MATHEMATICAL MODEL ANALYSIS OF GRAPHENE OXIDE THERMAL DEVELOPMENT

Summary. The thermal processing mathematical model of graphene oxide is a model that mathematically describes the changes that the material undergoes during thermal processing. This model takes into account the changes in the crystal structure of the material during thermal treatment and the effects of these changes on the properties of the material.


Introduction
Graphene oxide material can be processed at different temperatures and times during thermal processing. During this process, the chemical structure and crystal structure of the material may change, causing changes in the mechanical and thermal properties of the material[4, 5,6].
Mathematical modeling can be used to predict the changes of graphene oxide material during thermal processing. These models use thermal processing conditions (temperature, time, etc.) to calculate material properties.
For example, the thermal conductivity of graphene oxide material depends inversely on the thermal resistance (R) of the material. Therefore, hypothetical models can calculate the relationship of the thermal resistance of the material to the thermal conductivity. In addition, the effects of changes in material properties on other properties such as the mechanical strength and modulus of elasticity of the material can be predicted through modeling [7,8,9].
The thermal resistance of graphene oxide is inversely proportional to the thermal conductivity of the material[1,3,4]. That is, the higher its thermal conductivity, the lower its thermal resistance. This relationship can be expressed by Fourier's law: Here, Q represents the heat transfer rate; k represents thermal conductivity; A represents the heat transfer surface area; ΔT represents the temperature difference; and Δx represents the size of the temperature difference [10,11,12].
In this equation, thermal conductivity k refers to how a material is capable of conducting heat. A material with high thermal conductivity, such as graphene oxide, will have a lower thermal resistance as it will conduct heat faster. For example, if the thermal conductivity of graphene oxide is k = 2000 W/(m K) and the temperature difference is ΔT/Δx = 10 K/m, the heat transfer rate will be Q = -20000 A W/m². This value can be used to calculate the thermal resistance of graphene oxide.
During the thermal treatment of graphene oxide, the material is subjected to heat treatment, during which the temperature of the material rises. During this process, heat transfer takes place inside and outside the material. This can be analyzed using the Biote number (Bi).
The biote number expresses the ratio of thermal resistance and heat transfer. Bi is calculated by the following equation: Here, h is the heat transfer coefficient from the outer surface of the material to the environment; L is the characteristic size of the material; and k is the thermal conductivity of the material.
A material's Bi number indicates how quickly the material's heat treatment process responds to temperature. If the Bi number is large, the material reacts quickly to temperature and the heat treatment process takes place quickly [6,11,14].
For example, let's say that the heat transfer coefficient of graphene oxide from the outer surface to the environment is h = 100 W/(m² K), its characteristic size is L = 0.1 m, and its thermal conductivity k = 2000 W/(m K). In this case, the number Bi can be calculated as follows: This hypothetical modeling can be used to optimize the thermal processing conditions of graphene oxide material and can increase the material's use in different applications.