RESUMO

In this study, the effect of internal heat generation as well as the Biot number on the accuracy and applicability of lumped models in unsteady one-dimensional heat transfer problems is investigated. The simple classical lumped capacity approach and also improved lumped models based on the Hermite and polynomial approximation approaches were used to obtain the average temperature and heat flux in the spatial direction. The applicability of the lumped models was quantified using the dimensionless number B = hR/k and dimensionless heat source G = R²q°/(T₀ − T_∞) that depend on the objects geometry, thermal and physical properties, the value of internal heat generation, and on the environmental conditions they are subjected to. The range of application of different lumped models was analyzed by evaluation of the average relative error between the solution of approximate lumped models and a reference exact solution of the original partial differential equation for a whole time domain at B and −G numbers equal between 0 and 20. The results show that at the B numbers lower than 13, the variations of the relative error with the internal heat generation passes through a minimum at a dimensionless internal heat generation lower than 5, and, thus, in these ranges of B and G, the internal heat generation has increasing effect on the precision of the lumped models.