Heat Transfer Handbook part 55. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 532 NATURAL CONVECTION 1 Pr where Gr is the Grashof number based on a characteristic length L and Pr is the Prandtl number. These are defined as Gr Tm Pr a where v is the kinematic viscosity and a the thermal diffusivity of the fluid. These dimensionless parameters are important in characterizing the flow as discussed in the next section. The resulting boundary layer equations for a two-dimensional vertical flow with variable fluid properties except density for which the Boussinesq approximations are used are then written as Jaluria 1980 Gebhart et al. 1988 du dv dx dy du du dx dy gß T - Tœ 1 d L P dy dy PCp dx dy dy y dy j dx dy where the last two terms in the energy equation are the dominant terms from pressure work and viscous dissipation effects. Here u and v are the velocity components in the x and y directions respectively. Although these equations are written for a vertical two-dimensional flow similar approximations can be employed for many other flow circumstances such as axisymmetric flow over a vertical cylinder and the wake above a concentrated heat source. There are several other approximations that are commonly employed in the analysis of natural convection flows. The fluid properties except density for which the Boussinesq approximations are generally employed are often taken as constant. The viscous dissipation and pressure work terms are generally small and can be neglected. However the importance of various terms can be best considered by nondimension-alizing the governing equations and the boundary conditions as outlined next. Dimensionless Parameters To generalize the natural convection transport processes a study of the basic nondimensional parameters must be carried out. These parameters are important not only in simplifying the governing equations and the analysis but also in guiding experiments that may be carried out to obtain desired information on the process and in the presentation of the data for use in .
