Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection, radiation and flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration for computing. Closure for grey body radiation is a newly derived radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 h diurnal field experiments for 1/8 '' and 1 '' thick aluminum plates. (c) 2014 Elsevier Ltd. All rights reserved.