Modeling fin efficiency considering transverse temperature gradients in rocket engine cooling channels

Purpose. This study aims to improve the accuracy of methods for determining fin efficiency. Its goal is to derive calculation relationships for finning coefficients that account for transverse temperature non-uniformity within the fin cross-section. Design / Method / Approach. The article presents the reduction of the heat conduction equation for a fin to a dimensionless form, based on dimensional analysis of the variables involved. Further development relies on analyzing the results of numerical simulations and their subsequent generalization. To this end, the gradient descent method is applied, minimizing the quadratic error function. Findings. A criterial dependence has been formulated to complement the derived heat conduction equation. Test calculations and comparisons with numerical simulations in Ansys Fluent confirm an improvement in calculation accuracy when using the proposed equation. Theoretical Implications. This paper addresses factors previously neglected in the analysis of heat transfer in fins. The results of the study thus complement existing approaches to determining finning coefficients. Practical Implications. The derived criterial relationship will enhance the accuracy of heat transfer calculations in the chambers and gas generators of liquid rocket engines. Originality / Value. The paper introduces an original criterial relationship that accounts for temperature non-uniformity across the fin cross-section. Incorporating this factor improves calculation accuracy, highlighting the practical value of the developed equation. Research Limitations / Future Research. This study focuses on rectangular fins; therefore, the proposed model is not applicable to fins with variable thickness in the ducts of liquid propellant rocket engines (LPREs). Developing a fin model without these limitations will be the objective of future research on this topic. Article Type. Applied Research.