have been calculated through Equations 8 and 9. T h e positive curvature of the log T - log ( - du d j ) curve is tvpical of clay slurries, which exhibit Bingham fluid behavior ( 7 ) T h e range of shear stresses investigated is of interest because it is much lower than usual possible ranges in capillar) viscometers Conclusions
T h e inclined plane is a useful device for measuring shear stress-shear rate curves in the low shear-rate region for fluids \vhich exhibit no slip a t the solid surface. T h e same technique makes it possible to detect even minor effects of wall slip. T h e data obtained show that some slip takes place in the case of ChfC solutions. Original data are recorded by Ferrari-Bravo, Mililotti, and Raitano (3: 6, 7 7 ) and a copy will be sent on request. Acknowledgment
T h e first author is indebted to A. B. Metzner, University of Delaware, for stimulating discussion. Nomenclature a = limiting shear rate in infinitely dilatant fluid, set.-' A = see Equation 7 f = see Equation 10 g = gravity acceleration, cm./sq. sec. p , = see Equation 6 p = see Equation 16 q = liquid flow rate per unit width, cc./sec. cm. Q = total liquid flow rate, cc.isec.
u = velocity, cm./sec. u p = slip velocity, cm./sec. y = distance from free surface, cm. a = plane inclination, degrees p = see Equation 13 6 = liquid layer depth, cm. X = solvent layer width, cm. p = viscosity, g . / c m . sec. pa = solvent viscosity, g . / c m . sec. p = density, g./cc. T = shear stress, g./cm. sq. sec. T~ = shear stress a t wall, g./cm. sq. sec. i = limiting shear stress in infinitely plastic fluid, g./cm. sq. sec .
literature Cited (1) Dodge, D. M’.,Ph.D. thesis, Univ. of Delaware, Newark,
Del., 1957. (2) Eissenshitz, R., Rabinowitsch, B., Weissenberg, K., Mitt. Deut. Materialpriifungsanstalt. Aust. Sonderh. 9 , 91 (1929). (3) Ferrari-Bravo, A., Lab. Notebook, 1st. Chim. Ind., Univ. of Naples, Italy, 1963. (4) Hoffman, R. D., Myers, R . R., Trans. Soc. Rheol. 4, 119 (1960). (5) Metzner, A. B., Reed, J. C., A . I. Ch. E . J . 1, 434 (1955). (6) Mililotti, G., Lab. Notebook, 1st. Chim. Ind., Univ. of Naples, Italy, 1963. (7) Mooney, M., J . Rheol. 2 , 210 (1931). (8) Paslay, R. R., Slibar, A., Trans. Soc. Rheol. 2 , 255 (1958). (9) Portalski, S., Chem. Eng. Sci.18, 787 (1963). (10) Rabinowitsch, B., Z . Physik. Chem. 145, 1 (1929). (11) Raitano, V., chem. eng. thesis, Univ. of Naples, Italy, 1963. (12) Schultz-Grunow, F., Rheol. Acta 1 , 289 (1958). (13) Severs, E. T., Austin, J. M., Trans. Soc. Rheol. 1 , 191 (1957). RECEIVED for review February 3, 1964 ACCEPTED June 24, 1964
EFFECT OF TEMPERATURE DRIVING FORCE ON HEAT TRANSFER T O A NONEQUILIBRIUM CHEMICALLY REACTING GAS P . L . T . B R I A N A N D S. W . B O D M A N Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
The film theory solution is presented for heat transfer accompanied b y a chemical reaction having a finite reaction rate. Results a r e obtained for the NO2 decomposition reaction, but the use of dimensionless groups in the analysis allows general conclusions to b e m a d e for other chemical systems. The dimensionless temperature driving force, X, is varied from 0 to 2, corresponding to a driving force of 0 to 190” F, for the NO2 system. The results for X 0.4 agree to within 3% with results of a linearized theory for X = 0, but results = 2 deviate from the linearized theory b y as much as 23%. for A modification of the linearized theory results in an approximating equation which agrees with all of the results to within 3.7y0.
