Effects of Three Dimensional Flow Separation due to Non-uniform Heating on Laminar Mixed Convection in a Square Channel

Purpose – The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid. Design/methodology/approach – Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed. Findings – Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer. Originality/value – Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated.

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Numerical Analysis of Three-Dimensional Flow in an Industry-Size Hydrothermal Autoclave Subjected to Non-Uniform Heating

Volume 1: Fora, Parts A and B ◽

10.1115/fedsm2002-31403 ◽

2002 ◽

Author(s):

Hongmin Li ◽

Guo-Xiang Wang ◽

Edward A. Evans

Keyword(s):

High Temperature ◽

Numerical Analysis ◽

Three Dimensional ◽

Hydrothermal Growth ◽

Chamber Wall ◽

Heating Condition ◽

Uniform Heating ◽

Three Dimensional Flow ◽

Growth Environment ◽

Dimensional Flow

Hydrothermal growth is an important industrial process to produce piezoelectric crystals such as quartz. It takes place in a cylindrical container called an autoclave, which is filled with aqueous solution at a high temperature and a high pressure. The high temperature growth condition is maintained through electrical resistors on the outer surface of an autoclave. In practice there is a non-uniform heating condition in the circumferential direction. Many theoretical and numerical studies, however, assume an axisymmetric heating condition. This paper presents a numerical analysis of the three-dimensional heat transfer and fluid flow in hydrothermal growth due to such non-uniform heating. The analysis is based on an industry-size autoclave with an aspect ratio of 10. The non-uniform heating is introduced on the surface of both the lower dissolving chamber and the upper growing chamber of an autoclave with and without a baffle at the middle height. The flow and isotherm patterns were obtained with the temperature difference between the two chambers kept at 10 °C. The circumferentially non-uniform temperature has dramatic effects on the three-dimensional flow and therefore the temperature distribution in the autoclave. When the dissolving chamber is subjected to circumferentially non-uniform heating, a baffle is essential to create a uniform growth environment in the growing chamber. To obtain high quality single crystals, however, the temperature control on the growing chamber wall is more important than that on the dissolving chamber wall.

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