Analytical Solution for One-Dimensional Semi-Infinite Heat Transfer Problem with Convection Boundary Condition

Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems

“…Substituting for δ through 2.6 then shows n 2/ π − 2 ≈ 1.752. This is the approach suggested by Braga et al 28 . The entropy minimisation method of Hristov 11 involves matching exact and approximate expressions for u 2 x /u 2 at x 0.…”

Heat Balance Integral Method for One-Dimensional Finite Ablation

“…Initially, Goodman et al chose low values, such as n 2 (see Goodman and Shea [3,8,20]). Recently, the method has been refined by Braga et al [10,21] by choosing n to make the ablation times match with the exact solution. However, this latter method has two main drawbacks.…”

“…It does not guarantee good agreement with the temperature profile, and, more importantly, the temperature gradient that drives the ablation, for all time. To overcome the first problem, in which an appropriate n cannot be found analytically, in Braga et al [21], the authors use an average value of n taken from two similar problems with known exact solutions. For the second, they increase n from =4 to 7 between the preablation and ablation periods [10].…”

Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition

“…Myers [32] also mentioned a similar problem in the solution of the equation of the penetration depth when applying the classical heat-balance integral method (HBIM) and the double integration method (DIM) to the case of forced convection for Bi = 1. Braga et al [33] have solved the same problem, without specifying Bi and developed an expression about the penetration depth in terms of the Lambert W function.…”

“…The case has been solved by Braga et al [33] (the case with α = 1) and the penetration depth can be expressed by the Lambert W function.…”