Dead-core solutions for slightly non-isothermal diffusion-reaction problems with power-law kinetics

Boris Golman, Vsevolod V. Andreev, Piotr Skrzypacz

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The paper deals with dead-core solutions to a non-isothermal reaction- diffusion problem with power-law kinetics for a single reaction that takes place in a catalyst pellet along with mass and heat transfer from the bulk phase to the outer pellet surface. The model boundary value problem for two coupled non-linear diffusion-reaction equations is solved using the semi-analytical method. The exact solutions are established under the assumption of a small temperature gradient in the pellet. The nonlinear algebraic expressions are derived for the critical Thiele modulus, dead-zone length, reactant concentration, and temperature profiles in catalyst pellets of planar geometry. The effects of the reaction order, Arrhenius number, energy generation function, Thiele modulus, and Biot numbers are investigated on the concentration and temperature profiles, dead-zone length, and critical Thiele modulus.

Original languageEnglish
Pages (from-to)576-589
Number of pages14
JournalApplied Mathematical Modelling
Publication statusPublished - Jul 2020


  • Catalytic pellet
  • Dead zone
  • Diffusion and reaction
  • Non-isothermal reaction
  • Power-law kinetics
  • Semi-analytical solutions

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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