Effect of instantaneous change of surface temperature and density on an unsteady liquid–vapour front in a porous medium

  • Zafar Hayat KhanEmail author
  • Rashid Ahmad
  • Licheng Sun
Research Article


This article presents a comprehensive analysis of time dependent condensation model embedded in a porous medium with variations in liquid–vapour densities. Both similarity and asymptotic solutions for the unsteady liquid–vapour phase change front are obtained with the manifestation of various pertinent parameters. The obtained results are compared which congregate well as depicted clearly in graphs. Results indicate that with different diffusivity and contrast ratios, the similarity front parameter is found to be gradually declining with variation in a density ratio. We have shown for the condensation process, the ratio of sensible to latent heat is independent of time and is equal to the half of the Stefan number of the liquid phase.


unsteady liquid–vapour front porous medium Stefan number similarity and asymptotic solutions density variations 



The corresponding author is profoundly grateful to the financial support of the National Natural Science Foundation of China (Grant Nos. 51709191, 51706149, and 51606130), Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education (Grant No. ARES-2018-10), and State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (Grant No. Skhl1803).


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Copyright information

© Tsinghua University Press 2019

Authors and Affiliations

  • Zafar Hayat Khan
    • 1
    • 2
    Email author
  • Rashid Ahmad
    • 3
    • 4
  • Licheng Sun
    • 1
  1. 1.State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource & HydropowerSichuan UniversityChengduChina
  2. 2.Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of EducationTsinghua UniversityBeijingChina
  3. 3.School of Mathematics and PhysicsUniversity of QueenslandSt Lucia, BrisbaneAustralia
  4. 4.Faculty of Engineering SciencesGIK Institute of Engineering Sciences and TechnologyTopi, Swabi, KPKPakistan

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