Example 2: It is required to determine the cooling rates of a heated circular cylinder exposed to an air stream in terms of the heat transfer coefficient . This coefficient is defined as the energy lost per unit area per unit temperature difference between the cylinder and the air stream. Two experiments are proposed for estimating . In the first, the cylinder is heated to a temperature and suddenly placed in the air stream at a temperature . The heat transfer coefficient is then obtained from the cooling curve of the cylinder. In functional form, the cooling curve is given as

where is the cylinder temperature at any time , is the surface area, is the mass of the cylinder and is its specific heat. The experiment is stopped when the left side of the above equation is for which and