Steady fully developed mixed convection flow in a vertical parallel plate microchannel with bilateral heating and filled with porous material

Abstract

This study investigated analytically the hydrodynamic and thermal behaviour of a fully developed laminar, viscous, incompressible fluid in a vertical parallel plate microchannel taking into account the velocity slip and thermal jump at the walls. The governing equations are expressed in a dimensionless form using the dimensionless quantities. The method of undetermined coefficient was employed to obtain the closed-form expression for velocity, which is used to determine the skin friction. The solution obtained is then presented graphically and the results are discussed for various dimensionless parameters entering the problem. During the course of investigation, it is found that the critical values of the mixed convection parameter Gre (which is the ratio of the Grashof number Gr to the Reynolds number Re) led to flow reversal decrease with increase in Darcy number, while it increases with increase in Knudsen number Kn. Also, the Nusselt number Nu is found to increase with increasing Darcy number.

Keywords

Microfluidics vertical microchannel mixed convection temperature jump velocity slip Darcy number

Get full access to this article

View all access options for this article.

References

Tai

. Micro-mechanical systems (MEMS) and fluid flows. Annu Rev Fluid Mech 1998; 30: 579–612.

Palm

. Heat transfer in microchannels. Microscale Thermophys Eng 2001; 5: 155–175.

Sobhan

Garimella

. A comparative analysis of studies on heat transfer and fluid flow in microchannels. Microscale Thermophys Eng 2001; 5: 293–311.

Obot

. Toward a better understanding of friction and heat/mass transfer in microchannels – a literature review. Microscale Thermophys Eng 2002; 6: 153–173.

Rostami

Saniel

Mujumdar

. Liquid flow and heat transfer in microhannels: a review. Heat Technol 2000; 18: 59–68.

Rostami

Mujumdar

Saniel

. Flow and heat transfer for gas flowing in microchannels: a review. Heat Mass Transfer 2002; 38: 359–367.

Gad-el-Hak

. Flow physics in MEMS. Mech Ind 2001; 2: 313–341.

Guo

. Size effect on microscale single-phase flow and heat transfer. Int J Heat Mass Transfer 2003; 46: 59–149.

Guo

. Size effect on single-phase channel flow and heat transfer at microscale. Int J Heat Fluid Flow 2003; 24: 284–298.

10.

Morini

. Single-phase convective heat transfer in microchannel: a review of experimental results. Int J Therm Sci 2004; 43: 631–651.

11.

Aydin

Avci

. Thermally developing flow in microchannels. J Thermophys Heat Transfer 2006; 20: 628–632.

12.

Aydin

Avci

. Heat and fluid flow characteristics of gas in micropipes. Int J Heat Mass Transfer 2006; 49: 1723–1730.

13.

Avci

Aydin

. Analysis of micro-Graetz problem in a microtube. Nanoscale Microscale Thermophys Eng 2006; 10: 345–358.

14.

Avci

Aydin

. Analysis of laminar heat transfer in micro-Poiseuille flow. Int J Therm Sci 2007; 46: 30–37.

15.

Chen

Weng

. Natural convection in a vertical microchannel. J Heat Transfer 2005; 127: 1053–1056.

16.

Khadrawi

Othman

Al-Nimr

. Transient free convection fluid flow in a vertical microchannel as described by the hyperbolic heat conduction model. Int J Thermophys 2005; 26(3): 905–918.

17.

Avci

Aydin

. Mixed convection in a vertical parallel plate microchannel. Trans ASME, J Heat Transfer 2007; 129: 162–166.

18.

Eckert

ERG

Drake

. Analysis of heat and mass transfer , New York: McGraw- Hill, 1972.

19.

Oosthuizen

Naylor

. Introduction to convective heat transfer analysis , New York: McGraw-Hill, 1999; 158–167.