Sritam Parida,
Rosalin Pradhan,
Sidhartha Kumar Samal,
Bibhu Prasad Ganthia,
- Assistant Professor, Department of Electrical Engineering, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha, India
- Assistant Professor, Department of Electrical Engineering, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha, India
- Assistant Professor, Department of Electrical Engineering, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha, India
- Assistant Professor, Department of Electrical Engineering, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha, India
Abstract
Advanced nuclear reactors are characterized by strongly coupled nonlinear interactions among neutron kinetics, reactor power, fuel temperature, coolant temperature, reactivity, and coolant flow. Accurate mathematical representation of these interactions is essential for analysing reactor stability, thermal behaviour, and safe operating conditions. This study develops a nonlinear mathematical framework for coupled neutronic–thermal reactor dynamics by integrating point-reactor kinetics, delayed-neutron precursor equations, fuel and coolant energy balances, and temperature- dependent reactivity feedback. The reactor state is represented by neutron density, delayed-neutron precursor concentrations, fuel temperature, coolant temperature, pressure, and coolant mass-flow rate. The complete reactor behaviour is formulated as a nonlinear state-space system, , where represents the reactor state, denotes control variables, and contains physical parameters. A constrained multi- objective optimization function is formulated to minimize deviations in reactor power and temperature while satisfying neutronic, thermal, hydraulic, and safety constraints. Lyapunov stability analysis is incorporated to evaluate convergence toward the desired operating equilibrium, while normalized sensitivity coefficients quantify the influence of major reactor parameters on system performance. The proposed mathematical formulation provides a unified framework for analysing nonlinear reactor dynamics, stability, thermal performance, sensitivity, and operating-point optimization. The approach can serve as a theoretical basis for numerical analysis of advanced nuclear reactor systems under varying operating conditions.
Keywords: Nuclear reactor; nonlinear modelling; neutron kinetics; thermal dynamics; reactivity feedback; reactor stability; thermal hydraulics; mathematical optimization
[This article belongs to Journal of Thermal Engineering and Applications ]
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Journal of Thermal Engineering and Applications
| Volume | 16 | |
| Issue | 02 | |
| Received | 17/09/2026 | |
| Accepted | 18/09/2026 | |
| Published | 27/10/2026 | |
| Publication Time | 40 Days |