Semianalytical methods for heat and fluid flow between two parallel plates

Year 2015, Volume: 1 Issue: 3, 175 - 181, 01.03.2015

Balaram Kundu

https://doi.org/10.18186/jte.12495

Cited By: 4

Abstract

The present study attempts to investigate the effects the the viscous distribution in the conduction limit for both hydrodynamically and thermally fully developed, laminar flow of Newtonian fluid between two asymmetrically heated infinitely long parallel plates. Utilizing the assumptions routinely employed in the literature, we devise here a semi-analytical formalism to investigate the temperature distribution for two different flow configurations, i.e., the poiseuille flow and the simple shear driven flow. In the analysis, we give focus to the viscous dissipative effect arises because of the two individual aspects in case of shear-driven flow: the shear heating produced by the movable upper plate along with fluid friction, while only due to the internal fluid friction in case of Poiseuille flow. Finally, we show the variation of velocity and the temperature distribution in the flow field for several nondimensional parameters as emerge in the present study, and highlight their individual role in delineating the temperature distribution in the flow field, which essentially alters transient thermal transport characteristics of heat in different cases of flow dynamics

Keywords

Semianalytical, Temperature distribution, Transient, Velocity distribution

Semianalytical methods for heat and fluid flow between two parallel plates

Abstract

Keywords

-

References

• M. Gad-el-Hak, The fluid mechanics of micro-devices - The Freeeman Scholar Lecture, J. Fluids Eng., Vol. 121, pp. 5 – 33, 1999. [2] H.C. Brinkman, Heat effects in capillary flow I, Appl. Sci. Res., Vol. A2, pp. 120 – 124, 1951.
• K.C. Cheng, R..-S. Wu, Viscous dissipation effects on convective instability and heat transfer in plane Poiseuille flow heated from below, Appl. Sci. Res., Vol. 32, pp. 327 – 346, 1976.
• F.T. Pinho, P.J. Oliveira, Analysis of forced convection in pipes and channels with the simplified Phan-Thien- Tanner fluid, Int. J. Heat Mass Transf., Vol. 43, pp. 227– 2287, 2000.
• J. Lahjomri, K. Zniber, A.A. Oubarra, Heat transfer by laminar Hartmann’s flow in the thermal entrance-region with uniform wall heat-flux: the Graetz problem extended, Energy Convers. Manag, Vol. 44, pp. 11 – 34, 2003.
• D.A. Nield, A.V. Kuznetzov, M. Xiong, Thermally developing forced convection in a porous medium: parallel-plate channel with walls at a uniform temperature, with axial conduction and viscous- dissipation effects, Int. J. Heat Mass Transf., Vol. 46, pp. 643 – 651, 2003.
• H.M. Duwairi, B. Tashtoush, R.A. Damseh, On heat transfer effects of a viscous fluid squeezed and extruded between two parallel plates, Heat Mass Transfer, Heat Mass Transfer, Vol. 41, pp. 112 – 117, 2004.
• J.M. White, S.J. Muller, Viscous heating and the stability of Newtonian and Viscoelastic Taylor-Couette flows, Physical Review Letters., Vol. 84, pp. 5130 – 5133, 2000.
• O. Aydin, Effects of viscous dissipation on the heat transfer in a forced pipe, Part 1. Both hydrodynamically and thermally developed flow, Energy Conversion and Management, Vol. 46, pp. 757 – 769, 2005.
• O. Aydin, Effects of viscous dissipation on the heat transfer in a forced pipe flow, Part 2, Thermally developing flow, Energy Conversion and Management, Vol. 46, pp. 3091 – 3102, 2005.
• O. Aydin, M. Avci, Viscous-dissipation effects on the heat transfer in a Poiseuille flow, Applied Energy, Vol. 83, pp. 495 – 512, 2006.
• O. Aydin, M. Avci, Viscous-dissipation effects on the heat transfer in a Couette-Poiseuille flow between parallel plates, Applied Energy, Vol. 83, pp. 856 – 867, 2006.
• J. Sheela-Francisca, C.P. Tso, Viscous dissipation effects on parallel plates with constant heat flux boundary condition, Int. Commun. Heat Mass Transf., Vol. 36, pp. 249 – 254, 2009.
• J.L. Hudson, S.G. Bankoff, Heat transfer to steady coquette flow with pressure gradient, J. Chemical Engineering Science, Vol. 20, pp. 415 – 254, 1965.
• J. Sestak, F. Rieger, Laminar heat transfer to a steady couette flow between parallel plates, Int. J. Heat Mass Transf., Vol. 12, pp. 71 – 80, 1969.
• B. Kundu, K.-S. Lee, A Non-Fourier Analysis for Transmitting Heat in Fins with Internal Heat Generation, International Journal of Heat and Mass Transfer, Vol. 64, pp. 1153–1162, 2013.
• B. Kundu, K.-S. Lee, Fourier and non-Fourier heat conduction analysis in the absorber plates of a flat-plate solar collector, Solar Energy, Vol. 86, No. 10, pp. 3030– 3039, 2012.
• B. Kundu, K.S. Lee, Analytic solution for heat transfer of wet fins on account of all nonlinearity effects, Energy, Vol. 41, No. 1, pp. 354–367, 2012.
• B. Kundu, S. Wongwises, A decomposition analysis on convecting–radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient, Journal of the Franklin Institute, Vol. 349, No. 3, pp. 966–984, 2012.
• B. Kundu, G.K. Ghosh, An approximate analytical prediction about thermal performance and optimum design of pin fins subject to condensation of saturated steam flowing under forced convection, International Journal of Refrigeration, Vol. 32, No. 5, pp. 809–825, 2009.
• B. Kundu, P.K. Das, Performance and optimum design analysis of convective fin arrays attached to flat and curved primary surfaces, International Journal of Refrigeration, Vol. 32, No. 3, pp. 430–443, 2009