HEAT TRANSFER IN AGITATED NEWTONIAN AND NON-NEWTONIAN LIQUIDS

Abstract

This thesis presents an analytical as well as experimental investigation on heat transfer from the inner wall surface of a vessel to Newtonian and non-Newtonian power law liquids with radial flow agitation. Basically, it considers the liquid emerging from the rotating impeller to be in the form of a free jet which strikes the vessel wall surface to form a stagnation region of height equal to the width of impeller blade. Henceafter, the free jet transforms into two wall jets—one swings upward and the other swings downward along the wall surface. The region of wall jet has been analyzed theoretically on the principles of wall jet and equations for velocity and temperature profiles have been derived for the condition of constant heat flux on the vessel wall surface. Subsequently, the analysis has also provided the equations of wall temperature and heat transfer coefficient distribution on the heated inner wall surface of the vessel for the radial flow agitation of Newtonian and pseudoplastic power law liquids. The equation for local value of heat transfer coefficient of power law and Newtonian liquids are as follows: For power law liquids, i Nux= 1.644, (_Re)A2 (_Pr)J f£>W/0 (w +1)6 For Newtonian liquids, \x J Nux = 1.464 (Re)2 (Pr)3 — \x J kKj (5.39) (5.40) It is important to mention here that apparent viscosity has been used in the definition of dimensionless groups Re and Pr appearing in Eq. (5.39) for power law liquids. The analytical treatment has also expressed apparent viscosity as a function of impeller speed and diameter and physico-thermal properties including the values of flow and consistency indices of the power law liquid. Distribution of heat transfer coefficient on the heated inner wall surface of a vessel for the agitation of various Newtonian and non-Newtonian liquids by a turbine type impeller has been measured experimentally. The vessel and impeller dimensions conformed closely to standard geometric configuration. The wall surface was heated under the condition of constant heat flux (q = constant). The liquids used were water, 20% glycerine-water, 40% glycerine-water, 0.25% CMC-water, 0.67% CMC-water, 1% CMC-water, 0.06% PAA-water and 0.20% PAA-water solutions. The rotational speed of the impeller was varied from 2.50 to 9.22 rps. Wall surface temperatures were measured at eight locations on the vessel wall surface. The location were at the respective heights of 20, 50, 80, 120, 140, 160, 180, 200 mm from the bottom of vessel. Experimentally measured distribution of heat transfer coefficient on the vessel wall surface for both the types of liquids has conformed the existence of a stagnation region, and two wall jet regions on either sides of the stagnation region as envisaged in the theoretical analysis of this investigation. The prediction form analytically—obtained local heat transfer coefficient equations for Newtonian as well as non-Newtonian liquids have agreed very well with the experimental values. The maximum deviation between the two ranged from -20% to +30% for Newtonian and from -35% to +40% for non-Newtonian liquids. This has established the validity of the proposed analytical treatment. Thus analytically-obtained equations can be employed to predict the distribution of heat transfer coefficient of radially flowing Newtonian and non-Newtonian power law liquids on the heated inner wall surface of the vessel from the knowledge of measurable geometric and operation parameters and physico-thermal properties including flow and consistency indices of power-law liquids. Empirical correlations have also been developed by using least square curve fit method from the experimental values ofheat transfer coefficient in stagnation region for both the types of liquids used in this investigation. The resulting correlations are as follows: For Newtonian liquids, /V//„=0.75(Re)062(Pr)05 (61) For non-Newtonian liquids, Nua =0.67 (Re)006.86877 (/tP»_r\)0.33 0.14 r \ \Maw J Above equations have also been compared with the investigations of earlier researchers, namely, Akse et al (1967) and Askew &Beckmann (1965) for Newtonian type liquids. The theoretical analysis has further been extended to determine average heat transfer coefficient for entire wall surface of non-Newtonian power law and Newtonian liquids. Consequently, following equations of average heat transfer coefficient for both types of liquids have been obtained: in (6.2) For non-Newtonian liquids, Nu 3.287 i (/? + !)« (Re)2(Pr)/ i/v A V^y For Newtonian liquids, i i Nu= 2.928 (Re)2 (Pr)3 i XJ_^2 D OO £ (Re)2(Pr)3 1/ V^ J i 1 ZL D OO \^K Ju (5.44c) (5.46) Eq. (5.44c) has further been simplified into the following equation for the heat transfer coefficient of radially flowing power law liquids for (xs jH) - 0.5. -3 OQ7 I I M/=^^y(Re)2(Pr)3 (« + l) fv \ \Dj D. U. (5.45) The investigations of Strek (1963) and Lu et al (1995) for Newtonian liquids agreed with the values of average heat transfer coefficient predicted from Eq. (5.46) within a maximum deviation of -20% to +17% and -25% to +11%), respectively. Similarly, the investigation of Sandall & Patel (1970) and Gupta et al (1974) for non- Newtonian power law liquids also matched with the prediction of Eq. (5.44a) within a deviation of ±45% and from -37% to +50%, respectively. Thus, present theoretical analysis has succeeded in providing analytical equations to predict local and average values of heat transfer coefficient of radially flowing Newtonian and power law liquids over a heated wall surface of the vessel. An important corollary that has emerged out of the above is that for the situation where impeller submergence is half of the liquid height, heat transfer coefficient of a non-Newtonian power law liquid is the product of Nusselt number predicted by the correlation developed for Newtonian liquid and a constant, C. The value of constant, C IV K depends upon rheological parameter and is equal to (» +l) V^ J This simplifies the procedure of determination of heat transfer coefficient of non-Newtonian power law liquids without resorting to experimentation with power law liquids.