Mass and heat transfer by natural convection in a vertical cavity A. Bejan* This paper reports a fundamental study of laminar natural convection in a rectangular enclosure with heat and mass transfer from the side, when the buoyancy effect is due to density variations caused by either temperature or concentration variations. In the first part of the study scale analysis is used to determine the scales of the flow, temperature and concentration fields in boundary layer flow for all values of Prandtl and Lewis numbers. In particular, scale analysis shows that in the extreme case where the flow is driven by buoyancy due to temperature variations, the ratio of mass transfer rate divided by heat transfer rate scales as Le 1/2 only if (Pr> 1, Le < 1) or (Pr < 1, Sc < 1), and as Lo 1/3 if (Pr> 1, Lo > 1 ) or (Pr<l, Sc> 1). In the second part of the study, the boundary layer scales derived in the first part are used to determine the heat and mass transport characteristics of a vertical slot filled with fluid. Criteria for the existence of distinct thermal and concentration boundary layers in the slot are determined. Numerical solutions for the flow and concentration fields in a slot without distinct thermal boundary layers are reported. These solutions support further the method of scale analysis employed in the first part of the study Kegwords: convect/on, heat transfer, mass transfer, sca/e analysis This paper reports a fundamental study of natural convection in a vertical cavity filled with fluid, when the buoyancy effect is due to density variations caused by heat and mass transfer along the vertical sides of the cavity. Related to environmental applications involving the transport of water vapour and other chemical con- taminants across enclosed spaces, the focus of the work is on the boundary layer regime in which the rates of heat and mass transfer across the enclosure can greatly exceed the estimates based on the assumption of pure diffusion. Although the objective of this study is the boun- dary layer regime in the enclosures configuration, the first part is devoted to a detailed analysis of the scales describing the flow, temperature and concentration fields in the immediate vicinity of a single vertical wall immersed in a fluid reservoir with different temperature and concen- tration. Two decades of intensive research on enclosures in the presence of only heat transfer have shown that a theoretical understanding of the proper scales of en- closure flows is tied closely to the understanding of the scales of natural convection in isolated boundary layer flow 1. The same conclusion emerges in the parallel field of heat-transfer-driven natural convection in porous me- dia 2. An additional reason for sorting out the scales of a boundary layer first is that, currently, these scales are known only for flows in relatively narrow ranges of Prandtl and Schmidt numbers 3-v. Scaling work in the entire (Pr, So) domain is needed to convey an effective overview of the heat and mass transfer natural convection phenomenon. * Department of Mechanical Engineering and Materials Science, Duke - University, Durham, NC 27706, USA Received 10 October 1984 and accepted for publication on 31 January 1985 The boundary layer scales thus revealed are used to determine criteria for the existence of the boundary layer regime in an enclosure, that is, criteria for the correctness of using the heat and mass transfer scales of the boundary layer in order to evaluate the transport capability of the enclosure. The study concludes with numerical experiments focusing on the intermediate re- gime where only one boundary layer (temperature or concentration) is distinct, the other transfer process being governed by pure diffusion. Boundary layer formulation Consider the two-dimensional flow in the immediate vicinity of a vertical wall (Fig 1). The wall and the unaffected fluid reservoir are maintained at different temperatures, T o and Too, while the concentration of a certain constituent varies from C Oon the fluid side of the wall to Coo sufficiently far into the fluid reservoir. The vertical boundary layer flow is driven by the buoyancy effect associated with the density difference between wall fluid and reservoir fluid. The boundary layer momentum equation for this flow is: Ov ~v O2v g_ U ~x + V~y= V~xZ + p (Poo - P) (1) where u and v are the local velocity components, and 9, v, p and poo are the gravitational acceleration, kinematic viscosity, density and reservoir fluid density, respectively. Since the thermodynamic state of the fluid mixture depends on pressure, temperature and composition, in the limit of small density variations at constant pressure we can write: P ~P~o -pfl(T - Too) -p~c(C - Coo) (2) Int. J. Heat ~t Fluid Flow 0142-727X/85/030149-1153.00@ 1985 Butterworth 0 Co (Publishers) Ltd 149