Abstract
In this paper we study the effects of variable viscosity and thermal conductivity on the heat transfer in the pressure-driven fully developed flow of a slurry (suspension) between two horizontal flat plates. The fluid is assumed to be described by a constitutive relation for a generalized second grade fluid where the shear viscosity is a function of the shear rate, temperature and concentration. The heat flux vector for the slurry is assumed to follow a generalized form of the Fourier’s equation where the thermal conductivity k depends on the temperature as well as the shear rate. We numerically solve the governing equations of motion in the non-dimensional form and perform a parametric study to see the effects of various dimensionless numbers on the velocity, volume fraction and temperature profiles. The different cases of shear thinning and thickening, and the effect of the exponent in the Reynolds viscosity model, for the temperature variation in viscosity, are also considered. The results indicate that the variable thermal conductivity can play an important role in controlling the temperature variation in the flow.
Highlights
In fossil fuel combustion applications, coal particles are generally transported to the combustion chamber via either pneumatic or hydraulic transport [1,2]
We have suggesteed a new constitutive model for the heat flux vector with the thermal conductivity depending on the shear rate and temperature; we have studied the fully developed flow and heat transfer a of a slurry between two horizontal flat plates, where the upper plate is at a higher temperature
The fluid is assumed to be described by a constitutive relation for a generalized second grade fluid where the shear viscosity is a function of the shear rate, temperature and concentration
Summary
In fossil fuel combustion applications, coal particles are generally transported to the combustion chamber via either pneumatic or hydraulic transport [1,2]. Many of the experimental studies on the thermal conductivity of non-Newtonian fluids have been performed under static conditions [10,11]; very few studies have been conducted over a range of shear rates. Analytically studied the influence of shear-rate-dependent thermal conductivity upon the heat transfer characteristics of suspensions. Their theoretical study explained the increase of thermal conductivity by introducing the concept of micro-scale convection, which is induced by the rotation of particles in a shear flow. Charunyakorn et al [20] numerically studied the heat transfer in a slurry using a micro-encapsulated phase-change material, with a shear-rate-dependent thermal conductivity. The objective of the present paper is to study the heat transfer in the fully developed flow of a slurry, and explore the effects of shear-rate-dependent viscosity and thermal conductivity.
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