Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# Mould wall temperature

We define the temperature difference as:

T = TW − T

so that

$${{dT} \over {dt}} = {h \over {L{C_V}}}\left( {{T_W} - T} \right)$$

rearranging and integrating gives:

$$\int {{1 \over {\left( {{T_W} - T} \right)}}dT} = \int {{h \over {L{C_V}}}dt}$$

$$- \ln \left| {{T_W} - T} \right| = {h \over {L{C_V}}}t + c$$

where c is a constant.

Applying the boundary condition that T = TP when t = 0, we get:

$$c = - \ln \left| {{T_W} - {T_P}} \right|$$

so that the time taken for the liquid to cool to a given temperature is given by:

$$t = - {{L{C_V}} \over h}\ln \left| {{{{T_W} - T} \over {{T_W} - {T_P}}}} \right|$$