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

On Recent Developments in the Leading Edge Problem: Self-Similar Solutions to Momentum and Energy Equations of a Flat Plate