Two-time level finite-difference method for solving the downstream diffusion for flow between Parallel plates

Document Type : Original Article


1 Mechanical Power engineering department, Faculty of engineering, Ain Shams university

2 Math and Physics Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt


The heat transport equation for laminar flow between isothermal
parallel-plate channels in the entrance region is solved numerically. The
heat transport equation is solved using the rightward representation of
Barakat-Clark ADE method. The proposed numerical method uses the
two-time levels derivative to solve the unsteady term in the transport
equation. The unsteady term presented using two-time level derivative
at n and n+1 combined with backward derivative i and i-1. The heat
equation contains the unsteady term and the axial heat term. The heat
transfers within flow between two parallel plates. The results for the
local Nusselt number, the mean temperature, and thermal entry length is
shown. The analysis provides the temperature distribution considering
the axial heat conduction and the downstream diffusion. The results
show the effect of the upstream on the inlet temperature and ensure
the reliability of the proposed numerical method to solve the transport
equation including the unsteady term and the two-dimensional partial


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