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A steel tool (with the thermophysical properties of plain carbon steel) is at a uniform temperature...

A steel tool (with the thermophysical properties of plain carbon steel) is at a uniform temperature of 250°C after being used in a cutting operation. It then cools in air at 15°C with a convection heat transfer coefficient of 45 Wm–2K–1. The tool approximates a cylinder 15 mm in diameter and 120 mm in length. One end of the cylinder is insulated. (i) How long will it take for the cylinder to cool to 50°C? [10] (ii) Under the same conditions, would a longer cylinder of the same diameter cool to 50°C in a shorter time, the same time, or a longer time? Support your answer with equations and/or simple calculations. It is not necessary to repeat the full calculation for the new shape.

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