ME 546 Diffusion Problems in Thermal Sciences
Homework 2
1. Proove the Leibnitz’s rule for differentiation of an integral.
2. Rework the similarity transformation for the flow over a flat plate discussed in class,
this time eliminating the
“x” variable (i.e. coordinate along the plate), and expressing
“y” coordinate (i.e. coordinate
the new dependent variable as a function of the
perpendicular to the plate).
3. Remember Stoke’s second problem discussed in the class.
Try a similarity
transformation to this problem. Discuss the resulting equations.
4. Derive the similarity variable and the dimensionless form of the governing differential
equation for the plane stagnation flow. (Re: “Viscous Fluid Flow” White pp.153)
5. A semi-infinite plane medium is at a constant temperature
subjected to a time varying temperature
T0 . The wall is suddenly
Tw  T1 sin(  t ) .
i. Is there a steady periodic solution to this problem?
ii. Find the steady periodic temperature variation in the domain if
Tw  T0 .