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  3. Investigating mass and heat transfer by integral method in the natural displacement flow of fluid with a very small surface in the vicinity of an inclined and permeable wave-shaped surface and under a magnetic field

Investigating mass and heat transfer by integral method in the natural displacement flow of fluid with a very small surface in the vicinity of an inclined and permeable wave-shaped surface and under a magnetic field

Number of pages: 101 File Format: word File Code: 32292
Year: 2016 University Degree: Master's degree Category: Facilities - Mechanics
Tags/Keywords: color method - heat transfer - Integral method - Integral solution - Magnetic field - Magnetohydrodynamics - Mass transfer - Normal fluid movement - Wave inclined plate
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  • Summary of Investigating mass and heat transfer by integral method in the natural displacement flow of fluid with a very small surface in the vicinity of an inclined and permeable wave-shaped surface and under a magnetic field

    to obtain a master's degree
    in the field of mechanical engineering, energy conversion trend

    Abstract:

    In this thesis, the investigation of mass and heat transfer by an integral method in the flow of natural displacement of fluid with a very low frontal near the inclined wall The waveform is processed under the magnetic field. The wall is permeable and as a result, the fluid can be sucked into the wall or blown through it. The magnetic field is perpendicular to the wall and towards the inside, and the electric current is perpendicular to the plane formed by the magnetic field and the velocity of the fluid so that a magnetic force can be created in the direction of the flow or against it. To solve the governing equations, we first flatten the waveform plane by applying a coordinate transformation in the x and y parameters, and then convert the PDE equations into ODE equations by the integral method, and finally, we solve the governing equations using the fourth-order Rang-Kutta method and using Maple software.

    The final results show that the shear stress level and Nusselt number both increase with the angular increase. Also, with the increase of the magnetic parameter, the shear stress and the Nusselt number both decrease, and with the increase of the amplitude and frequency of the surface, the shear stress and the Nusselt number both decrease. Also, with the increase of Parantel number, shear stress and Nusselt number both increase. In addition, with increasing suction power, shear stress and Nusselt number both increase, and with increasing blowing power, shear stress and Nusselt number both decrease.          

     

    Key words: natural displacement heat transfer, wavy inclined plane, magneto-hydrodynamics, integral solution, Rung's method

    Preface:

    Many physical phenomena are involved and related to natural displacement. It is possible to observe the free displacement flow and its related heat transfer in a wide range of natural and industrial systems. Free flow in air, heat exchangers, solar energy collectors, drying technology, food processing technologies, electronic system cooling and nuclear reactor cooling are examples of free displacement flow.

    The basic difference between forced and free displacement is that in forced displacement, the engine that drives the current is external, but in free displacement this engine is inside the current. The wall-fluid temperature difference creates a natural and uniform cycle in the natural displacement, so that a bundle of fluid is heated near the hot wall and moves upward during expansion. Then this package is condensed in the vicinity of the cooled cold fluid and moves down on the other side to reach the hot surface again. This cycle has the ability to do work, that is, if we put the propellers in the current, it will rotate due to this current. This problem is the origin of wind power plants. But if there is no means to use the work of the cycle, the fluid will move quickly in the cycle and its potential work will be wasted in friction with fixed objects.

    Magnetic hydrodynamics (MHD) is a relatively new but important branch of fluid mechanics. Among its important fields in the industry, we can mention its practical role in cooling nuclear reactors with a small Perantel number (such as silver with a Perantel of 0.01 and bismuth with a Perantel of 0.021) [1, 2]. Magneto-hydrodynamics is the study of fluid flow that is a conductor of electric current and at the same time a magnetic field is applied to it so that the magnetic force generated is in the direction of the flow or against it.

     

     
     

     

     

    ________________________
    1 magneto hydrodynamic

    1-2 Review of past works :

    In 1989, Mollik and Yao [3] studied the free displacement flow along a vertical wavy plate and showed that the Nusselt number changes periodically along the plate. The wavelength of Nusselt changes is twice the wavelength of the plate, and the value of Nusselt number decreases with the increase of the heat boundary layer downstream of the flow. In 1991, Bhavani and Bergles [4] conducted an experimental study on the rate of free movement heat transfer over sinusoidal plates using the optical Mach-Zehnder interferometer method. They changed parameters such as the ratio of the amplitude to the wavelength of the plate and the angle of the plate and analyzed their effect on the heat transfer rate and found that as the ratio of the amplitude to the wavelength of the plate increases, the rate of heat transfer from the plate decreases. In 2001, Chamkha and Khalid [5] solved the correlation equation of mass and energy for free displacement flow along a flat inclined plate in a similar way and found that with increasing suction intensity, the number Nusselt increases and the Nusselt number decreases with increasing suction intensity.

    In 2002 Belkadi et al [6] investigated the natural displacement flow inside a cavity with an inclined wave plate and showed that the average Nusselt increases with the increase of the plane angle.

    In 2002 Wang [7] solved the combined displacement flow problem for non-Newtonian flow on an inclined plane. A wave was investigated. They showed that the effect of the wave shape of the plate on the thickness of the velocity and heat boundary layer decreases in high frontals. In 2004, Molhasin and Yao [8] investigated the effect of internal heat generation and its absorption along a vertical wave plate in a similar way. In 2005, Wang [9] investigated the mixed flow on an inclined plane. investigated the waveform in the presence of a magnetic field. They rewrote the governing equations with the help of the flow function and then solved the problem using the finite difference method. They showed that the friction coefficient and Nusselt number increase with increasing angle. Also, when the Prantel number increases, the heat transfer rate increases, but the friction coefficient decreases.

    In 2006 Yao [10] investigated the heat transfer along a wavy vertical plane whose changes were the result of two sine waves. His numerical results show that adding the second wave to the plate causes the temperature and velocity profile near the plate to change drastically and the amount of heat transfer decreases.  Also, the rate of heat transfer depends on the ratio of the amplitude and frequency of the plate wave.

    In 2007, Kandasamy and Hashem [11] investigated the heat transfer and mass transfer for natural displacement flow on an inclined plane in a hydromagnetic environment with suction and blowing in a similar way. They showed that with the increase in the suction power of the boundary layer, the velocity and heat decrease. Also, with the increase of the magnetic parameter of the boundary layer, the speed and heat increase.

    In 2007, Mulla Mamoun and Anwar Hossein [12] investigated the effect of radiation in a combined flow on a vertical wave plate using the finite difference method and found that the Nusselt number increases with the increase of the radiation parameter Rd. Also, with the increase of Rd, the thickness of the boundary layer of velocity and heat increases.

    In 2010, Sharma and Singh [13] studied the natural displacement flow along a isothermal vertical plane in the presence of a magnetic field with variable electrical conductivity for a fluid with very small frontal in a similar way. They showed that the fluid velocity and heat transfer rate decrease with the increase of electrical conductivity.

    In 2011, Tohid Hossein and Rita Mujumadar [14] investigated the natural displacement flow on a porous horizontal flat plate with blowing and suction in a similar way. They showed that with increasing suction power, the thickness of the boundary layer decreases the velocity and heat. Also, with the increase of the Prantel number, the thickness of the boundary layer decreases the velocity and heat.

    In 2011, Alim et al [15] investigated the heat conduction of the fluid in the boundary layer for the natural displacement flow on the vertical wave plate along with the heat generation by the finite difference method. They found that the friction coefficient and heat transfer rate increase with the increase of surface heat production. In addition, by increasing the thermal conductivity of the fluid near the edge of the plate, the coefficient of local friction and local Nusselt increases, but this result is reversed in the downstream of the flow.

  • Contents & References of Investigating mass and heat transfer by integral method in the natural displacement flow of fluid with a very small surface in the vicinity of an inclined and permeable wave-shaped surface and under a magnetic field

    List:

    Page

    Chapter One: Introduction

       1-1 Preface ..2

        1-2 Overview of past works.

         1-3 Description of the problem..

        1-4 Research method..

        Second: Magnetic Hydrodynamics

       Chapter 1-2 A history of magnetic hydrodynamics. 9 2-2 Electrodynamic equations in the subject of magnetic hydrodynamics. 10 2-2-1 Electric field and Lorentz force. 10 2-2-2 Ohm's law and volume Lorentz force. 11 2-2-3 Ampere's law. 12

    2-2-4 Faraday's law.12

             2-2-5 Summarizing..13

    Chapter three: Review of several analytical methods in solving Neuer-Stokes equations

    3-1 Scaling analysis method.15

        3-2 Integral method..20

        3-3-1 Similarity method..23

         3-3-2 Effect of flow through the wall: (blowing and suction) 25

    Chapter 4: Natural convection on an inclined plane and integral solution of governing equations

    4-1 Description of the problem.. 28

    4-2 Governing equations.. 29

    4-3 Integral solution of governing equations. 4-3-1 Integrating the governing equations. 32 4-3-2 Solving integral equations of momentum and energy Computer.40

         5-2 Effect of Surface Angle Changes ( ) 42

    5-3 Effect of Magnetic Parameter Changes 47

    5-4 Effect of Surface Oscillation Amplitude Changes 52

    5-5 Effect of Surface Oscillation Frequency Changes 57

    5-6 Effect of Prontel Number Changes 62 5-7 The effect of changes in suction and blowing speed on the surface. 67 67 Chapter 6: Conclusions and suggestions 6-1 Conclusion. 77 6-2 Suggestions.

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    [4]    Bhavnani, S., & Bergles, A. Natural convection heat transfer from sinusoidal wavy surfaces. W?rme- und Stoffübertragung, 26(6), 341-349. (1991)

    [5] Chamkha, A. J., & Khaled, A.-R. A. Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption. Heat and Mass Transfer, 37(2-3), 117-123. (2001)

     

    [6]    Adjlout, L., Imine, O., Azzi, A., & Belkadi, M. Laminar natural convection in an inclined cavity with a wavy wall. International Journal of Heat and Mass Transfer, 45(10), 2141-2152. (2002)

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    [8] Molla, M. M., Hossain, M. A., & Yao, L. S. Natural convection flow along a vertical wavy surface with uniform surface temperature in the presence of heat generation/absorption. International Journal of Thermal Sciences, 43(2), 157-163. (2004)

    [9] Wang, C.-C. Mixed convection boundary layer flow on inclined wavy plates including the magnetic field effect. International Journal of Thermal Sciences, 44(6), 577-586. (2005) [10] Yao, L.-S. Natural convection along a vertical complex wavy surface. International Journal of Heat and Mass Transfer, 49(1), 281-286. (2006)

    [11] Kandasamy, R., Hashim, I., Khamis, A., & Muhaimin, I. Combined heat and mass transfer in MHD. Combined heat and mass transfer in MHD free convection from a wedge with ohmic heating and viscous dissipation in the presence of suction or injection. Iranian Journal of Science & Technology, 31(A2). (2007)

     

      [12] Molla, M. M., & Hossain, M. A. Radiation effect on mixed convection laminar flow along a vertical wavy surface. International Journal of Thermal Sciences, 46(9), 926-935. (2007)

    [13] Sharma, P., & Singh, G. Effects of variable thermal conductivity, viscous dissipation on steady MHD natural convection flow of low Prandtl fluid on an inclined porous plate with Ohmic heating. Mechanica, 45(2), 237-247. (2010)

    [14] Hossain, M. T., Mojumder, R., & Hossain, M. A. Solution of natural convection boundary layer flow above a semi-infinite porous horizontal plate under similarity transformations with suction and blowing. Daffodil International University Journal of Science and Technology, 6(1), 43-51. (2011)

    [15] Alim, M., Alam, S., & Miraj, M. Effects of temperature dependent thermal conductivity on natural convection flow along a vertical wavy surface with heat generation. Int. J. Eng. & Tech. IJET-IJENS, 11(6), 60-69. (2011) [16] Razavi and Pourhossein. Aerospace Mechanics Quarterly (Heat Transfer and Propulsion), Volume 8, Number 2, Pages 85-92 (Summer 2013)

    [17] Kabir, K., Alim, M., & Andallah, L. Effects of Viscous Dissipation on MHD Natural Convection Flow along a Vertical Wavy Surface with Heat Generation. American Journal of Computational Mathematics, 3(02), 91. (2013)

    [18] Abdallah, M. S., & Zeghmati, B. Effects of the Wavy Surface on Free Convection-Radiation along an Inclined Plate. transformation, 1, 4. (2013)

    [19] Siddiqa, S., Hossain, M., & Saha, S. C. Natural convection flow with surface radiation along a vertical wavy surface. Numerical Heat Transfer, Part A: Applications, 64(5), 400-415. (2013)

     

     [20] Siddiqa, S., Hossain, M., & Saha, S. C. The effect of thermal radiation on the natural convection boundary layer flow over a wavy horizontal surface. International Journal of Thermal Sciences, 84, 143-150. (2014)

    [21] Bejan, A. The method of scale analysis: Natural convection in fluids. Natural Convection: Fundamentals and Applications. Hemisphere, Washington. (1985)

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    [23] Bhattacharjee, S., & Grosshandler, W. (1988). The formation of a wall jet near a high temperature wall under microgravity environment. Paper presented at the ASME 1988 National Heat Transfer Conference, Volume 1. [24] Costa, V. A time scale-based analysis of the laminar convective phenomena. International Journal of Thermal Sciences, 41(12), 1131-1140. (2002)

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    [26]  Herwig, H. W?rmeübertragung AZ. Berlin, Heidelberg, New York ua: Springer Verlag (VDI-Buch). (2000)

     

    [27]  T?pfer, K. Bemerkung zu dem Aufsatz von H. Blasius: Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z.Math. Phys, 60, 397-398. (1912)

    [28] Pohlhausen, E. Der W?rmeaustausch zwischen festen K?rpern und Flüssigkeiten mit kleiner Reibung und kleiner W?rmeleitung. ZAMM?Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 1(2), 115–121. (1921)

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Investigating mass and heat transfer by integral method in the natural displacement flow of fluid with a very small surface in the vicinity of an inclined and permeable wave-shaped surface and under a magnetic field
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