Fin efficiency and enhanced heat transfer analysis of a wetted pyramidal spine applicable in heat sinks via Schröder polynomial collocation method

Enhancement of heat transfer (HT) rate through fins is one of the prevalent options, and the highly adaptable design of fins enables their application in many systems, such as radiators and electronic cooling devices. Pyramidal spine fins (PSF) are designed to enhance HT and provide better performance compared with other fin designs. Due to their effectiveness, these fins are implemented in heat sinks. Motivated by this practical application, the current study examines the thermal behavior of a wetted PSF, taking into account the effects of both convection and radiation mechanisms. The highly nonlinear energy equation of PSF is converted into dimensionless form using appropriate dimensionless terms. To get the solution for the resultant equation, the Schröder polynomial collocation method (SPCM) is applied. The impact of important parameters on the thermal profile, HT rate, and efficiency of PSF is illustrated graphically to address the thermal performance. The study reveals that increasing the value of the radiation–conduction parameter from 0 to 0.2 and the conduction–convection parameter from 0 to 0.5 enhances the HT rate by approximately 1.35% and 28.08%, respectively. Additionally, a larger rate of heat transmission of about 2.23% is seen in the wetted PSF compared with the dry PSF.