Investigating mass and heat transfer in the natural displacement flow of water-aluminum oxide nanofluid under a constant magnetic field in a porous medium near a vertical wall

Dissertation

To obtain a master's degree

in the field of mechanical engineering (energy conversion)

Abstract

In this thesis, mass and heat transfer of water-aluminum oxide nanofluid in a two-dimensional porous medium is investigated And it is treated under the magnetic field and in the vicinity of the vertical wall. The boundary wall can be permeable or impermeable. The concentration and temperature of the wall surface is constant and it is located in the vicinity of the environment with temperature and concentration. The assumed magnetic field is constant and perpendicular to the wall and inward. In order to determine the effect of the presence of nanoparticles on the thermal conductivity of the base fluid, the Cove and Kleinstroer model [1] has been used, in which the thermal conductivity coefficient of the nanofluid is a function of the temperature of the nanofluid, the diameter of the nanoparticles and the base fluid, the volume fraction, and the Brownian motion effects of the nanoparticles. With the presence of nanoparticles, the dynamic viscosity of the nanofluid also varies according to the Brinkmann relation with the volume fraction. Choosing the volume fraction of nanoparticles in the range of up to , has resulted in a low concentration of the nanofluid and maintaining its Newtonian behavior. Slow, incompressible, non-Darcy flow and water and nanoparticles are assumed to be in thermal and concentration equilibrium, and the condition of non-slip between them prevails. When applying the governing equations to the problem of various heat losses such as viscosity losses and . . has been omitted. After converting the PDE equations resulting from applying the conservation of momentum, energy and mass with the help of similar solutions to the ODE equation system, the resulting system has been solved using the fourth-order Ranggutta method using appropriate software. The results show that the heat transfer coefficient increases with the increase in the volume fraction of aluminum oxide nanoparticles, increasing the Buoyancy number and the Soert number, and decreases with the increase in the Groschev number, Hartmann number, Lewis number, and Dufour number. On the other hand, with the increase of volume fraction, Hartmann number and Soret number, the mass transfer coefficient decreases and with the increase of Boyance number, Lewis number and Dufour number, the mass transfer coefficient increases. Also, the results show that the mass and heat transfer in the porous medium, in the suction state, is more than the blowing state or the impermeable state. rtl;">-1 Introduction

The porous environment and the phenomenon of heat and mass transfer in it is a subject that has attracted the attention of many researchers in different branches of science. Many experimental methods, theoretical studies and numerical simulations are used in this field in mechanical engineering, chemical engineering, civil engineering, geology, etc. . . This is a confirmation of the above claim.

Due to the wide and increasing use of porous media in various fields of engineering, there has always been a need for basic studies on how mass and heat transfer in porous media, because detailed investigations are a tool for improving engineering systems containing porous materials and raising their quality and efficiency. Among the above applications, we can mention thermal insulation of buildings, heat treatment in the ground, chemical catalytic reactors, groundwater pollution, ceramic industry, biological technology, energy storage units, heat exchangers, cooling, electronic devices, oil tanks and other such examples. On the other hand, in many cases, the miniaturization of heat transfer systems on the one hand and the increase of heat flux on the other hand, necessitates the need for heat transfer in a short time and with high intensity. In cases where there is a need to transfer a lot of heat flux from solid to fluid medium, existing methods such as changes in fluid dynamics, flow geometry, boundary conditions and so on. . . Alone, they cannot cope with the increasing demand of heat transfer control in existing processes. Therefore, there is an urgent need for new and innovative concepts to control heat transfer. Nanofluid technology offers a high potential for controlling systems subject to heat transfer in small volumes. This means that by adding additives to the base fluid, it is possible to improve its thermophysical properties. Meanwhile, external magnetic fields are effective in many natural flows and industries.A branch of studies that deals with the interaction between a magnetic field and a moving conducting fluid is called magnetohydrodynamics [1] MHD. Examining this branch depends on knowing the governing equations of magnetism and fluids and the effect of each of the parameters of these two knowledges on each other. In the current study, the effect of the MHD phenomenon on the fields of velocity, temperature and concentration as well as mass and heat transfer has been considered.

1-2 Review of past works

In 1988, Nakayama[2] and colleagues solved the integral for the non-Darcy free displacement flow on a flat surface. vertical and a vertical cone in a porous environment provided saturation [1]. They showed that the heat transfer rate decreases with the increase of Grashof number. This happens while the thickness of the dimensionless temperature boundary layer is directly related to the Grashof number and increases with its increase.

In 1999, Murthi[3] and Sanagh[4] investigated mass and heat transfer on a vertical flat plate located in a porous medium and under natural displacement[2]. They observed that the thickness of the dimensionless temperature boundary layer increases by decreasing the mass flux parameter, i.e. by changing the suction mode to the exhaust mode. As the Grashof number increases, the thickness of the boundary layer of dimensionless velocity decreases and the thickness of the boundary layer of dimensionless temperature and dimensionless concentration increases. Also, they concluded that with the increase of the surface mass flux, the reduction of Grashof number and also with the increase of the buoyancy rate parameter, the rate of heat transfer and dimensionless mass transfer will also increase.

In 2003, Wang[5] and his colleagues studied the mass and heat transfer in the vicinity of a vertical wall located in a porous environment and under natural displacement and assuming a non-Darcy flow[3]. They showed that the profile of dimensionless temperature, dimensionless velocity and dimensionless concentration increases with the reduction of mass flux, i.e. transition from the suction state to the injection state, by considering the Grashof number, Lewis number and buoyancy ratio constant. They also showed that the dimensionless heat transfer in the blowing state is more than other cases.

In 2004, Al-Amin [7] investigated the effect of dispersion on mass and heat transfer of natural convection in a porous medium and for Darcy and non-Darcy flow [4]. He concluded that the dimensionless heat transfer in the Darcy flow is more than the non-Darcy flow and with the increase of the non-Darcy flow parameter, the dimensionless heat transfer decreases and the dimensionless velocity profile decreases near the wall and increases as we move away from the beginning of the wall with the increase of the non-Darcy flow parameter. He also concluded that with the increase of the dispersion coefficient, the thickness of the boundary layer decreases, and the thickness of the dimensionless temperature boundary layer increases.

In 2006, Pall investigated the effect of magnetic field on the heat transfer of combined displacement on a heated vertical plate in a porous medium with variable porosity coefficient [5]. Assuming a constant wall temperature and higher than the ambient temperature, he reported that the thickness of the boundary layer of the dimensionless velocity will increase with the increase of the magnetic field parameter and the increase of the local inertia. While the thickness of the dimensionless temperature boundary layer increases with the reduction of the magnetic field parameter and the reduction of the local inertia.

In 2009, Mehdi[8] and Mohammad[9] investigated the effect of magnetohydrodynamics on the natural displacement flow on a wavy vertical plane in a porous medium under non-Darcy flow[6]. By assuming the wave amplitude to be constant, they showed that with the increase of Grashof number and magnetohydrodynamic parameter, the thickness of the boundary layer of the dimensionless velocity decreases and the thickness of the boundary layer of the dimensionless temperature increases. Also, they showed that by decreasing the wave amplitude, the magnetohydrodynamic parameter decreases and the Nusselt number increases.

In 2009, Rashidi[10] used the differential transformation method to solve the boundary layer equations under magnetohydrodynamics[7]. He showed that the dimensionless velocity decreases with the increase of the magnetohydrodynamic parameter. He also reported that the differential transformation method for the boundary layer equations and infinite condition does not have a good approximation, and to improve the inefficiency of this method, he used the D-TM-Pede method [11] and showed that the results obtained from this method are completely consistent with the numerical results. Heated vertical plate in porous polishing medium.