| Summary: | Heat transfer investigation of the mechanical device such as fin and mechanical face seals is crucial for the development of these elements in different applications. In this study, two analytical approaches (collocation and numerical methods) are used to study the thermal performance of fin and mechanical face seal in various operating conditions. In the mechanical face seal, the influence of significant parameters (thermal conductivity, operating temperature and heat convection coefficient) are investigated. In the fin study, the stretching and shrinking of the fin with different cross section are comprehensively discussed. Our findings reveal that the performance of these elements significantly varies in different operating conditions. Keywords: Nonlinear thermal equations, Fin, Mechanical face seal, Collocation method, Temperature distribution
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