Convective heat transfer for a gaseous slip flow in micropipe and parallel-plate microchannel with uniform wall heat flux: effect of axial heat conduction

Thermally developing laminar slip flow through a micropipe and a parallel plate microchannel, with axial heat conduction and uniform wall heat flux, is studied analytically by using a powerful method of self-adjoint formalism. This method results from a decomposition of the elliptic energy equation...

Full description

Saved in:
Bibliographic Details
Published in:Indian journal of physics 2018-06, Vol.92 (6), p.741-755
Main Authors: Haddout, Y., Essaghir, E., Oubarra, A., Lahjomri, J.
Format: Article
Language:English
Subjects:
Astrophysics and Astroparticles
Computational fluid dynamics
Conduction heating
Conductive heat transfer
Convective heat transfer
Decomposition
Fluid flow
Heat flux
Laminar flow
Mathematical analysis
Mathematical models
Original Paper
Partial differential equations
Physics
Physics and Astronomy
Rarefaction
Slip flow
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Thermally developing laminar slip flow through a micropipe and a parallel plate microchannel, with axial heat conduction and uniform wall heat flux, is studied analytically by using a powerful method of self-adjoint formalism. This method results from a decomposition of the elliptic energy equation into a system of two first-order partial differential equations. The advantage of this method over other methods, resides in the fact that the decomposition procedure leads to a selfadjoint problem although the initial problem is apparently not a self-adjoint one. The solution is an extension of prior studies and considers a first order slip model boundary conditions at the fluid-wall interface. The analytical expressions for the developing temperature and local Nusselt number in the thermal entrance region are obtained in the general case. Therefore, the solution obtained could be extended easily to any hydrodynamically developed flow and arbitrary heat flux distribution. The analytical results obtained are compared for select simplified cases with available numerical calculations and they both agree. The results show that the heat transfer characteristics of flow in the thermal entrance region are strongly influenced by the axial heat conduction and rarefaction effects which are respectively characterized by Péclet and Knudsen numbers.
ISSN:0973-1458
0974-9845
DOI:10.1007/s12648-017-1154-4