Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances

Table 1

Solution of (2.4)-(2.5).

𝜃𝑠,0	𝑋+𝜂𝜂+𝐻
𝜃𝑠,1	𝐴𝑋^36𝑋+𝜂^22+𝐵𝑋+𝜂𝐵−𝛽𝜉3
𝜃𝑠,2	𝐸𝑋^5𝑋120+𝜂^4𝑋24+𝐹^36+𝜂𝐹−𝛽𝜉3𝑋^22+𝐺𝑋−𝐺𝐻−𝐼
𝜃𝑙,0	𝑅1−1𝑋+𝑊−𝑅1𝐻𝑊−𝐻
𝜃𝑙,1	𝐶𝑋^36𝑋−𝑊^22𝑊+𝐷𝑋−𝑊𝐷+^33
𝜃𝑙,2	𝐽𝑋^5𝑋120−𝑊^4𝑋24+𝐿^36+𝑊^33𝑋−𝐿𝑊^22+𝑆(𝑋−𝑊)−2𝑊^5+15𝐿𝑊^33
𝜃𝑤,0	𝜉(𝑋+1)𝜂+𝐻
𝜃𝑤,1	𝛽𝑋𝜉𝐴^36𝑋+𝛽^22𝛽+𝐵𝑋+𝐵−3
𝜃𝑤,2	𝛽𝑋𝛽𝜉𝐸^5𝑋120+𝛽^4𝑋24+𝐹^36+𝛽𝐹−3𝑋^22−𝜉𝜂𝑇+𝐺𝐻+𝐼𝑅𝛽𝜂𝑋+𝜂𝑇−𝐺𝐻+𝐼𝛽𝜂
𝑔𝑜	1+𝑎𝜂+𝐻𝑊−𝐻
𝑔1	−1+𝑎𝜂+𝐻𝑊−𝐻𝜂𝐻𝜂+𝐻^2+𝛽𝜉+𝐻^33𝜂+𝐻^3−𝛾𝑎3
𝑔2	()𝐻𝐸−𝐾𝐽^4+𝐻24𝜂𝐸+𝑊𝐾𝐽^36+()𝐻𝐹𝐸−𝐿𝐾𝐽^22+𝐸𝜂𝐹−𝛽𝜉3𝑊−𝐾𝐽^33−𝑊𝐿𝐻+(𝐸𝐺−𝐾𝐽𝑆)