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 .