International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4157 2020 2020 Sciences of Mathematics, Computer Sciences, College of Health and Medical Techniques-Kufa Al-Furat Al-Awsat Technical University, Kufa, Iraq El El-Sayed Department of System Programming, South Ural State University, Chelyabinsk, Russia; Directorate of Environment in Najaf, Ministry of Environment, Najaf, Iraq Hussein Alkattan Delta Higher Institute of Engineering and Technology Department for Communications and Electronics Mansoura 35511, Egypt; Applied Science Research Center. Applied Science Private University, Amman, Jordan El-Sayed M. El El-kenawy Faculty of Artificial Intelligence, Delta University for Science and Technology, Mansoura, Egypt; Jadara Research Center, Jadara University, Irbid 21110, Jordan Marwa M. Eid We develop a neutrosophic framework for the 1-D transient heat equation that treats key thermal parameters as indeterminate rather than fixed or strictly probabilistic. Thermal diffusivity and source strength are represented by neutrosophic intervals; two extreme forward solves yield guaranteed envelopes u_min and u_max , from which we compute a core field u_mean =12 (u_min+u_max ), an absolute width W=u_max-u_min, and a relative indeterminacy index I=W(|u_mean  |+ε). Using an explicit FTCS discretization with stability enforced by α_max , we report decision-oriented diagnostics: spatio-temporal maps of u_mean ,W, and I; band plots along spacetime sections; percentile trajectories of I over time; coverage curves quantifying the fraction of space-time with I≤τ; and response surfaces showing sensitivity of u(x^( ^* ),T) to (α,S). Results demonstrate that, even when absolute spreads remain small, localized reliability losses can occur where u_mean  crosses zero, a regime routinely obscured by point-estimate modelling. The framework is transparent (envelopes + core), computationally light (two extreme runs), and compatible with neutrosophic statistics for data-driven interval setting. Beyond thermal diffusion, the method provides a conservative, explainable backbone for transport-driven decisions in materials, interfaces, and infrastructure subject to incomplete or evolving information. 2026 2026 309 323 10.54216/IJNS.270127 https://www.americaspg.com/articleinfo/21/show/4157