Hybrid integral transform solution for the analysis of drying in spherical capillary-porous solids based on Luikov equations with pressure gradient

• Luikov equations with pressure gradient effects considered for drying of capillary-porous solids of spherical geometry.
• The Generalized Integral Transform Technique (GITT) employed in the hybrid solution of the related equations.
• Parametric analysis performed to investigate the influence of the Bulygin and Luikov for filtration numbers.
• Comparisons of the results for the potential distributions demonstrated the robustness of the integral transform approach.

A hybrid solution based on the Generalized Integral Transform Technique (GITT) is obtained for the analysis of the Luikov equations including pressure gradient effects for drying of capillary-porous solids that have spherical geometry. First, the present results are compared with previous ones in the literature, as well as with those from the NDSolve routine (Mathematica system) for specific situations, in order to validate the numerical codes developed in the present work and to demonstrate the consistency of the final results. Additionally, the results for temperature, moisture and pressure fields are produced with different values of the governing parameters, illustrating the potential of the hybrid numerical–analytical GITT approach in solving drying problems with significant pressure variations, such as in highly intensive and fast drying processes. Therefore, for this purpose, five test-cases are considered in order to make a parametric analysis, which is performed in order to investigate the influence of typical governing parameters (Bulygin and Luikov for filtration numbers) for such a physical situation. The influence of the pressure field in the temperature and moisture distributions is also emphasized by analyzing a typical case of the drying problem of a ceramic material with the Luikov equations with two parameters, namely temperature–moisture model (TM Model) and with three parameters, those in the temperature–moisture–pressure model (TMP Model).