On the Heat Transfer Process in a System of Two Convex Bodies Separated by a Vacuum—Mathematical Description and Solution Construction
Year: 2026
Type: article
Abstract: This work presents a straightforward procedure for constructing the solution to the steady-state energy-transfer process in a system of two convex, opaque, gray bodies, with the aim of determining the temperature distribution within these bodies when separated by a vacuum. The methodology proposed in this work combines a sequence of elements that are functions obtained from the solution of uncomplicated, well-known linear, uncoupled heat transfer problems, thereby enabling solutions to be obtained using tools found in basic engineering textbooks. Specifically, these well-known problems resemble classical conduction-convection heat transfer problems, in which the boundary condition is described by the noteworthy Newton’s law of cooling. The limit of sequences of elements that are solutions to straightforward linear problems corresponds to the original, complex, coupled nonlinear problem. The convergence of these sequences is mathematically proven. The phenomenon (considered in this work) encompasses those involving black bodies. Since each element of the sequence arises from a well-known linear problem, numerical approximations can be used to obtain it, yielding a simple and powerful tool for simulations. Some presented results highlight the importance of considering thermal interaction between the two bodies, even in the absence of physical contact. In particular, the alterations in the temperature distributions of two separate gray bodies are explicitly shown to result from their thermal interaction.
Source: Thermo
Authors: Rogério Pazetto Saldanha da Gama, Rogério Martins Saldanha da Gama, Maria Laura Martins-Costa
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
Awards: G4869293561, G936013762
OpenAlex ID: W7124417280