Example (cont.)
Questions: (1) How do we determine the heat transfer coefficient, h?
There are a total of six parameters involving in this problem: h, V, D, n, kf, cp. The last two variables are thermal conductivity and the specific heat of the water. The temperature dependence is implicit and is only through the variation of thermal properties. Density r is included in the kinematic viscosity, n=m/r. According to the Buckingham theorem, it is possible for us to reduce the number of parameters by three. Therefore, the convection coefficient relationship can be reduced to a function of only three variables:
Nu=hD/kf, Nusselt number, Re=VD/n, Reynolds number, and
This conclusion is consistent with empirical observation, that is
Nu=f(Re, Pr). If we can determine the Reynolds and the Prandtle numbers, we can find the Nusselt number, hence, the heat transfer coefficient, h.