Mass Transfer in a Rigid Tube With Pulsatile Flow and Constant Wall Concentration
Bibliographic record
Abstract
An approximate-analytical solution method is presented for the problem of mass transfer in a rigid tube with pulsatile flow. For the case of constant wall concentration, it is shown that the generalized integral transform (GIT) method can be used to obtain a solution in terms of a perturbation expansion, where the coefficients of each term are given by a system of coupled ordinary differential equations. Truncating the system at some large value of the parameter N, an approximate solution for the system is obtained for the first term in the perturbation expansion, and the GIT-based solution is verified by comparison to a numerical solution. The GIT approximate-analytical solution indicates that for small to moderate nondimensional frequencies for any distance from the inlet of the tube, there is a positive peak in the bulk concentration C(1b) due to pulsation, thereby, producing a higher mass transfer mixing efficiency in the tube. As we further increase the frequency, the positive peak is followed by a negative peak in the time-averaged bulk concentration and then the bulk concentration C(1b) oscillates and dampens to zero. Initially, for small frequencies the relative Sherwood number is negative indicating that the effect of pulsation tends to reduce mass transfer. There is a band of frequencies, where the relative Sherwood number is positive indicating that the effect of pulsation tends to increase mass transfer. The positive peak in bulk concentration corresponds to a matching of the phase of the pulsatile velocity and the concentration, respectively, where the unique maximum of both occur for certain time in the cycle. The oscillatory component of concentration is also determined radially in the tube where the concentration develops first near the wall of the tube, and the lobes of the concentration curves increase with increasing distance downstream until the concentration becomes fully developed. The GIT method proves to be a working approach to solve the first two perturbation terms in the governing equations involved.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".