A Parametric Study of Flow Field and Heat Transfer Between Squeezing Disks

Abstract

Squeeze flow is a simple and extremely useful rheological technique by which a fluid is squeezed between the gap of two parallel bodies (Disks) under the action of a normal force. In general, one of the bodies is held fixed and the other body moves toward it. If used in a steady shearing mode, certain properties such as shear modulus can be de duced. However, squeeze flow is more frequently used to find the dynamic properties such as storage and loss modulus of viscoelastic materials. Commercially available rheometre devices like piezoelectric axial vibromter which is used to measure these properties, are only capable for a frequency range between 10 to 400Hz. The squeeze flow is generated between the disks gap can be varied between 20 to 200µm for a required sample volume 100µL. This allows for the measurements on a fluid with viscosity range 1 to 200 mPas. This device seems to be very promising; however, the volume of liquid required is too large and the viscosity that can be measured is too low to satisfy a number of industrial needs. It seems apparent that a device capable of measuring fluid properties into kHz range and measuring fluid’s properties into kHz range, operating on sub-µL volume and sub-µm gap is yet to be developed - a challenging task. The friction between the fluid and disks surface creates heat which modifies the fluid viscosity and velocity distribution. This temperature gradient plays a pivotal role in designs of high energy devices. A large number of physical phenomena involve natural convection, which are enhanced and driven by internal heat generation. The effect of internal heat generation is especially pronounced for low Prandtl number i.e metal fluids. The friction between fluid and disks surface also creates electric charges which flow with fluid flow. The motion of theses charges eventually creates a magnetic field in fluid domain. This magnetic field controls change in viscosity due to temperature gradient. According to Lenz’s law, motion of a conductor through a magnetic field, Lorentz force acts on fluid and modifies its motion, which makes the theory highly non-linear. The main purpose of this research is to gain a better understanding of the behavior of fluid flow and heat transfer between squeezing disks. The constitutive expression of un steady Newtonian fluid is employed in the mathematical formulation to model the flow between the circular space of porous and contracting disks. The expressions for fluid torque and magneto-hydrodynamic pressure gradient which the fluid exerts on disks are derived. The Soret and Dufour effects due to concentration and temperature gradients are investigated. It is depicted through graphs and numerical results that increase in Soret number and inertial forces increases the rate of heat flux and decreases mass flux. The effect of centrifugal and Coriolis forces due to the rotation of disks is also studied in detail and shown that increasing the rotational speed of the upper disk increases rate of heat transfer. For the very first time in literature, the Navier-Stokes equations of viscous fluid along with energy and concentration equations are investigated under the influence of variable magnetic field. The conservation equations with three dimensional Maxwell’s equations are taken into account and concluded that the fluid axial velocity and temperature in crease with increase in the axial component of magnetic field. The fluid’s pressure and torque on upper disk is also gaining strength as the azimuthal and axial component of magnetic field are increasing. Different flow regimes corresponding to disks rotations in same and opposite directions are found in radial and azimuthal velocity distribution. As viscosity and thermal conductivity changes with alteration in a magnetic field, there fore magnetic field dependent viscosity and magnetic field dependent thermosolutal con vection are investigated for the first time in fluid dynamics. During analysis, it has been observed that an increase in viscosity decreases the strength of azimuthal and axial com ponents of magnetic field. It is also observed that heat and mass coefficient are increasing the function of the rotational Reynolds number. An error analysis is conducted in this thesis to ensure the reliability of the analysis for the remaining minimal errors. The analysis is performed using 40th-order approxima tions. In the case of flexible disks, the self-esteem equations are solved using Parametric Continuation Method and the Homotopy Analysis Method (HAM) with an appropriate initial estimates and auxiliary parameters to compile an algorithm with accelerated and assured convergence. The validity and accuracy of HAM results is proved by comparison of the HAM solutions with numerical solver package BVP4c.