Linearization of Natural Convection From a Vertical Plate With Arbitrary Heat-Flux Distributions

A simple model is developed to predict the heat transfer characteristics of a vertical plate with arbitrarily prescribed surface heat-flux variations under a buoyancy-driven flow. The analysis is based on the linearized approximations to the boundary layer form of the conservation equations. Explicit, closed-form solutions for the surface temperature of the plate and fluid temperature distributions are obtained for the full range of Prandtl numbers. Surface heat-flux variations of discontinuous as well as continuous types are examined, and the results are compared with air data obtained by using various solution methods including numerical simulations. It is shown that the present predictions are in excellent agreement with those of other methods that are capable of producing exact solutions.