Volume 27 , Issue 1 , PP: 309-323, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Ghassan AL-Thabhawee 1 , Hussein Alkattan 2 , El-Sayed M. El-kenawy 3 * , Marwa M. Eid 4
Doi: https://doi.org/10.54216/IJNS.270127
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.
Neutrosophic modeling , Heat equation , Transient heat conduction , Interval uncertainty , Envelope propagation , Relative indeterminacy index (RII) , Thermal diffusivity , Source amplitude , Uncertainty quantification
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