A unified analytical solution and an approximate method are presented for calculating the time to cool or heat an object of simple shape to a given mean temperature, using a fluid with finite heat capacity in batch, parallel-flow, or counterflow modes. In the approximate method, an equivalent constant fluid temperature is calculated, which would give the same log-mean temperature difference. The cooling time at this equivalent temperature is found by conventional methods, then multiplied by a correction factor calculated from a simple regression equation.

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