An accurate numerical method for systems of differentio-integral equations associated with multiphase flow

Abstract

A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method, it solves the problem of systems of differential equations involving integral operators not previously considered by the Keller Box method. Two main preparatory stages are required: (i) a merging procedure for differential equations and conditions without integral operators and; (ii) a reduction procedure for differential equations and conditions with integral operators. The differencing processes are effectively simplified by means of the unit-step function. The nonlinear difference equations are solved by Newton method using an efficient block arrow-like matrix factorization technique. As an example of the application of this method, the systems of equations for combined gravity body force and forced convection in laminar film condensation can be solved for prescribed values of physical constants.

References in corpus (6)

• On thermal boundary layers on a flat plate subjected to a variable heat flux
• Thermal interaction between free convection and forced convection along a vertical conducting wall
• Mixed-convection laminar film condensation on a semi-infinite vertical plate
• Inclined wall plumes in porous media
• Heat transfer in the flow of a cold, two-dimensional draining sheet over a hot, horizontal cylinder
• Heat transfer in the flow of a cold, axisymmetric jet over a hot sphere

Cited by in corpus (11)

• On thermal boundary layers on a flat plate subjected to a variable heat flux
• Thermal interaction between free convection and forced convection along a vertical conducting wall
• Mixed-convection laminar film condensation on a semi-infinite vertical plate
• Heat transfer in the flow of a cold, two-dimensional draining sheet over a hot, horizontal cylinder
• Microwave probe sensing location for Venturi-based real-time multiphase flowmeter
• Heat transfer in the flow of a cold, axisymmetric vertical liquid jet against a hot, horizontal plate
• Heat transfer in the flow of a cold, axisymmetric jet over a hot sphere
• Influence of design parameters of upstream Venturi pipeline on multiphase flow measurement
• Laminar film condensation heat transfer on a vertical, non-isothermal, semi-infinite plate
• Dual solutions for opposing mixed convection in porous media
• Scaling rules for multiphase flow in vertical Venturis