The effect of sinusoidal protrusions on laminar free convection between vertical walls

Abstract

The effects of sinusoidal protrusions on steady laminar free convection between vertical walls is investigated in this paper. Numerical results are presented for various values of the size and spacing of the protrusions. In particular optimum values are found which yield maximum wall heat-transfer coefficients.

Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation

“…One might expect that a solution based on expanding in terms of S would become singular as Ra -+ Ra, when k = kc. This was confirmed in a preliminary report of our research (Kelly & Pal 1976) where it was shown by means of an eigenfunction expansion that A singularity was also noticed by Watson & Poots (1971) in their study of convection in a vertical slot as the Grashof number approaches the usual critical value (they also expanded in terms of 6). A singularity also exists in Busse's (1972) exact solution of the flow induced by internal heating in the form of a wave travelling between stressfree surfaces when one sets the frequency to zero, k = k,, and Ra = Ra,.…”

“…The first case might also be relevant to estimating the extent to which well-defined initial disturbances (such as imposed by Chen & Whitehead 1968) affect stability boundaries, etc., although our forcing is steady in time. The second case has some practical value in that one might want to make the boundary wavy if the mean Nusselt number could be increased (such a consideration seems to have motivated Watson & Poots (1971) in their study of how wavy boundaries affect laminar free convection flow between vertical walls). I n both cases, the amplitude of the variation (8) is assumed to be small (in a sense to be defined more exactly later), and an expansion is made in terms of 8.…”

Effect of Surface Undulations on Natural Convection in a Porous Square Cavity

“…The effect of sinusoidal protrusions on laminar free convection between vertical walls has been reported by Watson and Poots (1971), where as the free convection heat transfer in a viscous incompressible fluid confined between a long vertical cosine wavy wall and a parallel flat wall has been analysed by Vajravelu and Sastri (1978). A deviation in the Nusselt number results from that of the flat wall has been observed in both the cases.…”

“…Bhavnani and Bergles (1991) give a literature review of free convection heat transfer from vertical surfaces with surface roughness elements in continuum fluids. By approximating the small-scale roughness as periodic (sine or cosine) functions, Watson and Poots (1971), Vajravelu and Sastri (1978), Yao (1983), Moulic and Yao (1989), and Bhavnani and Bergles (1991) have studied the free convection in clear fluids, where as Riley (1988), Rees and Pop (1994a, b), and Murthy et al, (1997) studied the free convection heat transfer in porous media.…”

Spatially modulated thermal convection of viscoelastic fluids

“…Chen and Whitehead [15] evaluated the extent to which well-defined initial perturbations affect stable boundaries, although they were steady in time. The practical value is that one might want to make the boundary wavy if the mean Nusselt number could be increased, which have motivated Watson and Poots [16] to study the effects of wavy boundaries on laminar free convection in a flow between parallel vertical walls.…”