Spectral Heat Transfer Coefficient for Thermal Design Analysis - Part 1: Augmenting Law of Cooling for Non-Isothermal Wall

There are two major issues of interest in relation to Newton’s law of cooling. The first is its applicability for flow bounded by a non-isothermal wall where the surface temperature is non-uniform. The second is the restriction by the basic linear assumption. In terms of the first question, a general Green’s function-based framework exists but its implementation as a working method for practical applications has been lacking, attributable to the inherent locality of Green’s function. Instead of setting up and solving the local-local influence and response, a new Spectral Heat Transfer Coefficients (SHTC) method takes a different avenue. It sets up and solves global-to-local temperature-heat flux influences for a small number of low order spectral modes of wall temperature disturbances in a range of physically relevant and numerically resolvable length scales. The present work is aimed at applying the SHTC methodology to turbine blade aerothermal analysis. Two aerothermal regimes are considered respectively. In the first part (Part 1 of the two-part article), the SHTC approach is described and case-studied for a linear regime where the flow energy equation behaves linearly and the corresponding temperature field is passively dictated by the velocity field. In the companion paper (Part 2), the methodology will be extended to a nonlinear aerothermal regime, where the temperature field will be actively interacting with (rather than passively influenced by) the velocity field.