Numerical simulation of the effects of plate separation and inclination on heat transfer in buoyancy driven open channels S. Baskaya, M. K. Aktas, N. Onur Abstract Effects of plate separation and inclination on free convection between asymmetrically heated vertical and inclined parallel plates have been simulated. The upper isothermally heated plate is facing downwards, the lower plate is passively heated by the upper one. The plate inclinations are chosen to be 0  ; 30  ; 45  with respect to vertical position. Three-dimensional laminar numerical simulations are obtained by solving the full elliptic gov- erning equations using a commercial ®nite volume based computational ¯uid dynamics (CFD) code. Comparisons of computational results with experiments and data from the literature are made in terms of relevant dimensionless numbers. It was observed that plate spacing and inclina- tion in¯uence the overall heat transfer rate. List of symbols a; b correlation constants B buoyancy force g acceleration due to gravity h heat transfer coef®cient k thermal conductivity L length of plate Nu s Nusselt number based on s Nu L Nusselt number based on L Pe Peclet number P m motion pressure Pr Prandtl number q heat ¯ow from the heated plate Ra s Rayleigh number based on s Ra L Rayleigh number based on L Re Reynolds number s plate spacing T absolute temperature T 0 ambient temperature T H temperature of heated plate T C temperature of passively heated plate DT temperature difference, T H  T 0 u velocity component in the x-direction v velocity component in the y-direction w velocity component in the z-direction W width of plates x; y; z cartesian coordinates Greek symbols a thermal diffusivity b coef®cient of thermal expansion m laminar kinematic viscosity h inclination angle q density q 0 reference density 1 Introduction Needs for buoyancy driven ventilation appear in a variety of engineering applications, ranging from cooling of elec- tronic components and solar energy applications to cooling of nuclear reactor fuel elements. For an ef®cient application of natural convection to cooling processes it is necessary to fully understand the mechanisms of heat dissipation inside parallel-plate channels. Hence, an investigation into par- allel-plate channels has been performed concentrating on inclination and plate separation effects. An extensive review and discussion of natural convec- tion in enclosures and partial enclosures is given by Gebhart et al. [1]. A great number of analytical and experimental work has been carried out on this problem since Elenbaas [2] ®rst introduced the problem of natural convection between vertical parallel plates. Anand et al. [3] studied theoretically the effect of plate spacing on free convection heat transfer between heated plates. Optimum plate spacing for single channels were obtained from numerical calculations of the parabolic conservation equations. This work was extended by Morrone et al. [4] who calculated numerically optimum plate separations by solving the fully elliptic equations and incorporating large spaces at the channel extremes. Numerical results for the overall channel Nusselt number were obtained by Straat- man et al. [5] for inclined isothermal plates. Experimental validation was also made using a Mach-Zehnder interfer- ometer. They found a decrease of the overall heat transfer with increase in the inclination angle. However, their numerical study was only two-dimensional, three-dimen- sional effects were ignored. The above mentioned studies are related to symmetrically heated channels. An experi- mental and numerical investigation of natural convection in an asymmetrically heated vertical channel was per- formed by Sparrow et al. [6]. The most important ®nding reported is that a pocket of down¯ow and recirculation was Heat and Mass Transfer 35 (1999) 273±280 Ó Springer-Verlag 1999 273 Received on 3 November 1998 S. Baskaya M.K. Aktas N. Onur Gazi University Faculty of Engineering and Architecture Department of Mechanical Engineering 06570 Maltepe, Ankara, Turkey Correspondence to: S. Baskaya