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The NAPPLE algorithm for incompressible viscous flow on Cartesian grid system is extended to nonorthogonal curvilinear grid system in this paper. A pressure-linked equation is obtained by substituting the discretized momentum equations into the discretized continuity equation. Instead of employing a velocity interpolation such as pressure-weighted interpolation method (PWIM), a particular approximation is adopted to circumvent the checkerboard error such that the solution does not depend on the under-relaxation factor. This is a distinctive feature of the present method. Furthermore, the pressure is directly solved from the pressure-linked equation without recourse to a pressure-correction equation. In the use of the NAPPLE algorithm, solving the pressure-linked equation is as simple as solving a heat conduction equation. Through two well-documented examples, performance of the NAPPLE algorithm is validated for both buoyancy-driven and pressure-driven flows.

In this paper, the integration scheme is employed to solve a coupling problem of transient heat conduction and displacement due to thermal deformation. Based on the resulting displacement, gap or contact pressure on the interface of two thermoelastic bodies in imperfect contact is estimated. Such information is then used to determine the interfacial heat transfer between the two thermoelastic bodies. This again affects the temperature distribution and thus the thermal deformation. In the course of heat transfer and thermal deformation, effect of thermal rectification also is taken into account. Numerical solutions of transient and steady-state quantities including gap formation, normal stress, and temperature are demonstrated for a pair of stainless steel and aluminum with conforming shapes. Such an analysis of conduction-deformation interaction based on a finite-difference-like scheme has not been studied in the past.

Mixed convection along vertical cylinders and needles with uniform surface heat flux is investigated for the entire mixed convection regime. A single modified buoyancy parameter {chi} and a single curvature parameter {Lambda} are employed in the analysis such that a smooth transition from pure forced convection ({chi} = 1) to pure free convection ({chi} = 0) can be accomplished. For large values of the curvature parameter and/or Prandtl number, the governing transformed equations become stiff. Thus, a numerically stable finite-difference method is employed in the numerical solution in conjunction with the cubic spline interpolation scheme to overcome the difficulties that arise from the stiffness of the equations. Local Nusselt numbers are presented for 0.1 {le} Pr {le} 100 that cover 0 {le} {chi} {le} 1 ({infinity} {ge} {Omega}{sub x} {ge} 0) and 0 {le} {Lambda} {le} 50. For needles ({Lambda} {ge} 5), the local Nusselt numbers (Nu{sub x}/Re{sub x}{sup 1/2} + Gr{sub x}{sup 1/5}*) are found to be nearly independent of the buoyancy parameter {chi}. Correlation equations for the local Nusselt numbers are also presented.