Evaluation of the heat transfer rate increases in retention pools nuclear waste

Document Type: Reasearch Paper

Authors

Department of Mechanical Engineering, Islamic Azad University, Sari Branch, Sari, Iran.

10.7508/ijnd.2015.04.007

Abstract

In this paper, we have tried to find a solution for quick transfer of nuclear wastes from pools of cool water to dry stores to reduce the environmental concerns and financial cost of burying atomic waste. Therefore, the rate of heat transfer from atomic waste materials to the outer surface of the container should be increased. This can be achieved by covering the bottom of the pool space with conical fins (vertically) embedded in porous medium and allowing natural convection flow of Newtonian nanofluid upon it. In this research, we studied the rate of heat transfer by using such special space. In this study, Heat transfer boundary layer flow in Nano-fluidics shifting from a vertical cone in porous medium, two-dimensional, steady, incompressible and low speed flow have been considered and attempts  have been made to obtain analytical solutions for it. The obtained nonlinear ordinary differential equation has been solved through homotopy analysis method (HAM), considering boundary conditions and Nusselt number. Also, Nusselt number, which is an important parameter in heat transfer, is calculated using the obtained analytical solution by HAM. A comparison of the obtained analytical solution with the numerical results represented a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.

Keywords

Main Subjects


[1]      Ingham D. B., Pop I., (2002), Transport Phenomena in Porous Media Pergamon Press: Oxford

[2]      Nield D. A., Kuznetsov A. V., (2008), Natural convection about a vertical plate embedded in a bidisperse porous medium. Int. J. Heat Mass Transf. 51: 1658–1664.

[3]      Mahdy A., Hady F. M., (2009), Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect. J. Non-Newtonian Fluid Mech. 161: 37–41.

[4]      Ibrahim F. S., Hady F. M., Abdel-Gaied S. M., Eid M. R., (2010), Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect. Appl. Math. Mech. -Engl. Ed. 31: 675–684.

[5]      Yih K. A., (1999), Coupled heat and mass transfer by free convection over a truncated cone in porous media. VWT/VWC or VHF/VMF. Acta Mech. 137: 83–97.

[6]      Murthy PVSN., Singh P., (2000), Thermal dispersion effects on non-Darcy convection over a cone. Comp. Math. Applic. 40: 1433–1444.

[7]      Roy S., Anilkumar D., (2004), Unsteady mixed convection from a rotating cone in a rotating fluid due to the combined effects of thermal and mass diffusion. Int J. Heat Mass Transf. 47: 1673–1684.

[8]      Takhar H. S., Chamkha A. J., Nath G., (2004), Effect of thermophysical quantities on the natural convection flow of gases over a vertical cone. Int. J. Eng. Sci. 42: 243–256.

[9]      Singh P. J., Roy S., (2007), Unsteady mixed convection flow over a vertical cone due to impulsive motion. Int. J. Heat Mass Transf. 50: 949–959.

[10]  Kumari M., Nath G., (2009), Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection. Int. J. Heat Mass Transf. 52: 3064–3069.

[11]  Cheng C. Y., (2010), Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity. Int. Comm. Heat Mass Transf. 37: 1031–1035.

[12]  Choi S. U. S., (1995), Enhancing thermal conductivity of fluid with nanoparticles. Developments and applications of non-Newtonian flow. ASME FED 231/MD. 66: 99–105.

[13]  Khanafer K., Vafai K., Lightstone M., (2003), Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transf.  46: 3639–3653.

[14]  Buongiorno J., (2006), Convective transport in nanofluids. ASME J. Heat Transfer. 128: 240–250.

[15]  Daungthongsuk W., Wongwises S., (2007), A critical review of convective heat transfer nanofluids. Ren. Sustainable Energy Rev. 11: 797–817.

[16]  Oztop H. F., Abu-Nada E., (2008), Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int. J. Heat Fluid Flow. 29: 1326–1336.

[17]  Nield D. A., Kuznetsov A. V., (2009), The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by nanofluids. Int. J. Heat Mass Transf. 52: 5792–5795.

[18]  Nield D. A., Kuznetsov A. V., (2011), The Cheng–Minkowycz problem for the doublediffusive natural convective boundary-layer flow in a porous medium saturated by nanofluids. Int. J. Heat Mass Transf.  54: 374–378.

[19]  Ahmad S., Pop I., (2010), Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids. Int. Comm. Heat Mass Transf. 37: 987–991.

[20]  Khan W. A., Pop I., (2010), Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53: 2477–2483.

[21]  Kuznetsov A. V., Nield D. A., (2010), Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int. J. Thermal Sci. 49: 243–247.

[22]  Kuznetsov A. V., Nield D. A., (2010), Effect of local thermal non-equilibrium on the onset of convection in a porous medium layer saturated by a nanofluid. Transp. Porous Media.  83: 425–436.

[23]  Bachok N., Ishak A., Pop I., (2010), Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. Int. J. Thermal Sci. 49: 1663–1668.

[24]   Dehghan M., Shakeri F., (2007) Solution of a partial differential equation subject to temperature over specification by He's homotopy perturbation method. Physica Scripta. 75: 778–787.

[25]  Ziabakhsh Z., Domairry G., Esmaeilpour M., (2009), Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the Homotopy analysis method. Comm. Nonlin. Sci. Num. Simul. 14: 1284-1294.

[26]  Ziabakhsh Z., Domairry G., (2009), Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using Homotopy analysis method. Nonlinear Sci. 14: 1868-80.

[27]  Abbasbandy S., (2006), The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys. Lett. A. 360: 109–113.

[28]  Abbasbandy S., (2007), The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation. Phys. Lett. A. 361: 478–483.

[29]  Liao S. J., (2006), Series solutions of unsteady boundary-layer flows over a stretching flat plate. Stud. Appl. Math. 117:  239–264.