Dual-phase-lag heat transfer model in hydromagnetic second grade flow through a microchannel filled with porous material: A time-bound analysis

Dual-phase-lag heat transfer model in hydromagnetic second grade flow through a microchannel filled with porous material: A time-bound analysis

Mehari Fentahun Endalew Subharthi Sarkar* Gauri Shanker Seth Oluwole Daniel Makinde 

Department of Mathematics, Kalinga Institute of Industrial Technology (KIIT), Bhubaneswar-751024, Odisha, India

Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines Dhanbad), Dhanbad 826004, Jharkhand, India

Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa

Corresponding Author Email: 
sarkar.ism@gmail.com
Page: 
173-194
|
DOI: 
https://doi.org/10.3166/RCMA.28.173-194
| | | | Citation

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Abstract: 

An investigation is carried out to analyze effect of dual-phase-lag heat conduction model on the thermal and hydrodynamic behavior of MHD second grade fluid flow through a vertical microchannel filled with porous material. The governing partial differential equations are solved by using Laplace transform method while its inversion is done numerically using INVLAP subroutine of MATLAB. The numerical values of fluid velocity and fluid temperature are demonstrated graphically while skin friction and heat transfer rate are presented in tabular form for different values of pertinent flow parameters. Time bounded effects of various important flow parameters influencing unsteady MHD second grade fluid flow with dual-phase-lag heat conduction model has been captured and physically justified for the first time. It is found that an increment of the magnetic field parameter reduces fluid velocity because of Lorentz force that slows down the motion of fluid flow. The impact of second grade flow parameter turns out to be more articulated with the progression of time as well. In this paper, an attempt has been made to overpass the intermediate region of unsteady flow under dual-phase-lag heat transfer with unsteady flow under Fourier heat transfer. The novelty raised in this article will help to advance the design of mechanical systems in micro-devices involving second grade MHD flow where non-Fourier heat mode of transfer takes place.

Keywords: 

 dual-phase-lag heat transfer, microchannel, second grade fluid, porous material, MHD flow

1. Introduction
2. Mathematical formulation and solution of the problem
3. Discussion of results
4. Conclusions
  References

Ajibade A. O. (2014). Dual-phase-lag and Dufour effects on unsteady double-diffusive convection flow in a vertical microchannel filled with porous material. Proc. Inst. Mech. Eng., Part E: J. Process Mech. Eng., Vol. 228, pp. 272-85. https://doi.org/10.1177/0954408913500949 

Ali F., Aamina B., Khan I., Sheikh N. A., Saqib M. (2017). Magnetohydrodynamic flow of brinkman-type engine oil based MoS2-nanofluid in a rotating disk with hall effect. International Journal of Heat and Technology, Vol. 35, No. 4, pp. 893-902. https://doi.org/10.18280/ijht.350426

Catteneo C. (1958). A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte Rendus, Vol. 247, pp. 431–433.

Choi J. H., Yoon S. H., Park S. G., Choi S. H. (2016). Analytical solution of the Cattaneo-Vernotte equation (non-Fourier heat conduction). J. Korean Soc. of Marine Eng., Vol. 40, No. 5, pp. 389-396. https://doi.org/10.5916/jkosme.2016.40.5.389

Darbandi M., Shafii M. B., SafariMohsenabad S. (2009). Analysis of Non-Newtonian fluids in microchannels with different wall materials. In ASME 2009 7th Int Conf Nanochannels, Microchannels, and Minichannels, pp. 697-703. https://doi.org/10.1115/ICNMM2009-82256 

Hayat T., Abbas Z. (2008). Heat transfer analysis on the MHD flow of a second grade fluid in a channel with porous medium. Chaos, Solitons Fractals, Vol. 38, pp. 556-567. https://doi.org/10.1016/j.chaos.2006.12.004

Hayat T., Ahmed N., Sajid M., Asghar S. (2007). On the MHD flow of a second grade fluid in a porous channel. Comp. Math. Appl., Vol. 54, pp. 407-414. https://doi.org/10.1016/j.camwa.2006.12.036

Hetsroni G., Mosyak A., Pogrebnyak E., Yarin L. P. (2005). Fluid flow in micro-channels. Int. J. Heat and Mass transf., Vol. 48, pp. 1982-1998. https://doi.org/10.1016/j.ijheatmasstransfer.2004.12.019

Hollenbeck K. J. (1998). INVLAP. M: A matlab function for numerical inversion of Laplace transforms by the de Hoog algorithm. Medical Physics, Vol. 27, No. 2, pp. 58-70. 

Hoog F. R. D., Knight J. H., Stokes A. N. (1982). An improved method for numerical inversion of Laplace transforms. SIAM J. Sci. Stat. Comput., Vol. 3, pp. 357-366. https://doi.org/10.1137/0903022

Hooman K. (2008). Heat and fluid flow in a rectangular microchannel filled with a porous medium, Int. J. Heat and Mass transf., Vol. 51, pp. 5804-10. https://doi.org/10.1016/j.ijheatmasstransfer.2008.05.010

Hoyt J. W. (1999). Some applications of non-Newtonian fluid flow. In Rheology Series, Vol. 8, pp. 797-826. https://doi.org/10.1016/S0169-3107(99)80008-2

Khadrawi A. F., Al-Nimr M. A. (2007). Unsteady natural convection fluid flow in a vertical microchannel under the effect of the dual-phase-lag heat-conduction model. Int. J. Thermophys., Vol. 28, pp. 1387-400. https://doi.org/10.1007/s10765-007-0207-x

Khadrawi A. F., Othman A., Al-Nimr M. A. (2005). Transient free convection fluid flow in a vertical microchannel as described by the hyperbolic heat conduction model. Int. J. Thermophys, Vol. 26, No.3, pp. 905-918. https://doi.org/10.1007/s10765-005-5586-2

Khan I., Ellahi R., Fetecau C. (2008). Some MHD flows of a second grade fluid through the porous medium. J.  Porous Media, Vol. 11, pp. 389-400. https://doi.org/10.1615/JPorMedia.v11.i4.50 

Khan M., Hashim Fetecau C. (2012). On the exact solutions for oscillating flow of a MHD second-grade fluid through porous media. Special Topics Rev Porous Media: Int. J., Vol. 3, pp. 13-22. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v3.i1.20

Patidar S., Kumar S., Srivastava A., Singh, S. (2016). Dual phase lag model-based thermal analysis of tissue phantoms using lattice Boltzmann method. Int. J. Therm. Sci., Vol. 103, pp. 41-56. https://doi.org/10.1016/j.ijthermalsci.2015.12.011

Rostami A. A., Mujumdar A. S., Saniei N. (2002). Flow and heat transfer for gas flowing in microchannels. Rev. Heat and Mass transf., Vol. 38, pp. 359-36. https://doi.org/10.1007/s002310100247

Rukolaine S. A. (2014). Unphysical effects of the dual-phase-lag model of heat conduction. Int. J. Heat and Mass transf., Vol. 78, pp. 58-63. https://doi.org/10.1016/j.ijheatmasstransfer.2014.06.066

Samiulhaq Ahmad S., Vieru D., Khan I., Shafie S. (2014). Unsteady magnetohydrodynamic free convection flow of a second grade fluid in a porous medium with ramped wall temperature. PloS One, Vol. 9, No. 5, pp. e88766. https://doi.org/10.1371/journal.pone.0088766

Sarkar S., Seth G. S. (2016). Unsteady hydromagnetic natural convection flow past a vertical plate with time-dependent free stream through a porous medium in the presence of Hall current, rotation, and heat absorption. Journal of Aerospace Engineering, Vol. 30, No. 1, pp. 04016081. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000672

Seth G. S., Kumbhakar B., Sarkar S. (2014). Unsteady hydromagnetic natural convection flow with heat and mass transfer of a thermally radiating and chemically reactive fluid past a vertical plate with Newtonian heating and time dependent free stream. International Journal of Heat and Technology, Vol. 32, No. 1-2, pp. 87-94. 

Seth G. S., Sarkar S., Mahato G. K. (2013). Effects of hall current on hydromagnetic free convection flow with heat and mass transfer of a heat absorbing fluid past an impulsively moving vertical plate with ramped temperature. International Journal of Heat and Technology, Vol. 31, No. 1, pp. 85-95. 

Seth G. S., Sarkar S., Nandkeolyar R. (2015). Unsteady hydromagnetic natural convection flow past an impulsively moving vertical plate with Newtonian heating in a rotating system. Journal of Applied Fluid Mechanics, Vol. 8, No. 3, pp. 623-633. https://doi.org/10.18869/acadpub.jafm.73.238.22724

Shen C. (2006). Rarefied gas dynamics: fundamentals, simulations and micro flows. 

Singh J. K., Rohidas P., Joshi N., Begum S. G. (2017). Influence of hall and ion-slip currents on unsteady MHD free convective flow of a rotating fluid past an oscillating vertical plate. International Journal of Heat and Technology, Vol. 35, No. 1, pp. 37-52. https://doi.org/10.18280/ijht.350106

Sobhan C. B., Peterson G. P. (2008). Microscale and nanoscale heat transfer: Fundamentals and engineering applications. CRC Press. https://doi.org/10.1201/9781420007114

Sultan Q., Nazar M., Ahmad I., Ali U. (2015). Flow of second grade fluid between two walls induced by rectified sine pulses shear stress. J. Mech., Vol. 31, No. 5, pp. 573-582. https://doi.org/10.1017/jmech.2015.22

Tzou D. Y. (1995a). A unified field approach for heat conduction from macro-to micro-scales. J. Heat Transf., Vol. 117, pp. 8-16. https://doi.org/10.1115/1.2822329

Tzou D. Y. (1995b). The generalized lagging response in small-scale and high-rate heating. Int. J. Heat and Mass Transf., Vol. 38, pp. 3231-3240. https://doi.org/10.1016/0017-9310(95)00052-B

Tzou D. Y. (2014). Macro-to microscale heat transfer: The lagging behavior. John Wiley and Sons. https://doi.org/10.1002/9781118818275

Vernotte P. (1961). Some possible complications in the phenomena of thermal conduction. Compte Rendus, Vol. 252, pp. 2190-2191.

Xu M., Wang L. (2005). Dual-phase-lagging heat conduction based on Boltzmann transport equation. Int. J. Heat and Mass Transf., Vol. 48, pp. 5616-5624. https://doi.org/10.1016/j.ijheatmasstransfer.2005.05.040

Zhang Z. M. (2007). Nano/microscale heat transfer. McGraw Hill 2007, New York. https://doi.org/007143674X