TY - JOUR
T1 - Transient heat conduction in a solid slab using multiple-scale analysis
AU - Bautista, O.
AU - Méndez, F.
AU - Campos, I.
PY - 2005/12
Y1 - 2005/12
N2 - In this paper we study the unsteady heat conduction due to a sudden temperature step in the external surfaces of a solid slab. In order to estimate the temperature profile in the solid, we applied the multiplescale perturbation technique by identifying the "early" and "late" transient regimes for small values of the Biot number, Bi. In this sense, we have re-visited the classical lumped method, incorporating this particular case as an asymptotic limit, which is fully described by the "late" regime for small values of Bi. Once the temperature distribution is analytically predicted, this solution is compared against the exact solution and with other analytical results obtained by using regular perturbation techniques, for different values of the Biot number Bi. Observing a good agreement between the corresponding comparisons, we obtain a very simple and useful formula to predict the nondimensional temperature of the solid slab.
AB - In this paper we study the unsteady heat conduction due to a sudden temperature step in the external surfaces of a solid slab. In order to estimate the temperature profile in the solid, we applied the multiplescale perturbation technique by identifying the "early" and "late" transient regimes for small values of the Biot number, Bi. In this sense, we have re-visited the classical lumped method, incorporating this particular case as an asymptotic limit, which is fully described by the "late" regime for small values of Bi. Once the temperature distribution is analytically predicted, this solution is compared against the exact solution and with other analytical results obtained by using regular perturbation techniques, for different values of the Biot number Bi. Observing a good agreement between the corresponding comparisons, we obtain a very simple and useful formula to predict the nondimensional temperature of the solid slab.
UR - http://www.scopus.com/inward/record.url?scp=43449098281&partnerID=8YFLogxK
U2 - 10.1007/s00231-005-0005-6
DO - 10.1007/s00231-005-0005-6
M3 - Artículo
SN - 0947-7411
VL - 42
SP - 150
EP - 157
JO - Heat and Mass Transfer/Waerme- und Stoffuebertragung
JF - Heat and Mass Transfer/Waerme- und Stoffuebertragung
IS - 2
ER -