A novel approach in integral solution of laminar natural convection induced by a line heat (original) (raw)

Linan and Kurdymov [6] studied numerically the laminar free convection induced by a line heat source at small Grashof numbers, using the Boussinesq equations, in stream function-vorticity (ω − ψ) variables. Wang et al. [7] studied the transient laminar natural convection from horizontal cylinders, and they used the (ω − ψ) equations. Ayani et al. [8] investigate the effect of radiation on laminar natural convection induced by a line heat source and concluded a considerable departure from the Boussinesq-based solution and from the boundary layer results. All the additional equations applied in the analytical solutions are strongly dependent to experimental data and some simplifying assumptions. In this paper, the additional equation is based on the physics of the flow obtained using the governing equations of the phenomena. In addition, no more simplifying assumptions are applied. Governing Equations Laminar natural convection flow from a horizontal line heat source, figure 1, assuming the end effects of the source, is negligible, is governed by continuity equation, the two-dimensional Navier-Stocks equations using Boussinesq approximation and the energy equation [3]. Figure 1. Problem under consideration Based on the physical configuration shown in Figure 1, the governing equations in the Cartesian coordinate system take the following form :