Evidence map›Paper›PMID 40715214›Full record

ArticleScientific reports2025

Modelling cross-diffusion in MHD Williamson nanofluid flow over a nonlinear stretching surface via Morlet wavelet neural networks.

Khalid Arif, Syed Tauseef Saeed, Muhammad Naeem Aslam, Jihad Younis, Arshad Riaz, Salman Saleem

Abstract read
In one paragraph

Article in Scientific reports, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

0numbers the graph read from it
0cells of the map it votes in
1citing papers in PubMed
–field-weighted citation impact
1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

1 citing paper in PubMed.

  1. Article
4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

6 authors.

Khalid ArifDepartment of Mathematics and Statistics, The University of Lahore, Lahore, 54770, Pakistan.
Syed Tauseef SaeedDepartment of Mathematics and Statistics, The University of Lahore, Lahore, 54770, Pakistan. tauseef.saeed@math.uol.edu.pk.
Muhammad Naeem AslamDepartment of Mathematics, Lahore Garrison University, Lahore, 54770, Pakistan.
Jihad YounisDepartment of Mathematics, Aden University, Aden, Yemen. jihadalsaqqaf@gmail.com.
Arshad RiazDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, 54770, Pakistan.
Salman SaleemDepartment of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

In this paper, a new numerical technique was developed to investigate magnetohydrodynamic (MHD) flow of Williamson nanofluid past a nonlinear stretching surface imbedded in a porous medium laden with Soret and Dufour effects. The control equations, which are highly nonlinear partial differential equations, are first converted into ordinary differential equation (ODEs) using similarity transformation and then are solved effectively by the hybrid computational method applying Morlet Wavelet Neural Networks (MWNNs) combined with a heuristic optimizers neural network and particle swarm as MWNNs-PSO-NNA. The proposed MWNNs-PSO-NNA shows a very low mean square error and Theil's Inequality Coefficient indicating that the accuracy of the model. To check the convergence and validation of the proposed approach, computing the hundred independent runs for statistical metrics. The fitness function, MSE and TIC values ranging from 10

Indexed as

Heuristic optimizationMagneto hydrodynamics (MHD)Morlet wavelet neural networksSoret and Dufour effectsWilliamson nanofluid

Identifiers

PMID40715214
PMCPMC12297273

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Registered trials

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.