Problem 1 Consider the steady and two-dimensional laminar boundary-layer flow of a very low Prandtl number fluid (such as a liquid metal) of constant thermophysical properties with constant and uniform free-stream velocity U and temperature Tx over a flat plate. Let the plate be isothermal at Tw. Assume that the temperature profile in the thermal boundary layer at any x from the leading edge can be approximated as a function of the distance y normal to the plate by the relation T(x,y)=A+Bsin(Cy) a) Calculate A,B and C. b) By using Energy Integral Equation develop an expression for the thermal boundary layer thickness T(x), and c) An expression for the local Nusselt number Nux. Hint: For very low Prandtl number we may assume u=U. Explain why? Problem 2 Consider the steady and two-dimensional laminar boundary-layer flow of constant thermophysical properties with constant and uniform free-stream velocity U and temperature Tx over a flat plate. Let there be an unheated starting region that extends a distance x0 from the leading edge and the plate be maintained at a constant temperature Tw for x>x0. Assuming linear velocity and temperature profiles in the respective boundary layers and neglecting viscous dissipation, develop an expression for local Nusselt number Nux applicable to such x>x0 where r