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Mathematical Modeling and Optimal Design of Thermal Insulation Layers of A Ship Provision Cold-Storage Room

Aiming at the optimal design of the thermal insulation layers of the ship provision cold-storage room under high temperature environment, a mathematical model was formulated for the heat transfer system. The distribution of temperature for the inner wall of the cold-storage room and the influence of various parameters on the temperature were studied by programming method. Firstly, the method of separation of variables was used to determine the steady-state distribution of temperature on each thermal insulation layer. Then, the interpolation method was adopted to replace the partial derivative in the equation and the definite condition by the difference, discretizing the partial differential equation into a linear equation. Eventually, the Gauss-Seidel method was utilized to solve the weak diagonally dominant equation, showing that the solution was convergent and stable. For optimal design of thicknesses required for the single-layer and multi-layer of the thermal insulation layers of the ship provision cold-storage room, the combination of bisection method and nested intervals was applied based on the principles of qualitative analysis and trial calculation in this paper. The control method and optimal design of the layers' thicknesses under the given temperature conditions were confirmed. The speed and accuracy of the formulated mathematical model were assessed, both showing a proper performance.