Mathematical analysis of threshold temperature attainment in polypropylene during oven heating at 500oC

Novrianti; Noverina Alfiany; Afifah Rizka; Corry Handayani

doi:10.58712/jerel.v5i3.232

Authors

Novrianti Department of Mechanical Engineering, Sekolah Tinggi Teknologi Nasional, Indonesia
Noverina Alfiany Department of Mathematics and Data Science, Universitas Andalas, Indonesia
Afifah Rizka Department of Industrial Engineering, Sekolah Tinggi Teknologi Nasional, Indonesia
Corry Handayani Department of Mechanical Engineering, Sekolah Tinggi Teknologi Nasional, Indonesia

DOI:

https://doi.org/10.58712/jerel.v5i3.232

Keywords:

polypropylene, thermal attainability, ordinary differential equations, threshold temperature, Newtonian heating

Abstract

Polypropylene (PP) heating is governed by heat-transfer conditions, whereas its subsequent thermal degradation depends on temperature, holding time, and the surrounding atmosphere. Before incorporating degradation kinetics, it is essential to determine whether a prescribed temperature threshold can be attained under a given heating condition. This study presents an analytical investigation of threshold-temperature attainability in PP using a Newtonian heating model derived from the lumped thermal capacitance approach. The first-order ordinary differential equation is solved abalytically to examine the temperature response, equilibrium, asymptotic stability, monotonicity, finite-time threshold reachability, and paramter sensitivity. An idealized oven source temperature of 500° C is considered, while the initial material temperature and effective heating-rate constant are treated as model parameters. The analysis establishes that for K > 0 and T₀< T_a, a prescribed threshold temperature T_c is attainable in finite time if and only if T₀< T_c< T_a . The corresponding threshold attainment time is derived explicitly. The sensitivityu analysis shows that increasing the initial temperature or effective heating-rate constant reduces the attainment time, whereas increasing the threshold temperature extends it. Furthermore, the normalized sensitivity of the attainment time to the heating-rate constant is exactly -1, inidicating an inverse proportional relationship. The main contribution is a systematic mathematical characterization of threshold-temperature attainability and its parameter dependence, extending the interpretation of the conventional Newtonian heating model without introducing a new heat-transfer law or degradation-kinetics model. Since no experimental data are used, the findings are limited to the idealized mathematical framework and do not represent experimentally validated heating times or predictions of PP degradation.

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