Heat Transfer of Gas Flow through Microchannels using Extended Navier–Stokes Equations

Abstract

In this paper, the temperature profile of hydrodynamically fully developed, laminar, nonisothermal, and incompressible gas flow through rectangular microchannels is modelled using Extended Navier–Stokes Equation (ENSE). A semianalytic solution is obtained for the proposed model in its total velocity form, using integral transform technique. Further, the relation between Nusselt number, Knudsen number, and Prandtl number under various aspect ratios was analysed. The results obtained show excellent agreement with existing measurements.

Keywords:

• Extended Navier–Stokes equation
• Integral transform technique
• Rectangular microflow
• Slip flow region

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

R. Deena

R Deena is currently working as an assistant professor (SG) in the department of Mathematics, PSG College of Technology, Coimbatore. She has 15 years of teaching experience. Her research interest is fluid dynamics–heat transfer. She is a life member in ISTE. She handles Mathematics courses for both BE and ME programmes. She is currently working in heat transfer in microchannels using nanofluids. Corresponding author. Email: e-mail: [email protected].

G. Sai Sundara Krishnan

G Sai Sundara Krishnan is a professor in the department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore. He has more than 23 years of teaching experience. His research focuses on digital topology, algebraic topology and fluid dynamics. He has guided 4 PhDs and is currently supervising more than 8 research scholars, under Anna University, Chennai, in the fields of topology, fluid dynamics and soft set theory. he is the programme coordinator of MSc Applied Mathematics Programme. Email: [email protected]