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

Figure 6

𝐸_𝑀(𝑚) for HBIM (solid line) and RIM (dashed line), minimum errors shown as asterisks. (a) 𝛽=1, diamonds show errors for 𝑚=1.5531, 𝑚=1.5514 (obtained by matching 𝑢_𝑥 at 𝑥=0), 𝑚=1.5463 (CIM) and 𝑚=2. (b) 𝛽=10, diamonds show errors for 𝑚=1.5061, 𝑚=1.5060 (matching 𝑢_𝑥 at 𝑥=0), 𝑚=1.5056 (CIM) and 𝑚=2.

(a)

(b)