Abstract
A numerical study was undertaken of the naturally occurring laminar convective heat transfer from a slender cuboid with a relatively narrow cross-section (square) and an exposed top surface. The cuboid was perpendicularly placed on an adiabatic flat base plate and two types of surface boundary conditions were considered. The slender cuboid was inclined relative to the vertical axis at angles ranging from 0 to 180 degrees. The flow was considered symmetrical along the vertical axis of the slender cuboid. The equations governing the system were numerically solved in terms of dimensionless variables using FLUENT software. From the results obtained, mean Nusselt numbers over the slender cuboid were calculated using parameters such as: the Rayleigh number for heat flux, Ra*; the Rayleigh number, Ra; the slender cuboid dimensionless width, i.e., the ratio of the width to the height of the heated slender cuboid, W = w/h; and the position of the slender cuboid relative to the vertical, φ. Simulation results were produced for the boundary conditions of constant temperature, constant heat flux, and for Pr = 0.7. The effects of these parameters on the mean Nusselt number for the combined and for the individual surfaces of the slender cuboid are presented and the mean Nusselt numbers are correlated.
Highlights
A numerical investigation was undertaken of the natural laminar convective heat transfer from an inclined slender cuboid with a relatively narrow cross-section and an exposed top surface
The slender cuboid was perpendicularly attached to a plate and two types of surface boundary conditions were considered, constant wall temperature and constant wall heat flux in particular
The Ra*, the heat flux Rayleigh number, dependent on the height, h, of the heated slender cuboid, is set as the length scale, and q0w h/k is set as the temperature scale
Summary
A numerical investigation was undertaken of the natural laminar convective heat transfer from an inclined slender cuboid with a relatively narrow cross-section (square) and an exposed top surface. The slender cuboid positions considered were inclined relative to the vertical axis at angles ranging from 0 (pointing upward) to 180 degrees (pointing downward) from the vertical. The slender cuboid was perpendicularly attached to a plate and two types of surface boundary conditions were considered, constant wall temperature and constant wall heat flux in particular. The cuboid consisted of flat surfaces attached to each other at 90◦ angles. The relationship between the natural flows over the heated plates that formed the slender cuboid, shown, is of reasonable engineering practical significance. The interactions between the thermal and fluid flow fields over a cuboid of this kind in various positions are relatively complicated and need to be determined
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