A finite-difference procedure, is employed to predict the turbulent flow and heat transfer in horizontal, inclined and vertical pipes when influenced by buoyancy. The flow is treated as parabolic; and the turbulence model used involves the solution of two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate. Results are presented for the velocity and temperature fields, and the associated flow-resistance and heat-transfer coefficients. The predictions for horizontal and vertical pipes have been compared with the available experimental results, and the agreement obtained is good.

This paper is concerned with the prediction of three-dimensional turbulent flows around bodies of arbitrary shape, with particular emphasis on a ship's hull. Two solution methods are compared employing a non-orthogonal coordinate system, in which the surface of the body is arranged to coincide with a coordinate surface. The velocity components are solved for the axial, radial and circumferential components in the cylindrical-polar system from which the non-orthogonal coordinates are derived. The partial-differential equations governing the flows under consideration are solved by two finite-difference methods for three-dimensional, parabolic1and partially-parabolic2flows. Turbulence is accounted for through a two-equation model of turbulence developed by Harlow and Nakayama3and modelled by Launder and Spalding.4Solutions are presented for flow around a ship's hull which demonstrate the potential of the present methods.