An analytical and experimental investigation of the effect of large wall roughness elements of the natural convection heat transfer in rectangular enclosures

Author

Md Ruhul Amin

Date of Award

8-1989

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mechanical Engineering

Major Professor

Robert J. Krane

Committee Members

J.R. Parsons, J.W. Hodgson, J.J. Perona

Abstract

The purpose of this research was to determine the effects of placing large roughness elements on the hot vertical wall of a two-dimensional, rectangular enclosure on the rate of natural convection heat transfer across that enclosure. The enclosure of interest is assumed to be vertically-oriented with isothermal vertical walls maintained at two different temperatures, to have adiabatic horizontal walls, and to be completely filled with a Newtonian fluid.

Both sinusoidal and rectangular roughness elements were investigated; however, the main focus of this investigation was on the use of rectangular elements. The roughness elements were assumed to be designed such that the total amount of fluid in the enclosure was equal to the amount of fluid in the corresponding smooth-walled enclosure. The consequences of not complying with this assumption were explored and shown to be significant. Both numerical and experimental investigations of the problem were performed. The numerical solutions of the natural convection flows of interest in smooth-walled enclosures and enclosures containing either sinusoidal or rectangular roughness elements were obtained using the NACHOS finite element code. The experimental work was performed solely for the purpose of validating the NACHOS code for laminar, natural convection flows in two-dimensional enclosures containing large wall roughness elements. The code was shown to predict the temperature distributions in the fluid measured with a Mach-Zehnder interferometer and local wall heat flux (local Nusselt number) distribution measured with a Wollaston prism interferometer within the experimental uncertainty. Thus, the NACHOS code was successfully verified for the purposes of the present work.

An extensive parametric study was performed using NACHOS. The effects of adding wall roughness elements on the rate of natural convection heat transfer across an enclosure are reported in terms of the ratio of the overall Nusselt number in an enclosure containing roughness elements to the overall Nusselt number in the smooth-walled enclosure [(Nu)_R)/(Nu)_S] with the same aspect ratio, W/H. The highest value of (Nu)_R)/(Nu)_S (the greatest enhancement of the heat transfer) found in this work was 1.355; which was obtained at a Grashof number, Gr_H, of 4.07 X 10^{6 in an enclosure containing four sinusoidal elements. The sinusoidal elements were shown to not only increase the rate of heat transfer near the bottom of the hot vertical wall, but to significantly increase the local rates of heat transfer on those segments of the cold vertical wall that are directly opposite to the elements. This effect was not observed in any of the flows investigated when rectangular elements were employed.}

The ratio of Nusselt numbers,(Nu)_R)/(Nu)_S, for enclosures containing rectangular roughness elements was shown to be a function of the Grashof number, Gr_H, the Prandtl number, Pr, the aspect ratio of the enclosure, W/H, and the amplitude. A, the period, σ, and the phase shift, σ₀, of the roughness element array. The values of all of these parameters, except that of the phase shift, σ₀, are shown to significantly affect the ratio of overall Nusselt numbers, (Nu)_R)/(Nu)_S.

Recommended Citation

Amin, Md Ruhul, "An analytical and experimental investigation of the effect of large wall roughness elements of the natural convection heat transfer in rectangular enclosures. " PhD diss., University of Tennessee, 1989.
https://trace.tennessee.edu/utk_graddiss/11543