Generalized mathematical model of Brinkman fluid with viscoelastic properties: Case over a sphere embedded in porous media

Siti Farah Haryatie, Mohd Kanafiah and Abdul Rahman, Mohd Kasim and Syazwani, Mohd Zokri (2022) Generalized mathematical model of Brinkman fluid with viscoelastic properties: Case over a sphere embedded in porous media. Axioms, 11 (11). pp. 1-16. ISSN 2075-1680. (Published)

Generalized Mathematical Model of Brinkman Fluid with Viscoelastic Properties.pdf
Available under License Creative Commons Attribution.

Download (1MB) | Preview


The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this attempt aims to demonstrate the behavior of fluid flow in porous regions, using the Brinkman viscoelastic model for combined convective transport over a sphere embedded in porous medium. The governing partial differential equations (PDEs) of the proposed model are transformed into a set of less complex equations by applying the non-dimensional variables and non-similarity transformation, before they are numerically solved via the Keller-Box method (KBM) with the help of MATLAB software. In order to validate the model for the present issue, numerical values from current and earlier reports are compared in a particular case. The studied parameters such as combined convection, Brinkman and viscoelastic are analyzed to obtain the velocity and temperature distribution. Graphs are used to illustrate the variation in local skin friction and the Nusselt number. The results of this study showcase that when the viscoelastic and Brinkman parameters are enlarged, the fluid velocity drops and the temperature increases, while the combined convection parameter reacts in an opposite manner. Additionally, as the Brinkman and combined convection parameters are increased, the physical magnitudes of skin friction and Nusselt number are increased across the sphere. Of all the parameters reported in this study, the viscoelastic parameter could delay the separation of boundary layers, while the Brinkman and combined convection parameters show no effect on the flow separation. The results obtained can be used as a foundation for other complex boundary layer issues, particularly in the engineering field. The findings also can help researchers to gain a better understanding of heat transfer analysis and fluid flow properties.

Item Type: Article
Additional Information: Indexed by Scopus
Uncontrolled Keywords: Brinkman fluid; numerical solution; porous region; sphere; viscoelastic fluid
Subjects: Q Science > QA Mathematics
Faculty/Division: Institute of Postgraduate Studies
Center for Mathematical Science
Depositing User: Mrs Norsaini Abdul Samat
Date Deposited: 01 Aug 2023 07:18
Last Modified: 01 Aug 2023 07:18
Download Statistic: View Download Statistics

Actions (login required)

View Item View Item