TEM – Lecture 9 Exercises

Steps for resolution: 1- Power per apple? 2 - Apple Surface temperature? 3 - Apple (spherical) central temperature. How could one estimate the weight loss per storage month in the refrigerator? Are Apples living or dead organisms?

Resolution The Mass and the volume of an apple are: The thermal power of an apple is: The heat generated per cubic meter of apples is:

Surface Heat Flux and Temperature Whole heat generated inside an apple has to leave across its surface and thus: 0.01 The heat is generated uniformly inside the apple. Assuming it spherical the equation is:

Assuming radial symmetry, i. e. , that isothermals are spherical (i. e Assuming radial symmetry, i.e., that isothermals are spherical (i.e. that the temperature changes only along “r” and assuming stationary conditions: C1 has to be zero, otherwise the temperature gradient would be infinity at r=0

Integration constant C is a function of the apple surface temperature. And finally one gets: This equations shows that temperature is maximum at r=0, i.e., at the apple’s center and that it temperature increases as the heat generated increases and as thermal conductivity decreases as was expected. In fact apples are stored at a low temperature to reduce biological activity, generating less heat and loosing less weight.