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In this paper, we present a numerical investigation of natural convection heat transfer and entropy generation for a rhombic enclosure with inclination angle, ϕ = 30°, filled with a porous medium. The left and right surface walls of the enclosure are confined to cold temperature bath while we impart non-uniform, varying temperature distribution with unequal phase angles along the top and bottom wall. The flow inside the enclosure is steady, two-dimensional, incompressible and laminar, and the working fluid is air (Pr = 0.71). Numerical experiments have been performed using finite element method-based software COMSOL Multiphysics 5a for Darcy number and Rayleigh number in the extent of 10−4–10−2 and 103–106, respectively, in addition to phase deviation angles varying in the range from 0 to π. The amplitude parameter associated with the temperature delineation of the bottom and top walls is kept constant. The realizations from the numerical investigation are exhibited by streamlines and isotherms, local and average heat transfer Nusselt number along with the local distribution of heat transfer and fluid friction irreversibilities. The rate of heat transfer demonstrates non-monotonic trends and can be considerably influenced by the interplay of the phase shift angle, Rayleigh number and Darcy number. Upon increasing the value of phase shift angle from 0 to π, average Nusselt number initially decreases and thereafter shows an increase in its value. As the Darcy number increases, average Nusselt number for the bottom wall increases, while for the top wall it strongly depends on phase shift angle. In terms of entropy generation, it is found that the significant contributor to irreversibility is induced by heat transfer and the location of maximum entropy varies with the change in phase angle. More specifically, minimum entropy generation for any value of Rayleigh number and Darcy number is obtained for a phase shift angle of π/4 and maximum for 3π/4. The concomitant transport characteristics bear significance from the context of design of thermal systems pertaining to the theme of non-uniform heating with the phase angle being a crucial design parameter. [ABSTRACT FROM AUTHOR]

Highlights • MHD natural convection inside a rhombic enclosure filled with nanofluid is studied. • Effect of Rayleigh number, Hartmann number and inclination angles of the enclosure are examined. • The presence of the magnetic field is more perceptible in dictating Nu at higher Ra. • Operating zone of Ra depicting the negative efficacy of nanofluid is presented. • Entropy generation decreases with increase in both Ha and inclination angle. Abstract The present work analyses magnetohydrodynamic natural convection heat transfer and entropy generation in rhombic enclosures filled with Cu-water nanofluids. Numerical simulations were executed for varying Rayleigh number (Ra) in the range 103–106, Hartmann number (Ha) in the range 0–100 and inclination angles of the enclosure (30°, 45° and 60°) considering three different volume fractions of the nanofluid (1%, 3% and 5%). The results indicate that at low Ra , the heat transfer rate remains invariant with the variation in Ha. At high Ra (≥105), the presence of the magnetic field is more perceptible implying that the reduction in heat transfer rate with the increase in magnetic field intensity is far more significant. The heat transfer rate enhances with the increase in inclination angle for all Ha for Ra =103 and 104. However, at high Ra (=105 and 106) the trend becomes contrasting due to the interplay of buoyancy and Lorentz forces. There exists an operating range of Ha in the convection regime wherein the efficacy of the nanofluid in augmenting the heat transfer rate is negated when compared to the corresponding performance of the base fluid. The concomitant thermal identity resulting due to the combined interactions of Hartmann number and volume fraction of the nanofluid have been presented. The entropy generation rate decreases with the increase in Ha for all values of Ra and inclination angles of the enclosure. [ABSTRACT FROM AUTHOR]

In this work, we study numerically the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bottom wall. The effect of Darcy number is significant in dictating the Nusselt number only for higher values of Rayleigh number and the variation is more profound for larger values of Darcy number. The variation of entropy generation rate is significant with the Darcy number only for higher values of Rayleigh number. The entropy generation due to heat transfer is the significant contributor of irreversibility at low values of Darcy number, while for larger values of Darcy number and Rayleigh number entropy generation due to fluid friction becomes dominant. [ABSTRACT FROM AUTHOR]