Mathematical model for heat transfer in variable thickness fins for rocket engines

Purpose. This article aims to develop a mathematical model for a fin in the cooling system of liquid propellant rocket engines. The objective is to enable calculations for fins with arbitrary thickness variation. The developed mathematical model will be valuable and in demand for calculating heat transfer in the chambers of liquid propellant rocket engines produced using additive manufacturing technologies. Design / Methodology / Approach. The study employs theoretical research methods. The temperature distribution along the fin’s height is derived by applying established heat transfer laws to the control volume under consideration. Findings. The study resulted in a mathematical model for a fin of variable thickness. The model was transformed into a dimensionless form to improve the accuracy of solving the equation numerically. Next, test calculations were performed using the proposed model. Theoretical Implications. This study builds upon existing models of heat transfer in fins and significantly extends the scope for further analysis by allowing for arbitrary variations in fin thickness. Practical Implications. The developed mathematical model can be applied to calculate the fin efficiency when designing cooling systems for combustion chambers, gas generators, and other components of liquid propellant rocket engines. Originality / Value. The article presents an original approach to calculating heat transfer in fins with variable thickness, enhancing its value for practical calculations. It can also serve as a reference for developing similar mathematical models. Research Limitations / Future Research. This study is focused on fins used in the cooling systems of liquid propellant rocket engine chambers. Therefore, the developed model is applicable only to fins where the longitudinal dimension significantly exceeds the transverse dimension. Future research could explore optimizing fin shapes to enhance heat transfer efficiency.