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

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.

Free convection at different locations of adiabatic elliptic blockage in a square enclosure

“…The governing equations for the two-dimensional steady flow following the invocation of the equations that govern the steady two-dimensional flow, considering the Boussinesq approximation and neglecting radiation and viscous dissipation, can be formulated in the following manner [6,33,[39][40][41][42]: Continuity equation:…”

“…Turkyilmazoglu [32] studied nonuniform heating in free convection and found the best heat deletion rate close to the top wall of a cavity. Bilal et al [33] studied the power law fluid in a square cavity and found that heat conduction rises as the Rayleigh number increases, driven by the generation of temperature variations within the fluid domain. Sondur et al [34] performed a benchmark simulation on fluid flow inside a square cavity and they showed that the most accurate results were found for the steady flow solver Open FOAM which took a comparatively short time.…”

Heat Transfer Investigation in Plus-Shaped Enclosure Using Power Law Fluid: A Finite Element Approach

“…The illustration in Figure 1 depicts the physical layout of the problem. Considering the above assumptions, we utilize the following governing equations to represent the flow phenomenon [38][39][40][41] ∂u ∂x…”

A review of phase change materials and heat enhancement methodologies

“…They concluded that heat transfer rate between PCM and HTF has been enhanced significantly because of extended surface of vertical fins. Use of fins with PCMs in electronics is numerically investigated by Bilal, Khan, et al (2022b), Lacroix andBenmadda (1997), andNayak et al (2006) and it is found that the rate of heat transfer is enhanced up to a certain number of fins. Other than number of fins, fins geometry is also effective in heat transfer rate enhancement, such as rod-type fins.…”