Conduction Heat Transfer in a Truncated Conical Shell

ABSTRACT

In the present paper, the conduction heat transfer through a conical shell, having a half cone angle of 45° has been considered. Two different methods were employed in order to determine the conduction heat transfer through the shell. The first method is based on semi-analytical treatment, where the cone was divided into a number of equivalent cylindrical shells and the overall heat transfer was calculated by summing up the heat transfer rates through these individual shells. In the second method, the conduction heat transfer through the conical shell was numerically simulated using curvilinear coordinates. All the length scales were normalised with respect to the height (or length) of the truncated cone. The dimensionless values of both the inner radius at the smaller end of the cone and the shell thickness were varied between 0.1 and 1. It was observed that the semi-analytical approach produces fairly good approximation for heat transfer (obtained from the numerical simulations) when the shell thickness is small. Finally, from the calculated results, a correlation was obtained in order to determine the inner radius of the equivalent cylindrical shell, which was found to be a linear function of the shell thickness, for quick and accurate calculation of the heat transfer.

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