Discussed in this paper is the initial development of the unsteady laminar two-dimensional thermal-fluid problem of free convection from an inclined elliptic cylinder.The fluid is taken to be viscous and incom- pressible and the Boussinesq approximation has been implemented to describe the driving buoyancy force. In Part 2 a numerical method for solving the governing Navier-Stokes and heat equations will be outlined. The numerical procedure involves both finite difference and spectral methods.The dictating equations are posed in a stream function/vorticity formulation and are solved subject to the isothermal and no-slip conditions on the surface along with uniform and quiescent far-field conditions applied at a sufficiently large distance.A conformal transformation well suited to handle the elliptic geometry is introduced.In addition,the coordinates are rescaled to take into account the evolving thermal boundary-layer structure.The numerical scheme is specifically designed and implemented to capture the important physical behaviour of the initial flow.Part 2 will emphasize on reconciling the numerical solution with the analytical solution reported in Part 1 for small times.
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