aspg-21-4157-1791472332 20261008151212 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2026 27 1 Ghassan AL-Thabhawee Sciences of Mathematics, Computer Sciences, College of Health and Medical Techniques-Kufa Al-Furat Al-Awsat Technical University, Kufa, Iraq Hussein Alkattan El-Sayed M. El-Kenawy 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 =1/2 (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 space/time 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 309 323 4157 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.270127 https://www.americaspg.com/journal/21/article/4157 https://www.americaspg.com/storage/71760735097.pdf