International Journal of Emerging Multidisciplinaries: Mathematics

Corresponding Author

Sardar Muhammad Bilal

Document Type

Research Article

Subject Areas

Applied Mathematics and Computations


Free convection; Carreau fluid; Square enclosure; Uniformly heating; FEM.


Heat transfer aspects induced by natural convection in enclosures have promising utilizations and essence from theoretical as well as practical prospective like in, nuclear and chemical reactors, electronic devices, cooling, polymeric processes, solar power collection and so forth. After viewing aforementioned extensive practical importance present communicatn is addressed to explain the flow attributes of Non-Newtonian Carreau fluid model in a square cavity. For non-elastic Carreau fluid model expressing the stress and strain relations at infinite and zero stress magnitude. Mathematical formulation of problem is conceded by obliging conservation laws of momentum and energy. A square enclosure with unit dimension is assumed by providing no-slip constraints at all extremities whereas bottom wall is uniformly heated. In order to maintain state of thermal equilibrium in which upper wall is adiabatic and lower and left wall is kept heated and right wall is considered as cold.by incorporation above restrictions on formulated problem equation are attained in partial differential dimensional form. Later on, these expressions are transmuted into dimensionless form by executing variables. Numerical simulation, based on infinite element method by utilizing COMSOL multi physics commercial software is computed. For this purpose, firstly preprocessing involving the steps of meshing at different refinement level is carried out. After this influence of involved dimensionless parameters as flow concerning profile is manifested through graphs and tables. Validation of result is also provided by constructing comparison with existing literature. Grid independence test for heat transfer coefficient is also performed. Engineering interest quantities like kinetic energy, local and average Nusselt number is also computed.

Receive Date

2022-10-06 23:57:39

Publication Date