Characteristic transport lengths (CTLs) in porous medium evaluated with classic diffusion solutions under infinite Biot number condition
Abstract In process engineering practice, including those in food industry, simple mathematical solutions are more useful. Learned assumptions are necessary to support effective simplifications. Previously it has been suggested that for a conduction and convection coupled system, there is an approximately linear temperature or concentration gradient between the surface and the average temperature, which occurs at a ‘fixed location’ within the conduction domain. The local temperature at the point is also said to be similar as the average temperature. This gradient is thus approximately the same as the temperature gradient at the interface between the conduction domain and the convection medium when thermal properties are considered constants. The distance from the surface to this ‘fixed location’ is marked as the characteristic transport length (CTL), which is a fraction of the size of the conduction medium. The previous findings were based on the agreements between the numerical solutions and compartmental, and then integral solutions in different occasions The argument has been validated among moderate Biot numbers (Bi) of 0.3. Similarly, one should find that the diffusional mass transfer process has the same property due to the same mathematical nature involved. Here, the mass diffusion process has been analyzed to yield the CTLs for the cases of infinite Biot number, where the analytical solutions for longer times for semi-infinite slab, infinite cylinder and sphere are available which can be put to great use. When applying these classical solutions for the above purpose, there are still new discoveries, which are interesting to report here.