Abstract
This work is devoted to the determination of the analytical solution of the problem of the laminar forced convection of the Jeffery-Hamel slip flow through a convergent microchannel. The analytical solution is obtained by using a self-adjoint formalism of the functional analysis. The solution represents an extension of the solution obtained in the conventional continuum flow by considering the boundaries slip conditions at the wall and the streamwise heat conduction. This extension has been done by using a new matrix operator of three dimensions in the Hilbert space. The results show that the thermal characteristics are strongly influenced by the Reynolds, Prandtl and Knudsen numbers, the aperture angle of the channel and the streamwise heat conduction.
Highlights
The study of laminar forced convection of the Jeffery-Hamel slip flow through a convergent microchannel is of fundamental and practical importance
This slip velocity and temperature jump are related to the Knudsen Kn number, which plays an important role at a microscale due to the interaction between molecules and the wall
For large value of angle (ψ = 20°) and for a given Kn, the uniform temperature profile for each curve is established for a negative axial distance in the upstream section very far from the entrance, indicating that the temperature field in the microchannel is very affected by the effect of streamwise heat conduction
Summary
The study of laminar forced convection of the Jeffery-Hamel slip flow through a convergent microchannel is of fundamental and practical importance This type of flow is often applied in industrial processes using forced convection heat transfer, such as cooling of microelectronic components, micro-heat exchanger design and chemical engineering. This work presents an analytical solution to the problem of forced convection and the development of the temperature field in the thermal entrance region of the Jeffrey-Hamel convergent microchannel in a rarefied environment. This approach is based on a powerful method of self-adjoint formalism. The effects of different dimensionless parameters used in this problem, such as Reynolds, Prandtl and Knudsen numbers and the channel aperture angle, on hydrodynamic and thermal characteristics are quantified and analyzed in the slip flow interval range 10−3 ≤ Kn ≤ 10−1
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