University of Roorkee
Roorkee, India
The theory of micropolar fluid presents a satisfactory mathematical model for the description of behaviour of many industrially important fluid like colloidal solutions, liquid crystals, polymeric fluids and in flows though narrow passage. Like in human arteries or in lubrication flows. The fluid flow is governed by two basic and independent vectors (i) classical velocity vector representing translation and (ii) micro-rotation vector representing spin velocity.
The aim of present paper is to analyse the fully developed free connection micro-polar fluid flow in a vertical circular pipe maintained at a constant temperature including the effects of frictional heating and distributed heat sources and sinks. the mathematical model has been taken in cylindrical systems. the governing set of partial differential equations has been changed to set coupled ordinary but non-linear, differential equations using similarity transformations. These equations are solved numerically using FINITE ELEMENT TECHNIQUES (FEM). The results are then compared with that obtained through QUASILINEARIZATION TECHNIQUE. The transient velocity, micro-rotation and temperature profiles are shown graphically. The velocity and the temperature decreases with the increase in dissipation parameter. It may be concluded that micro-element concentration introduces to effects of coolant. Moreover a low rate of heat transform is attained through micro elements.
Thus this analysis provides a method of achieving decreased rate of heat transfer through additives which is of immense help in combustion chambers, exhaust nozzles and porous walled flow reactors.
The FEM is an efficient method for boundary value problems as the coefficient assembly matrix is block diagonal and accuracy is maintained even with an non-uniform mesh. Moreover the gradient boundary conditions and irregular boundaries can be managed more efficiently which is an added advantage.