Numerical Study of Natural Convection of Power Law Fluid in a Square Cavity Fitted with a Uniformly Heated T-Fin

• Published in: Mathematics (Basel) Vol. 10; no. 3; p. 342
• Main Authors: Bilal, Sardar, Khan, Noor Zeb, Shah, Imtiaz Ali, Awrejcewicz, Jan, Akgül, Ali, Riaz, Muhammad Bilal
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-02-2022
• Subjects: Differential equations; Discretization; Domains; Enclosures; Energy; finite element method; Finite volume method; Fluid flow; Free convection; Heat exchangers; Heat flux; Heat transfer; heated T-fin; Investigations; Kinetic energy; laminar free convection; Liquid flow; Mathematics; Non-Newtonian fluids; Nuclear power plants; Parameters; Partial differential equations; Power law; power-law fluid; Rayleigh number; Rheological properties; Rheology; Shear thickening (liquids); Shear thinning (liquids); square cavity; Temperature gradients; Thermal engineering; Thickening
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10030342

Flow of a liquid in an enclosure with heat transfer has drawn special focus of researchers due to the abundant thermal engineering applications. So, the aim of present communication is to explore thermal characteristics of natural convective power-law liquid flow in a square enclosure rooted with a T-shaped fin. The formulation of the problem is executed in the form of partial differential expressions by incorporating the rheological relation of the power-law fluid. The lower wall of the enclosure along with the fin is uniformly heated and vertical walls are prescribed with cold temperature. For effective heat transfer within the cavity the upper boundary is considered thermally insulated. A finite element based commercial software known as COMSOL is used for simulations and discretization of differential equations and is executed incorporating a weak formulation. Domain discretization is performed by dividing it into triangular and rectangular elements at different refinement levels. A grid independence test is accomplished for quantities of engineering interest like local and average Nusselt numbers to attain accuracy and validity in results. Variation in the momentum and thermal distributions against pertinent parameters is analyzed through stream lines and isothermal contour plots. Measurement of the heat flux coefficient along with the calculation of kinetic energy against involved parameters is displayed through graphs and tables. After the comprehensive overview of attained results it is deduced that kinetic energy elevates against the upsurging magnitude of the Rayleigh number, whereas contrary behavior is encapsulated versus power-law index n. Elevation in the Nusselt number for the shear thinning case i.e., n=0.5 adheres as compared to Newtonian i.e., n=1  and shear thickening cases  i.e., n=1.5. It is perceived that by the upsurging power-law index viscosity augmentations and circulation zones increases. Heat is transferred quickly against Rayleigh number (Ra) due to production of temperature difference in flow domain.