{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,7]],"date-time":"2026-06-07T07:58:43Z","timestamp":1780819123513,"version":"3.54.1"},"reference-count":50,"publisher":"Wiley","license":[{"start":{"date-parts":[[2021,12,11]],"date-time":"2021-12-11T00:00:00Z","timestamp":1639180800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2021,12,11]]},"abstract":"<jats:p>This article develops the semianalytical analysis of couple stress hybrid nanofluid free stream past a rotating disc by applying the magnetic flux effects and radiation of thermal energy. The analysis of such kind of mixed convective flow is most important due to numerous industrial applications such as electronic devices, atomic reactors, central solar energy equipment, and heat transferring devices. The impact of variable permeability is also considered in the study. The permeability of the disc obeys the Darcy-Forchheimer model. The hybrid nanofluid is composed of water, titanium dioxide, and aluminum oxide. The set of governing equations in the PDE form are transformed to couple ODEs by applying similarity transformations. The ODE set are solved by applying the technique of HAM. The graphs of impacts of numerous physical parameters over momentum, energy, and concentration profiles are drawn in computer-based application Mathematica 11.0.1. In the sundry physical parameters, the porosity parameter, Reynolds number, inertial parameter, Prandtl number, Schmidt number, couple stress, and quotient of rotational momentum to elongating rate are included. During the analysis, it is found that the momentum profile of the couple stress hybrid nanofluid enhances with local inertial parameter, couple stress parameter, porosity parameter, and Reynolds number but declines for the growth in Hartmann number. Heat transfer rate enhances for radiation parameter but decreases in variable for temperature, thermal stratification parameter, thermophoresis parameter, and Brownian parameter.<\/jats:p>","DOI":"10.1155\/2021\/2522155","type":"journal-article","created":{"date-parts":[[2021,12,11]],"date-time":"2021-12-11T18:05:08Z","timestamp":1639245908000},"page":"1-18","source":"Crossref","is-referenced-by-count":9,"title":["MHD Analysis of Couple Stress Hybrid Nanofluid Free Stream over a Spinning Darcy-Forchheimer Porous Disc under the Effect of Thermal Radiation"],"prefix":"10.1155","volume":"2021","author":[{"given":"Muhammad","family":"Zubair","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar, 25120 Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Jawad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Swabi, Swabi, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0808-4504","authenticated-orcid":true,"given":"Ebenezer","family":"Bonyah","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rashid","family":"Jan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan, 23200 Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","volume-title":"Enhancing Thermal Conductivity of Fluids with Nanoparticles","author":"S. 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