  We provide an overview of the leading edge problem in this paper. We have
used a self-similar function having a dependence on both the self-similar
variable $\eta$ and Reynold's number R to covert the momentum and energy
equations into a fourth-order, non-linear partial differential equation (PDE)
and a second-order, non-linear PDE respectively. Attempts have been made to
solve the energy equation in a variety of ways, which include solving the PDE
approximating the terms of the order $\mathcal{O}(R^{2})$ and solving the PDE
via the method of characteristics, but mostly being able to solve the energy
PDE sans solving the momentum PDE. The complexities involved in solving the
momentum PDE have been discussed and plausible approximate solutions have been
given. The importance of boundary conditions and how they influence the
solution to the energy PDE has been discussed. We have also shown how the
energy PDE can be defined as a well-posed hyperbolic initial-boundary value
problem in the leading edge. We conclude the paper by showing an approximate
solution to the heat transfer coefficient and plot its characteristic behavior.
