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The investigation of entropic variations in the thermal transport mechanism produced by buoyantly driven temperature gradients has attracted significant attention because of excellent physical significance. Therefore, the prime consent to manipulate the current investigation is to explore the impact of change in the aspect ratio of the trapezoidal cavity in the optimization of the entropy phenomenon. After attaining motivation from its practical essence different entropies including thermal, viscous, and local are estimated. Additionally, global quantities such as average Bejan and Nusselt numbers calculated along with total entropy are measured against flow concerning parameters (aspect ratio (AR), Rayleigh number (Ra) and irreversibility ratio (ϕ )). Numerical experiments are performed by implementing a finite element approach using open-source software renowned as COMSOL Multiphysics. Before the accomplishment of the outcomes, confirmation of the numerical technique is assured by establishing grid sensitivity testing. Comparison of results between present and previous studies is also demonstrated. A wide range of involved sundry parameters varying from 10 - 4 ≤ ϕ ≤ 10 - 2 , 10 2 ≤ Ra ≤ 10 5 and 0.25 ≤ AR ≤ 0.75 are accounted. It is concluded that by escalating the aspect ratio from 0.50 to 0.75, the magnitude of the local entropy enhances from 3370 to 3424. It is revealed that the highest value of viscous entropy that is, 45, is achieved at Ra = 105 and by keeping the aspect ratio of enclosure equal to 0.75, whereas, the thermal entropy approaches 2 for the same situation of parameters. The magnitude of the average Bejan number reaches unity at AR = 0.5 and Ra = 105, whereas for low and high aspect ratios it depicts a magnitude less than 1 for the same Rayleigh number. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, equations of motion for the process of calendering using a non-Newtonian upper-convected material calendering with the porous rolls are modeled and analyzed. Lubrication approximation theory is used to simplify the equations of motion. The non-dimensionalized equations are solved for the pressure and velocity profiles. Engineering interest quantities such as maximum pressure, power input and roll separating forces are obtained numerically by using composite Simpson's rule. Using response surface methodology, sensitivity analysis is also applied to analyze the effects of Reynolds number and viscoelastic parameter on the sheet thickness, roll separating forces and power input. It is examined that the involved parameter Reynolds number has a greater impact on velocity distribution, pressure distribution and detachment point which are suitable for the process of calendering. The roll separating force and the power input decrease for increasing the values of viscoelastic parameter. The sheet thickness is positively sensitive toward Reynolds number and viscoelastic parameter, while roll separating forces and power input are negatively sensitive to lower and middle levels of input parameters. [ABSTRACT FROM AUTHOR]