steady mhd flow of micropolar fluid between two rotating cylinders ...

where T118rθTrθ= is the non dimensional stress.Ω2( μ + k )Hence the coefficient of skin friction on the innerand outer cylinders is given by2TrθC f = at R=a and R=b–h (22)2ρUwhere U = Characteristic velocity = bΩ 2This can be written in the following non-dimensionalform as2TrθC f = at r=r 0 and r=1–e (23)ReTORQUEThe torque acting on the cylinders about the commonaxis of the cylinders is given byτ = ( Trθ × 2π R) × R . (24)Hence the non dimensional torque on inner and outercylinders are calculated asτin20= 2π rand τ 2π ( 1- e)outTrθr = r 02Trθr = 1-e= (25)RESULTS AND DISCUSSIONSThe velocity filed is considered along tangential(azimuthal) direction only. In fact we can start withnonzero radial velocity and come to conclude that itshould vanish by considering continuity equation andthe condition that there is no suction on the walls.(See Channabasappa, Umapathy and Nayak [10].)We have investigated the effects of the Hartmannnumber M, the porous lining thickness parameter e,Reynolds number Re, coupling number c and couplestress parameter s on azimuthal velocity v, microrotationvelocity C and the coefficient of skin frictionat the inner and outer cylinders are numericallyobtained and are depicted through Figures 2 to 19.The azimuthal velocity v and Micro-rotation velocityC are computed for different values of M and e.Figures 2–7 shows the azimuthal velocity v and microrotationvelocity C against distance r for differentvalues of M at a fixed value of porous lining thicknessparameter e = 0.1, 0.3, 0.4. We have observed that vdecreases as e increases and C increases as eincreases. Both v and C decrease as M increases. It isobserved that the nature of velocity profiles v isincreasing with distance where as the nature ofrotation C is increasing and decreasing as Mincreases. But for small values of M, C is decreasingwith r. When M takes large values, the values of Care near to zero. i.e rotation of the particles can beneglected.The Figures 2, 4 and 6 of velocity v are in goodagreement with the results obtained by Bathaih andVenugopal [12] and Subotic and Lai [17], when thereis no applied magnetic field (the curve with M=0.0001 indicates almost no magnetic field). Figures8 and 9 give the velocity profiles v and C fordifferent values of c. From this it is clear that anincrease in coupling parameter c increases the valuesof both the velocities v and C. i.e. if micro-polarityof the fluid increases, the velocity v and microrotationC will also increase. In Figures 10 and 11 thevelocity profiles v and C plotted against Re. FromACTA TECHNICA CORVINIENSIS – Bulletin of Engineeringthis it is clear that an increase in Re increases boththe velocities.Figure 2. Variation of v with r at e = 0.1Figure 3. Variation of C with r at e = 0.1Figure 4. Variation of v with r at e = 0.3Figure 5. Variation of C with r at e = 0.32013. Fascicule 3 [July–September]