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Mathematical Study of the Temperature Changes in a Hot Body after Quenching, Assuming Various Conditions of Heat Flow from the Surface .—(1) Assuming no thermal resistance at the surface, theoretical cooling curves for a steel ball and a steel plate are computed (Fig. 1). (2) Assuming constant thermal resistance, the general equation is derived for the case of a cylinder of finite length (Eq. 17). (3) Assuming a vapor layer which conducts the heat to a liquid layer at rest, the general solutions for the temperatures at the surface of a large body (Eq. 41) and of a plate (Fig. 5) are obtained. (4) Assuming that the heat after passing through the vapor layer is carried away by convection at a uniform rate, the equation and curves are obtained for the case of a plate (Eq. 58; Fig. 6). Heat Flow from a Metal Cylinder Quenched in Water .—By comparing various experimental cooling curves with the theoretical curves obtained above, it is evident that after the first stage of quenching none of the assumed conditions correspond to the facts. It is found that the rate of transfer of heat through the surface is not constant but is an exponential function of the temperature of the surface. Smaller cylinders seem to have less specific heat flow. The discrepancy with theory is doubtless due to the neglect of the bubbling which begins almost immediately. Reheating of the surface of a body immediately after quenching, due to sudden formation of a steam jacket, does not occur. Reheating as evidenced by structural investigation may occur in a later phase of quenching.
Physical Review – American Physical Society (APS)
Published: Sep 1, 1922
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