Mixed convection flow in a vertical channel with temperature dependent viscosity and flow reversal: An exact solution

Mixed convection flow in a vertical channel with temperature dependent viscosity and flow reversal: An exact solution

Basant K. Jha Michael O. Oni 

Ahmadu Bello University, Zaria 810222, Nigeria

Corresponding Author Email: 
michaeloni29@yahoo.com
Page: 
607-613
|
DOI: 
https://doi.org/10.18280/ijht.360225
Received: 
23 October 2017
| |
Accepted: 
3 May 2018
| | Citation

OPEN ACCESS

Abstract: 

An exact solution of steady fully developed mixed convection flow of viscous, incompressible fluid in a vertical channel having temperature dependent viscosity with asymmetric wall heating is obtained in this article. The Reynold model is used to capture the variation of viscosity as an exponential function of temperature and the governing equations are solved analytically. The solutions obtained are graphical represented and the effects of viscosity variation parameter, mixed convection parameter and wall temperature difference ratio on fluid velocity and skin-friction are investigated. In addition, the condition for occurrence of reverse flow at the channel walls is also established. During the course of numerical computation, it is found that an increase in viscosity variation parameter increases both fluid velocity as well as skin-friction at the heated wall. Furthermore,] the magnitude of flow reversal increases with increase in viscosity variation parameter around the cold region while the role of wall temperature difference ratio is to minimize the occurrence of reverse flow.

Keywords: 

mixed convection,vertical channel, temperature dependent viscosity, flow reversal, exact solution

1. Introduction
2. Mathematical Analysis
3. Results and Discussion
4. Conclusions
Nomenclature
  References

[1] Lavine AS. (1988). Analysis of fully developed opposing mixed convection between inclined parallel plates. Warme-und Stoffubertragung. Springer, Berlin 23: 249-257. 

[2] Lavine AS. (1993). On the linear stability of mixed and free convection between inclined parallel plates with fixed heat flux boundary conditions. Int. J. Heat Mass Transfer 1373-1387.

[3] Tao LN. (1991). On combined free and forced convection in channels. ASME Journal of Heat Transfer 82: 233–8.

[4] Hamadah TT, Wirtz RA. (1991). Analysis of laminar fully developed mixed convection in a vertical channel with opposing buoyancy. ASME Journal of Heat Transfer 113: 507-10.

[5] Barletta A. (1998). Laminar mixed convection with viscous dissipation in a vertical channel. Int. J. Heat Mass Transfer 41: 3501-3513.

[6] Lin HT, Wu KY, Hoh HL. (1993). Mixed convection from an isothermal horizontal plate moving in parallel or reversely to a free stream. Internat. J. Heat Mass Transfer 36:3547–3554.

[7] Herwig H, Wicken G. (1986). The effect of variable properties on laminar boundary layer flow. Warme-und Stof-Fubertrag 20: 47–57.

[8] Jha BK, Babatunde A. (2016). Steady fully developed natural convection flow in a vertical annular microchannel having temperature dependent viscosity: An exact solution. Alexandria Eng. J. 55(2): 951-958. http://dx.doi.org/10.1016/j.aej.2016.02.023

[9] Shome B, Jensen M.K. (1995). Mixed convection laminar flow and heat transfer of liquids in isothermal horizontal circular ducts. Int. J. Heat Mass Transfer 38: 1945-1956. 

[10] Makinde OD, Chinyoka T. (2012). Analysis of unsteady flow of a variable viscosity reactive fluid in a slit with wall suction or injection J. Petrol. Sci. Eng. 94(95): 1-11. 

[11] Hossain MA, Munir MS. (2000). Mixed convection flow from a vertical flat plate with temperature dependent viscosity. Internat. J. Thermal.Sci. 39: 173-183.

[12] Klemp K, Herwig H, Selmann M. (1990).  Entrance flow in channel with temperature dependent viscosity including viscous dissipation effects. Int. Proceedings of the Third International Congress of Fluid Mechanics. Cairo, Egypt 3: 1257-1266.

[13] Kumari M. (2001). Variable viscosity effects on free and mixed convection boundary-layer flow from a horizontal surface in a saturated porous medium – variable heat flux. Mech. Res. Commun. 28: 339–348.

[14] Umavathi JC, Ojjela O. (2015). Effect of variable viscosity on free convection in a vertical rectangular duct. Int. J. Heat Mass Transf. 84: 1-15.

[15] Hady FM, Bakier AY, Gorla RSR. (1996).  Mixed convection boundary layer flow on a continuous flat plate with variable viscosity. Heat Mass Transf. 31: 169-172.

[16] Mahmud MAA. (2007). A note on variable viscosity and chemical reaction effects on mixed convection heat and mass transfer along a semi-infinite vertical plate. Math. Probab. Eng. http://dx.doi.org/1155/2007/41323 

[17] Pop I, Gorla RSR, Rashidi M. (1992). The effect of variable viscosity on flow and heat transfer to a continuous moving flat plate. Internat. J. Engrg. Sci. 30 (1): 1-6.

[18] Elbashbeshy EMA, Bazid MA.A. (2000). The effect of temperature dependent viscosity on heat transfer over a continuous moving surface. J. Phys. D: Appl. Phys. 33: 2716-2721.

[19] Ling JX, Dybbs A. (1987). Forced convection over a flat plate submersed in a porous medium: Variable viscosity case, ASME Paper 87-WA/HT-23. ASME Winter Annual Meeting, Boston, Massachusetts, pp. 13-18.

[20] Jha BK, Oni MO, Aina B. (2016). Steady fully developed mixed convection flow in a vertical micro-concentric-annulus with heat generating/absorbing fluid: an exact solution. Ain Shams Engineering Journal http://dx.doi.org/ 10.1016/j.asej.2016.08.005

[21] Liepsch DW. (1990). Effect of blood flow parameters on flow patterns at arterial bifurcations- studies in models. In blood flow in large arteries: Applications to atherogenesis and clinical medicine (ed. Liepsch D.W.), pp. 63-76. Basel, Switzerland: Karger.

[22] Kazakidi A, Plata AM, Sherwin SJ, Weinberg PD. (2011). Effect of reverse flow on the pattern of wall shear stress near arterial branches. J. R. Soc. Interface 8: 1594-1603. http://dx.doi.org/10.1098/rsif.2011.0108

[23] Sparrow EM., Chrysler GM, Azevedo LF. (1984). Observed flow reversal and measured-predicted Nusselt numbers for natural convection in one-sided heated vertical channel. ASME Journal of Heat Transfer 106(2): 325-332.

[24] Ostrach S. (1954).  Combined natural and forced convection laminar flow heat transfer of fluids with and without heat sources in channels with nearly varying wall temperatures. NACA TN 3141.

[25] Leitzke AF. (1954).  Theoretical and experimental investigation of heat transfer by laminar natural convection between parallel plates. NACA report 1223.

[26] Cebeci T, Khattab AA, LaMont R. (1982).  Combined natural and forced convection in vertical ducts. Heat Transfer 82, Proceedings of 7th international Heat Transfer Conference, Munich, West Germany 2: 419-424.

[27] Aung W, Worku G. (1986). Developing flow and flow reversal in mixed convection in a vertical channel with asymmetric wall temperatures. J. Heat Transfer 108: 485-488.

[28] Aung W, Worku G. (1986). Theory of fully developed, combined convection including flow reversal. J. Heat Transfer 108: 299-307.

[29] Prasad KV, Vajravelu K, Vaidya H, Raju B.T. (2015). Heat transfer in a non-newtonian nanofluid film over a stretching surface. Journal of Nanofluids 4(4): 536-547(12).

[30] Oni MO. (2017). Combined effect source, porosity and thermal radiation on mixed convection flow in a vertical annulus: An exact solution. Engineering Science and Technology, an International Journal 20: 518-527. 

[31] Prasad KV, Mallikarjun P, Vaidya H. (2017). Mixed convective fully developed flow in a vertical channel in the presence of thermal radiation and viscous dissipation. Int. J. of Applied Mechanics and Engineering 22(1): 123-144. http://dx.doi.org/10.1515/ijame-2017

[32] Prasad KV, Vaidya H, Vajravelu K. (2015). MHD mixed convection heat transfer in a vertical channel with temperature-dependent transport properties. Journal of Applied Fluid Mechanics 8(4): 693-701.

[33] Reynolds O. (1886). Phil Trans Royal. Soc. London, pp. 177: 157.

[34] Syeda HT, Shohel M. (2002). Entropy generation in a vertical concentric channel with temperature dependent viscosity. Int. Commun. Heat Mass Transf. 29: 907-918.