and engineers analyze the building plans and materials. In order to do so, they must utilize mathematical modeling. In this case, an architect acquired a client who needs a dome-shaped structure made of brick, much like the domes seen on the Taj Mahal. The goal of this hypothetical scenario is to understand how mathematical modeling can help account for heat flow. The volume of the dome and thickness of the dome structure must first be calculated. The engineers can use this volume to gather the necessary data and use the R-Value of the material to account for insulation. Once the general construction is complete, the heat loss throughout the day can be calculated, and the engineers can determine whether the amount of heat lost throughout the day is acceptable.

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