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Abstract
A numerical study of double - diffusive mixed convection within a two ¬dimensional, horizontal and rotating annulus for two different cases of the inner cylinder rotation has been investigated. This study has wide engineering applications such as the technologies involved in the chemical vapor deposition processes for the semiconductors device fabrications. The migration of the species is known to be sensitive to the magnitude of rotational speed which is a crucial parameter in drying technologies, printing and crystal growth applications. Other technologies including melting and solidification processes in rotating furnace are likely candidates for such applications. Thesis consists of the following chapters:
Chapter One:
This chapter contains an introduction about the usage and importance of the double diffusive convection in a horizontal annulus in many engineering and industrial applications. The literature review contains the most important previous investigations in this field and in the end of the chapter; the aim of the present work is presented.
Chapter Two:
The mathematical formulation for the double diffusive mixed convection within a two dimensional, horizontal and rotating annulus explains the method of calculating the pressure inside the annulus. The schematic diagrams are plotted for the two different cases of the inner cylinder rotation to explain the boundary conditions. The transport equations for momentum, energy and mass are converted into the dimensionless form by using the dimensionless variables and then solved using the finite volume technique developed by Patankar and Spalding. This technique was based on the discretization of the governing equations using the central differencing in space. A uniform grid distribution was taken in both radial and angular directions. The iteration method used in this program is the line by line procedure. Then the equations used to obtain the local and average Nusselt and Sherwood numbers at the outer surface of the inner cylinder are derived. Also, the equations used to obtain the shear stress acting at the outer surface of the rotating inner cylinder are given. To check the validity of the present model, a comparison was made with the published results and a good agreement was found.
Chapter Three:
This study includes the effect of buoyancy forces generated by the density and concentration gradients and the forced convection effect introduced by the rotation of the annulus. These effects are generally represented by the Grashofnumber and the ’rotational’ Reynolds number, respectively. It is common practice to present the combined effect of both numbers in terms of Richardson number which is the ratio of Grashof number to the square of Reynolds number. This term indicates the importance of the buoyancy forces to the rotational ones and its impact on the flow and heat transfer within the considered system. Another important parameter is the Buoyancy ratio number which accounts for the strength of the concentration gradient to its thermal counterpart. Also, it is important to study the effect of Lewis number which represents the ratio between the thermal diffusivity and the mass diffusivity and finally, the investigation was made for different types of fluids
with different Prandtl number. The study covers the three main types of fluids; the liquid metals’ (low values ofPrandtl number), the heavy oils (high values ofPrandtl number) and the mind fluid (e.g. air and water). The study covers a wide range for 0.01:S Ri:S 100, -15 :s N :s 15,0.01 :s Le :s 100, and 0.01 :s Pr:S 100. All the results are made for a constant radius ratio; cr = 2 and a constant thermal Grashof number; GrT = 104• The streamlines, isotherms and iso-concentrations are plotted for different Richardson number, Buoyancy ratio and Lewis number in the selected range in this study for each selected fluid (liquid metals, air, water and heavy oils) to see their behavior. The effect of these parameters on both local Nusselt and Sherwood numbers are presented and studied. Also, the effect of these parameters on the shear stress acting at the outer surface of the inner rotating cylinder is investigated for the counter clockwise rotation.
Chapter four:
In this chapter, the effect of the investigation parameters on the average Nusselt and Sherwood numbers within two concentric, horizontal cylinders will be presented and discussed for the clockwise and counter clockwise rotations. On the other hand, a comparison was made between the two rotation directions to select the best direction of the inner cylinder rotation to enhance both heat and mass transfer. Three main parameters were found to have a significant effect on this selection; Prandtl number, Richardson number and the Buoyancy ratio. Useful correlations for both average Nusselt and Sherwood numbers in terms of Prandtl number, Buoyancy ratio, Lewis number and Richardson number are given. These correlations can be used in heat and mass transfer problems as well as the design of thermal equipments.
Chapter five:
And finally, chapter five which is the last chapter contains the conclusions of present work, a brief summary of the results, recommendations and some of studying points which proposed to be studied in the future.