Enhancement of natural convection heat transfer of pin fin having perforated with inclination angle

The development of the perforated fin had proposed in many studies to enhance the heat transfer from electronic pieces in modern devices. this paper presents a new design by using inclined perforated for a pin fin. perforated with rectangular section and different angles of inclination was considered. signum function is used for modeling the variable heat transfer area. set of parameters to handle the conduction and convection area were calculated. degenerate hypergeometric equation (dhe) was used for modeling the complex energy differential equation and then solved by kummer's series. in the validation process,the finite element technique was used. the big reliability of the presented model comes from the high agreement of the validation results about (0.3%),therefore,the mathematic model has big dependability to deal with the inclined perforated fin. two geometric models and range of the rayleigh number from ra=1 × 105 to ra=1× 106 were considered. the results show the increase of the inclination towards the max angle leads to the enhancement of the temperature difference,heat transfer,and effectiveness with and without the change of other parameters. improved of heat transfer ratio and effectiveness are ranging from 18% to 50%.