Instantaneous heat transfer coefficients (h) for flows of various fluids (mercury, air, water, and motor oil) over plates inclined at various angles have been fundamentally examined. We have discovered three distinctive regimes, in which fluids behave interestingly. In regime I, as h increases, instantaneous heat transfer rates (q) decrease, defying our physical intuition. Regime II exhibits maxima in q-versus-h curves. In regime III, h becomes a strong function of time especially for t is an element of [0, 1 s], revealing the possible deficiency of traditional lumped-capacitance models. Results of computational simulations are obtained using COMSOL commercial package whose algorithm is based on the Galerkin finite element method, and exhibit qualitatively-correct trends when compared with classical solutions for steady-state cases. (C) 2015 Elsevier Ltd. All rights reserved.