Showing papers by "Suhas V. Patankar published in 1978"

A new finite-difference scheme for parabolic differential equations

Abstract: Finite-difference methods for unsteady heat conduction are considered. It is shown that the Crank-Nicolson scheme, although unconditionally stable in the mathematical sense, produces physically unrealistic solutions when the time step is large. The fully implicit scheme shows more satisfactory behavior, but is less accurate for small time steps. A new scheme is presented that is satisfactory for the entire range of time steps. It is also shown how the scheme can be applied to boundary-layer situations. The performance of the new scheme is demonstrated by its application to a heat conduction problem and a boundary-layer problem

Development of wall and free plumes above a heated vertical plate

Abstract: An analysis has been made to determine the successive stages of development as the natural convection boundary layer on a steadily heated vertical plate evolves into a plume. Both the wall plume and the free plume are investigated. The wall plume develops along an adiabatic wall which is the vertical extension of the heated plate. The free plume is created as the boundary layer streams away from the upper edge of the plate. Since the plate is heated on only one of its faces, the free plume is initially unsymmetric. The development of these plumes does not admit similarity-type boundary layer solutions, and numerical techniques were, therefore, employed, with results being obtained for Prandtl numbers of 0.7, 2, 5, and 10. It was found that at sufficient downstream distances both plumes attain their respective fully developed behaviors (i.e., similar profiles at successive streamwise stations). For the wall plume, the development for all Prandtl numbers is completed at a position that is about five plate lengths above the leading edge of the heated plate. The development length for the free plume for Pr = 0.7 is about the same as that for the wall plume, but about 30 plate lengths are required for the development of the free plume when Pr = 10. The fully developed free plume is symmetric.

Laminar heat transfer in a pipe subjected to a circumferentially varying external heat transfer coefficient

Abstract: Numerical techniques have been used to solve the thermally developed regime for a laminar pipe flow that exchanges heat with a fluid environment in the presence of a circumferentiatly varying external heat transfer coefficient. By making use of the fact that the temperature distributions have similar shapes at successive streamwise locations, the three-dimensional temperature field was scaled to two dimensions. The resulting Two-dimensional eigenvalue problem was solved by a rapidly converging automated scheme that successively refines an initial guess. Solutions were obtained for two circumferential distributions of the external heat transfer coefficient respectively intended to model forced and natural convection cross flows. The circumferential average heat transfer coefficient was found to be quite insensitive to the imposed circumferential variations. The local wall heat flux is nearly circumferentially uniform when the mean value of the external coefficient is high. On the other hand, at low mean va...