Laminar Counterflow Parallel-Plate Heat Exchangers: Exact and Approximate Solutions Articles uri icon

publication date

  • October 2010

start page

  • 4885

end page

  • 4898

issue

  • 21-22

volume

  • 53

international standard serial number (ISSN)

  • 0017-9310

electronic international standard serial number (EISSN)

  • 1879-2189

abstract

  • Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and
    neglects longitudinal conduction both in the fluid and in the plates.
    The solution for the temperature field involves eigenfunction expansions
    that can be solved in terms of Whittaker functions using standard
    symbolic algebra packages, leading to analytical expressions that
    provide the eigenvalues numerically. It is seen that the approximate
    solution obtained by retaining the first two modes in the eigenfunction
    expansion provides an accurate representation for the temperature away
    from the entrance regions, specially for long heat exchangers, thereby
    enabling simplified expressions for the wall and bulk temperatures,
    local heat-transfer rate, overall heat-transfer coefficient, and outlet
    bulk temperatures. The agreement between the numerical and theoretical
    results suggests the possibility of using the analytical solutions
    presented herein as benchmark problems for computational heat-transfer
    codes.