Spreadsheet numerical simulation for developing laminar free convection between vertical parallel plates

Abstract

A detailed spreadsheet simulation for laminar free convection with simultaneously thermally and hydrodynamically developing boundary layer in the entrance region between two vertical parallel plates is presented. The boundary layer governing equations are expressed in an implicit finite difference form. This results in sets of algebraic equations. These sets of algebraic equations are solved simultaneously using a non-iterative scheme. Spreadsheet setup for the developing fluid and heat flow problems, the powerful abilities of the spreadsheet and macro creation for automated solutions are emphasized. Plots of the results are presented using the spreadsheet-built-in powerful graphical facilities. The spreadsheet simulation results are compared with presently obtained results for the same problem via a FORTRAN code. Moreover, the numerically obtained developing axial velocity and temperature profiles at large distance downstream the entrance, for high enough channels, show excellent agreement with the available fully-developed analytical profiles. Flow and heat transfer parameters such as the channel height required to naturally induce a specific flow rate, the local and averaged Nusselt number and the amount of heat absorbed by the fluid through the channel have been calculated for a fluid of Pr=0.7, air, under two types of thermal boundary conditions. These boundary conditions are namely boundary conditions of the first and third kind.