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MATHEMATICAL ANALYSIS OF LAMINAR COUNTERFLOW PARALLEL PLATE HEAT EXCHANGERS FOR LARGE PRANDTL AND PECLET NUMBERS

DOI: 10.1615/ICHMT.2008.CHT.1070
20 pages

Marcos Vera
Departmento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, 28911 Leganés, Spain

Amable Linan
Dept. de Motopropulsión y Termofluidodinámica, E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain

Abstrakt

Multilayered counterflow parallel plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, assumes that the Prandtl and Peclet numbers of the flow are both large compared to unity, as typically occurs for most non-metallic liquids in applications. For simplicity, a hydrodynamically developed laminar flow is considered, and longitudinal conduction is neglected both in the fluid and in the plates.
The theoretical model for the bulk fluid, based on an eigenfunction expansion procedure, is solved by means of standard symbolic algebra packages. This leads to analytic expressions for the eigenfunctions in terms of Whittaker functions, which can then be used to evaluate the eigenvalues numerically.
In a second step, we present an asymptotic analysis of the thermal entrance region that provides the temperature distribution near the inlet. According to the local, near-inlet, solution, the dimensionless temperature grows along the plate as ξj, where ξ is the dimensionless distance from the inlet section, and the exponent, 0 < j < 1/3, depends only on k = (A2/A1)1/312)1/3(k2/k1), a lumped parameter defined in terms of the ratios of the wall velocity gradients, Ai, thermal diffusivities, αi, and thermal conductivities, ki, of the fluids entering, i = 1, and exiting, i = 2, the heat exchanger. Closed-form analytical expressions for the exponent j are given, which, together with order of magnitude estimates, lead to accurate estimations of the maximum temperature gradient (and therefore thermal stress) experienced by the separating plate.
Fully numerical simulations performed using standard finite-difference methods show very good agreement with the analytical results obtained from the global and local analyses, both for the bulk fluid and plate temperatures. This suggests the possibility of using the analytical solutions presented here as a benchmark problem for computational heat transfer codes.

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