An evaluation of methods for predicting turbulent heat transfer in rough pipes has been made with the intention of obtaining a better understanding of the transfer processes involved and of providing a general design equation, valid for all types of roughness shapes and distributions. The equations of Martinelli, Nunner, and Mattioli, along with an empirical method suggested by Epstein, have been tested using the available experimental data. In addition, particular attention has been given to a proposed method which makes use of the velocity profile equations of Rouse and von Karman in Lyon's fundamental equation for the Nusselt number. The results indicate that the proposed method is not successful, largely because of ignorance of velocity conditions near the walls of rough pipes. Mattioli's equation also does not give a satisfactory correlation of experimental results. Epstein's empirical method, which, in the pertinent dimensionless groups, uses friction velocity and equivalent sand-roughness height of the roughness elements in place of the average fluid velocity and the pipe diameter, respectively, shows promise but requires further investigation. Nunner's equation and Martinelli's (simplified) equation give good prediction of the experimental results and are recommended for use at present, providing 0.5 < Pr < 1.0. The success of these latter equations gives support to the hypothesis that the fluid adjacent to a rough wall is probably in laminar motion. Using Nunner's model of the flow conditions in rough pipes, equations have been derived for predicting temperature profiles from velocity profile data. Generally, the absolute agreement between predicted profiles and Nunner’s experimental profiles is good, but the influences of Re and especially f are not too well accounted for. Nunner's conclusion that temperature and velocity profiles in rough pipes are not similar is substantiated by the results. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

Experimental measurements have been made of the simultaneous rates of mass and heat transfer for the surface evaporation of water into air from a simple cubic, a rhombohedral, and two orthorhombic assemblages of uniform celite spheres, in the particle Reynolds number range 300-1200. The measurements were confined to the pre-determined constant rate drying period of the spheres. No appreciable differences in mass and heat transfer factors were found for the various assemblages, except for the cubic, which exhibited lower transfer factors at the higher Reynolds numbers. This is explained qualitatively by the fact that the cubic configuration shows a considerably larger free projected cross-sectional area than the others, thus allowing for greater fluid channelling. Various methods proposed by investigators of randomly packed beds for correlating mass transfer by the inclusion of fractional void volume functions in the mass transfer factor and/or the Reynolds number were tested for the stacked assemblages. None of these methods completely correlated the results. Galloway's fluid friction data for the two orthorhombic assemblages were recalculated and showed similar friction factors to those obtained by Martin for identical packings of brass spheres. Ergun's criteria for complete and for no longitudinal fluid mixing were applied to the various assemblages. The results for the cubic assemblage suggest the possibility of considerable air mixing therein. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

Heat, mass and momentum transfer rates have been measured in two stacked beds of porous spheres having equal fractional void volume but different orientation with respect to the direction of fluid flew. An air-water system was studied under essentially adiabatic conditions over a Reynolds number range 100-1200. Orientation had negligible effect on heat and mass transfer rates though considerable effect on friction factor. An explanation for this behaviour is presented in terms of a difference in the degree of turbulent wake formation for the two assemblages, similar to that observed in comparable banks of closely packed staggered and in-line heat exchanger tubes. The experimental results contradict simple analogies between momentum, heat and mass transfer which show a direct proportionality between total friction factor and heat and mass transfer factor. Measured friction factors were about 50% in excess of those obtained by Martin for similar assemblages of smooth metal spheres. This is explained by the higher surface roughness of the refractory-like spheres used in the present investigation. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

Heat transfer and friction data were obtained for air flow through seven commercial pipes with equivalent sand roughness ratios varying from 0.020 to 0.00041 in the Reynolds number range 10,000 - 80,000. Heat transfer for a given power loss decreased with increasing roughness ratio except at very high power losses, where this trend was to some extent reversed. The results for the Karbate pipe were somewhat out of line with those for standard pipes. This is attributed to a difference in the nature of the Karbate roughness. In the plots of friction factor and j[subscript H] versus Reynolds number, the experimental data show that j[subscript H] continues to decrease with Reynolds number when friction factor has become constant for a rough pipe. This fact contradicts not only Reynolds' simple turbulence analogy and Colburn's modification thereof, which are in other respects inapplicable, but is also at odds with the more rigorous analogy of Taylor and Prandtl and the similar, semi-empirical equation of Pinkel. It is, however, in agreement with the Karman analogy, which also gives a good absolute prediction of the heat transfer data. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

Heat transfer measurements were made in a heat exchanger where air flows parallel to an unbaffled tube bundle and where steam is condensing inside the tubes. The tubes were one-inch outside diameter and were arranged in a square lattice with one-inch clearance between adjacent tubes. The Reynolds Number range covered in this investigation was 630 - 8220. Pseudo-j(h)-factors have been calculated for the air film in the central unit cell and are presented along with the results of Miller et al and Inayatov and Mikeev, who worked with other lattice arrangements. The present data are insufficiently numerous and too unreliable for empirical correlation, but they do show a trend which is consistent with the work of the above investigators. The temperature measurements showed an apparent dissymmetry inside the shell of the heat exchanger, and suggestions are made for the improvement of these measurements for more dependable results. Further work that can be done, using the present set-up with slight modifications, is also cited. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

This work considers the conjugate convective heat transfer between a sphere containing heat sources and a concentric envelope maintained at a specified constant temperature. The space between the two is filled with an essentially incompressible fluid. Steady, laminar and rotationally symmetrical free convection is assumed to take place over the gap width and conduction is the sole transport mechanism considered inside the core. Two limiting cases, of an inner sphere of infinitely large relative heat conductivity, leading to an isothermal core to fluid interface; and of the converse case of small conductivity leading to a constant flux interface are considered separately. The analysis of heat transport leads to the solution of the governing equations through regular perturbation expansions with the Grashof number as main parameter. The ratio of conductivities, radius ratio and Prandtl number appear as secondary parameters. Streamlines, isovorticity curves and isotherms are obtained for various combinations of the parameters. The velocity distribution is determined and both local and overall values of the Nusselt number are obtained. A flow visualization test was undertaken and the core surface temperature distribution was determined experimentally. Reasonable qualitative agreement with the analysis is found. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This thesis presents experimental results of combined free aid forced convection laminar heat transfer for water flowing through a circular horizontal tube with uniform wall heat flux. The Reynolds number ranged from 100 to 2000, and changes in heat transfer rate allowed a variation, of Grashof number from 300 to 30,000. The Prandtl number ranged from 4 to 9. The effect of secondary flow created by free convection occurring at higher Grashof number indicates an increase in Nusselt number up to 200 per cent. For the fully-developed region two tentative correlations are given. The expression Nu = 48/11 + 0.047 Pr¹′³(Re Ra)¹′⁵correlates 53 per cent of the data to within ± 10 per cent. Another slightly more accurate expression which correlates 68 per cent of the data to within ± 10 per cent, but does not satisfy the pure forced convection, is Nu = 2.41 + 0.082 Pr¹′³ (Re Ra)¹′⁵. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A theoretical analysis and experimental results are presented for .free convection and combined free and forced convection from a heated horizontal surface. The principal objective was to investigate a laminar boundary layer flow which had been shown, theoretically only, to form above a heated surface. This boundary layer flow is fundamentally different from flows above inclined or vertical surfaces since the driving force or buoyancy force acts perpendicular to the primary boundary layer motion. The flows analyzed are those for which the system of partial differential equations describing the flow can be reduced to simultaneous total differential equations. The method involves the introduction of similarity parameters and then the numerical integration of the resulting simplified system of total differential equations. These solutions are restricted, for 2-dimensional flow, to a semi-infinite surface, and for axially-symmetrical flow, to an infinite disc. In conjunction with the former only free convection is considered while for the latter combined convection is considered as well. The flow was examined experimentally with a semi-focusing colour schlieren system. From the photographs it may be concluded that the semi-infinite surface analysis would correctly portray a physical flow. The flow, though, remains laminar for a short distance only and then breaks down into an unstable cellular pattern. The axially-symmetrical analysis, although it yielded analytically a valid boundary layer solution, appears to have no physical parallel above a disc of finite radius. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This thesis presents a study of some of the factors affecting direct contact, liquid-liquid heat transfer from a continuous phase of 0.0%, 56.02%, 73.07%, and 77.06% glycerine-water solutions to a dispersed phase, which is vapourizing, of isopentane or cyclopentane. An average heat transfer coefficient based on the initial area, the total evaporation time, the total heat transferred, and the .temperature driving force at the end of evaporation was calculated. This coefficient was correlated to the parameters of the systems by the dimensionless groups of continuous phase Prandtl number, dispersed phase Prandtl number, and a viscosity ratio. The results are compared to the works of Klipstein, Sideman and Prakash. A comparison made between the photographic and dilatometric method of volume measurement showed the dilatometric method to be the best for this type of work. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

The effects of viscous dissipation on the flow phenomena and heat transfer rate for fully developed laminar flow through vertical ducts and passages has been analysed under the condition of combined free and forced convection. The fluid properties are considered to be constant except for the variation of density in the buoyancy term of the momentum equation. The thermal boundary condition of uniform heat flux per unit length in the flow direction has been considered. The investigation is carried out for two geometries; (a) Circular ducts and (b) Concentric annuli. The governing momentum and non-linear energy equations are solved for the circular duct by three methods; (i) Power Series Method (ii) Galerkin's Method and (iii) Numerical Integration Method. The solutions for the concentric annuli are obtained by Numerical Integration Method. Results for the velocity and temperature distribution in the flow field are obtained, and information of engineering interest like Nusselt numbers have been evaluated. For combined free and forced convection, the momentum and energy equations are coupled, and hence viscous dissipation affects both the velocity and temperature fields. The effect of viscous dissipation on the velocity field is to reduce the flow velocity near the heated wall(s) and thus it counteracts the effect of free convection on the velocity field for the present study of heating in upflow. The effect of viscous dissipation on the temperature field is to act as a heat source in the fluid and reduce the temperature differences in the system. Viscous dissipation opposes the externally impressed heating and reduces the heat transfer rate when the surface transfers heat to the fluid. Consequently, lower Nusselt number values are obtained when viscous dissipation is taken into consideration. The quantitative effect of viscous dissipation on Nusselt number is found to be small for the case of circular ducts. However, for flow through annular passages and for the corresponding values of the same parameters, the effect of viscous dissipation on the heat transfer rate may not be ignored. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate