Chapter 6, Problem 6.42P

A major contributor to product defects in electronic modules relates to stresses induced during thermal cycling (intermittent heating and cooling). For example, in circuit cards having active and passive components with materials of different thermal expansion coefficients, thermal stresses are the principal source of failure in component joints, such as soldered and wired connections. Although concern is generally for fatigue failure resulting from numerous excursions during the life of a product, it is possible to identify defective joints by performing accelerated thermal stress tests before the product is released to the customer. In such cases, it is important to achieve rapid thermal cycling to minimize disruptions to production schedules.
A manufacturer of circuit cards wishes to develop an apparatus for imposing rapid thermal transients on the cards by subjecting them to forced convection characterized by a relation of the form ${\overline{Nu}}_L=C{\mathrm{Re}}_L^m{\mathrm{Pr}}^n,$ where $m=0.8$ and $n=\mathrm{0.33.}$ However, he does not know whether to use air $\left(k=0.026\text{W/m}\cdot \text{K,}v=1.6\times {10}^{-5}{\text{m}}^{\text{2}}\text{/s,}\mathrm{Pr}=0.71\right)$ or a dielectric liquid $\left(k=0.064\text{W/m}\cdot \text{K,}v={10}^{-6}{\text{m}}^{\text{2}}\text{/s,}\mathrm{Pr}=25\right)$ as the working fluid. Assuming equivalent air and liquid velocities and validity of the lumped capacitance model for the components, obtain a quantitative estimate of the ratio of the thermal time constants for the two fluids. What fluid provides the faster thermal response?