TRANSIENT FLOW OF AN EXPONENTIALLY VISCOUS FLUID IN A RECTANGULAR DOMAIN

Dumitru Vieru^†, Nehad Ali Shah^‡

Abstract: This paper investigates the motion of an advanced shear-thinning model for paint. The study examines the liquid’s flow in a rectangular domain bounded by two parallel flat plates subjected to Robin type boundary conditions. The governing equations are integrated numerically for both pressure driven and pressure gradient free flows. Under certain conditions relating the material coefficients to the velocity gradient, exact analytical solutions are also derived. The impact of material properties on paint behavior was also assessed.

Keywords: paint, shear-thinning fluid, analytical solutions, finite sine-cosine Fourier transform.

MSC: 76Axx.

DOI 10.56082/annalsarscimath.2026.4.245

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^*Accepted for publication on September 22, 2026
^†dumitru.vieru@academic.tuiasi.ro, Department of Theoretical Mechanics, Gheorghe Asachi Technical University of Iasi, Romania
^‡nehadali199@yahoo.com, Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 4, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997