×

High Péclet number heat exchange between cocurrent streams. (English) Zbl 0994.76025

Summary: This paper analyses the heat transfer between two cocurrent laminar flows in parallel channels. For high values of Peclét number \(Pe\), a boundary layer arises near the wall separating the streams. Matched asymptotic expansions are used to obtain approximate solutions. We consider arbitrary inlet temperatures and derive higher-order corrections of boundary value problem. The separating wall is supposed to be sufficiently thin to neglect the heat conduction in it. Analyticity and adiabatic conditions at the outer walls impose restrictions on the inlet temperatures. It turns out, however, that only the inlet temperatures at the wall separating the two fluids enter the leading-order problem. The Nusselt numbers thus calculated are in the leading order proportional to \((Pe/x)^{1/3}\), where \(x\) is the stream-wise coordinate. We obtain an estimate of the thickness of separating wall to validate the matched asymptotic expansions. It is also demonstrated that the asymptotic analysis is unable to describe the heat exchange of counterflowing fluids.

MSC:

76D99 Incompressible viscous fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
80M35 Asymptotic analysis for problems in thermodynamics and heat transfer
PDFBibTeX XMLCite
Full Text: DOI