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The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.
Rocznik
Tom
Strony
123--144
Opis fizyczny
Bibliogr. 25 poz., tab., wykr.
Twórcy
autor
- Department of Mathematics, VSK University Vinayaka Nagar, Ballari-583 104, Karnataka, INDIA
autor
- Department of Studies and Research in Mathematics Tumkur University Tumkur, 572 103, INDIA
autor
- Department of Mathematics SSA Government First Grade College Ballari -583 101, Karnataka, INDIA
Bibliografia
- [1] Aung W. and Worku G. (1986): Theory of fully developed combined convection including flow reversal. – ASME J. of Heat and Transfer, vol.108, pp.485-488.
- [2] Zanchini E. (1998): Effect of viscous dissipation on mixed convection in a vertical channel with boundary conditions of the third kind. – Int. J. of Heat and Mass Transfer, vol.41, pp.3949-3959.
- [3] Barletta A. (1998): Laminar mixed convection with viscous dissipation in a vertical channel. – Int. J. Heat and Mass Transfer, vol.41, pp.3501-3513.
- [4] Boulama K. and Galanis N. (2004): Analytical solution for fully developed mixed convection between paralel vertical plates with heat and mass transfer. – J. of Heat Transfer, vol.126, pp.381-388.
- [5] Barletta A., Magyari E. and Keller B. (2005): Dual mixed convection flows in a vertical channel. – Int. J. of Heat and Mass Transfer, vol.48, pp.4835-4845.
- [6] Prasad K.V., Vaidya H. and Vajravelu K. (2015): MHD mixed convection heat transfer in a vertical channel with temperature-dependent transport properties. – Journal of Applied Fluid Mechanics, vol.8, No.4, pp.693-701.
- [7] Raptis A. (2001): Radiation and flow through a porous medium. – J. of Porous Media, vol.4, pp.271-273.
- [8] Bakier A.Y. (2001): Thermal radiation effects on mixed convection from vertical surfaces in saturated porous media. – Int. Comm. of Heat and Mass Transfer, vol.28, pp.243-248.
- [9] Raptis A. and Perdikis C. (2004): Unsteady flow through a highly porous medium in the presence of radiation. – Transport Porous Media, vol.57, pp.171-179.
- [10] Grosan T. and Pop I. (2007): Thermal radiation effect on fully developed mixed convection flow in a vertical channel. – Technische Mechanik, vol.27, pp.37-47.
- [11] Bég O.A., Zeuco J., Takhar H.S. and Bég T.A. (2008): Network numerical simulation of impulsively – started transient radiation-convection heat and mass transfer in a saturated Darcy-Forchheimer porous medium. – Non Linear Analysis: Modeling and Control, vol.13, pp.281-303.
- [12] Ghosh S.K. and Bég O.A. (2008): Theoretical analyses of radiative effects on transient free convection heat transfer past a hot vertical surface in porous media. – Non Linear Analysis: Modelling and Control, vol.13, pp.419-432.
- [13] Özişik M.N. (1987): Interaction of radiation with convection. – In: Hand book of Single-Phase Convective Heat Transfer (Kakaç, S.; Shah, R.K.; Aung W., Eds.). Wiley, New York, pp.19.1-19.3.
- [14] Zhou J.K. (1986): Differential transform and its applications for electrical circuits. – Wuhan, Huarjung University Press.
- [15] Arikoglu A. and Ozkol I. (2010): Vibration analysis of composite sandwich beams with viscoelastic core by Rusing differential transform method. – Composite Structures, vol.92, pp.3031–3039.
- [16] Bert C.W. (2002): Application of differential transforms method to heat conduction in tapered fins. – ASME Journal of Heat Transfer, vol.124, pp.208–209.
- [17] Chu H.P. and Chen C.L. (2008): Hybrid differential transform and finite difference method to solve the nonlinear heat conduction problem. – Comm. in Nonlinear Science and Numerical Simulation, vol.13, pp.1605–1614.
- [18] Chu H.P. and Lo C.Y. (2008): Application of the hybrid differential transform-finite difference method to nonlinear transient heat conduction problems. – Numerical Heat Transfer Part A, vol.53, pp.295-307.
- [19] Joneidi A.A., Ganji D.D. and BabaelahiM. (2009): Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. – Int. Comm. Heat and Mass Transfer, vol.36, pp.757–762.
- [20] Rashidi M.M., Laraqi N. and Sadri S.M. (2010): A novel analytical solution of mixed convection about an inclined flat plate embedded in a porous medium using the DTM-Padé. – Int. J. of Thermal Sciences, vol.49, pp.2405–2412.
- [21] Hessameddin Yaghoobi and Mohsen Torabi (2011): The application of differential transformation method to nonlinear equations arising in heat transfer. – Int. Comm. in Heat and Mass Transfer, vol.38, pp.815–820.
- [22] Baytaş A.C., Liaqat A., Groşan T. and Pop I. (2001): Conjugate natural convection in a square porous cavity. – Heat Mass Transfer, vol.37, pp.467-473.
- [23] Aung W. and Worku G. (1986): Developing flow and flow reversal in a vertical channel with asymmetric Wall temperature. – ASME Journal Heat Transfer, vol.108, pp.299-304.
- [24] Batchlor G.K. (1954): Heat transfer by free convection across a closed cavity between vertical boundaries At different temperatures. – Quarterly of Applied Mathematics, vol.12, pp.209-233.
- [25] Cheng K.C. and Wu R.S. (1976): Viscous dissipation effects on convective instability and heat transfer in plane Poiseulle flow heated from below. – Applied Scientific Research, vol.32, pp.327-346.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
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Bibliografia
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bwmeta1.element.baztech-11a47fe8-c25e-4369-bdf4-3bbaab0028f8