Abstract
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.
Highlights
Natural convection is an abundant phenomenon generated by density differences which may arise in many settings like air craft surfaces, melt spinning, drying and coating technologies, computers chips, solar paneling, wind chiller, hydraulic pumps, molten metals, heat dissipation fins, hydrothermal reservoirs, filtration processes, nuclear waste storing, solidification of castings, liquefaction gases and biofilm growth
The current disquisition analyzes the thermal attributes of the power-law liquid enclosed in a square cavity with the insertion of a uniformly heated T-fin
The formulation of the problem is demonstrated in the context of intricate dimensionless partial differential structuring
Summary
For comprehensive examination of non-Newtonian liquids they are characterized into two main classes, namely, the shear thinning and thickening liquids This classification has raised the essence of non-Newtonian fluids in multiple advanced processes like food formation, oil refining, heating and cooling systems and nuclear power plant, polymerization, friction reduction, flow traces and so forth. Natural convection is an abundant phenomenon generated by density differences which may arise in many settings like air craft surfaces, melt spinning, drying and coating technologies, computers chips, solar paneling, wind chiller, hydraulic pumps, molten metals, heat dissipation fins, hydrothermal reservoirs, filtration processes, nuclear waste storing, solidification of castings, liquefaction gases and biofilm growth In view of their superb practical utility, researchers have conducted studies. Agreement of the presently computed results is made by constructing a comparison with results published by Roy et al [30]
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