William S. Janna

Mass transfer from a sublimating naphthalene cylinder to a crossflow of air

Average Sherwood numbers based on experimental results were determined for a sublimating naphthalene cylinder subjected to a crossflow of air. The range of Reynolds numbers for all tested cylinders was from 4700 to 141 000. The nominal diameters of the tested cylinders were 25·4, 50·8 and 76·2 mm (i.e. 1, 2 and 3 inches respectively). The average uncertainty of the reported data was estimated to be ±9·7%. The experiments were performed using an open-loop wind tunnel. The test cylinders were cast using molten naphthalene and the test method involved naphthalene sublimation. The resultant expression is given in dimensionless form.

NEWTONIAN AND NON-NEWTONIAN FLUIDS: VELOCITY PROFILES, VISCOSITY DATA, AND LAMINAR FLOW FRICTION FACTOR EQUATIONS FOR FLOW IN A CIRCULAR DUCT

Newtonian fluid flow in a duct has been studied extensively, and velocity profiles for both laminar and turbulent flows can be found in countless references. Non-Newtonian fluids have also been studied extensively, however, but are not given the same attention in the Mechanical Engineering curriculum. Because of a perceived need for the study of such fluids, data were collected and analyzed for various common non-Newtonian fluids in order to make the topic more compelling for study. The viscosity and apparent viscosity of non-Newtonian fluids are both defined in this paper. A comparison is made between these fluids and Newtonian fluids. Velocity profiles for Newtonian and non-Newtonian fluid flow in a circular duct are described and sketched. Included are profiles for dilatant, pseudoplastic and Bingham fluids. Only laminar flow is considered, because the differences for turbulent flow are less distinct. Also included is a procedure for determining the laminar flow friction factor which allows for calculating pressure drop. The laminar flow friction factor in classical non-Newtonian fluid studies is the Fanning friction factor. The equations developed in this study involve the Darcy-Weisbach friction factor which is preferred for Newtonian fluids. Also presented in this paper are viscosity data of Heinz Ketchup, Kroger Honey, Jif Creamy Peanut Butter, and Kraft Mayonnaise. These data were obtained with a TA viscometer. The results of this study will thus provide the student with the following for non-Newtonian fluids: • Viscosity data and how it is measured for several common non-Newtonian fluids; • A knowledge of velocity profiles for laminar flow in a circular duct for both Newtonian and non-Newtonian fluids; • A procedure for determining friction factor and calculating pressure drop for non-Newtonian flow in a duct.Copyright

Determination of Discharge Coefficient for Ball Valves With Calibrated Inserts

The valve coefficient was measured for 1, 1-1/4, 1-1/2 and 2 nominal ball valves. A recently designed orifice insert was used with these valves to obtain smaller valve coefficients. Orifice inserts were threaded into the body of a ball valve just upstream of the ball itself. The valve coefficient was measured for every insert used with these valves, and an expression was determined to relate the orifice diameter to other pertinent flow parameters. Two dimensionless groups were chosen to correlate the collected data, and expressions were developed that can be used as aids in sizing the orifice insert needed to obtain the desired valve coefficient. The study has shown that a 2nd order polynomial equation as well as a power law equation can both be used to predict the desired results. Knowing pipe size and schedule, the diameter of the orifice insert needed to obtain the required valve coefficient can be approximated with minimum error. An error analysis performed on the collected data shows that the results are highly accurate, and that the experimental process is repeatable.Copyright

Mass transfer from a sublimating p-dichlorobenzene or naphthalene cylinder to a crossflow of air

The average Sherwood number as a function of the Reynolds number was determined experimentally for a sublimating cylinder exposed to a cross-flow of air. The sublimation technique was used to obtain the mass transferred from the cylinder to the air. The test cylinder was fabricated of either naphthalene or p-dichlorobenzene. The resultant body of experimental data was characterized by the expression Sh = 0·278Re0·628 with a correlation coefficient of 0·99. The Schmidt number Sc was assumed to be constant for each chemical. Uncertainty analysis indicated that the experimental value of the Sherwood number lay within 9·7% of the true value. The Sherwood number ranged from 55 to 600 for a Reynolds number range of 4720-160000.

Parametric study of heat transfer to an ice cylinder melting in air

A cylinder of ice was formed and suspended by a string from the end of a cantilevered beam. The beam had strain gages attached that were calibrated so that the weight of the ice cylinder was known during the time that it melted. Data on weight versus time were thus obtained and used to calculate values of Nusselt and Rayleigh Numbers over discrete intervals of time. The geometry of the ice cylinder precluded an exact determination of surface area and characteristic length for the time interval of interest. Consequently, three proposed expressions for characteristic length were tried and the one that yielded the highest correlation between Nusselt and Rayleigh numbers was selected as giving the best description. An equation was derived for each case.

Heat transfer from turbulent water flow in a tube to a cooled isothermal wall

Abstract A device was constructed to establish a constant wall temperature for the isothermal cooling of the turbulent flow of water in a tube. The flow was fully developed hydronamically but developing thermally. Data obtained were used to derive an equation to predict the Nusselt number using the method of least squares. An existing equation for developing flow was tested to determine how well it fit the data. The derived equation of this study has a correlation coefficient of 0.877 and a standard deviation of 19.0.

Calculations of Pressure Drop in a Circular Duct Using the Traditional Method Compared to That Using the Constricted Flow Diameter

The traditional method of calculating pressure drop in a pipe that conveys a fluid involves use of the Moody Diagram. This diagram is a correlation of data with friction factor plotted as a function of Reynolds number and relative roughness. A new graphical representation of these data has been formulated, and makes use of what is known as the constricted flow diameter. The background for this new correlation is based on using a pipe diameter less twice the average roughness height. A new “modified” Moody Diagram has been produced based on the constricted flow diameter. The presence of roughness features on the inside pipe wall has an effect on the flow along the pipe surface which is not accounted for in the traditional Moody diagram. The new diagram accounts for this effect. To demonstrate the use of the new diagram, several example problems have been formulated and solved using the traditional and the modified diagrams. Calculations indicate that at the smaller pipe sizes, the use of the constricted flow diameter yields significantly different results from those obtained in the traditional way. These results have a major influence on modeling flows in mini- and in micro-channels. Laminar and turbulent flows are both affected.Copyright

Collaboration of Technical Editing Students With Mechanical Engineering Seniors in a Capstone Design Course

An innovative capstone design course titled “Design of Fluid Thermal Systems,” involves groups of seniors working on various semester-long design projects. Groups are composed of 3 or 4 members that bid competitively on various projects. Once projects are awarded, freshmen enrolled in the “Introduction to Mechanical Engineering” course are assigned to work with the senior design teams. The senior teams (Engineering Consulting Companies) function like small consulting companies that employ co-operative education students; e.g., the freshmen. In Fall 2006, the Engineering Consulting Companies also worked with students enrolled in a Technical Editing (TE) course—“Writing and Editing in the Professions”—within the English Department. The TE students would be given reports or instructional manuals that the Mechanical Engineering (ME) students had to write as part of their capstone project, and the resulting editing of their documents would be done by these TE students. Subsequently, the ME students were given a survey and asked to comment on this experience. In addition, the TE students were also surveyed and asked to comment as well. It was concluded that the collaboration should continue for at least one more cycle, and that the TE students were more favorably inclined toward this collaboration than were the engineering students.Copyright

A “Boundary Layer” Method of Obtaining an Approximate Solution to the Infinite Fin Problem

The classical infinite fin problem is considered in this study. First the exact solution is stated in which temperature, heat transfer rate, effectiveness and fin efficiency are all given. Then the boundary layer method is used to obtain alternative solutions in polynomial form. Boundary conditions are written for this method, and applied in various combinations to an assumed temperature profile. First, second, and third order approximate solutions are derived. Temperature profiles obtained from these solutions are compared to that calculated from the exact solution. It is shown that as more terms are included in the assumed profile, the resultant expression better fits the exact solution. Very good agreement between the third order and exact solution was obtained. Also derived from the approximate solutions was a distance along the fin beyond which the temperature difference between the fin and the surroundings is negligible. This arbitrary distance is analogous to the boundary layer thickness for boundary layer flow over a flat plate.Copyright

A ‘Boundary Layer’ Method for Obtaining an Approximate Equation for the Velocity–Time History of an Accelerating Sphere

A sphere starting from rest in a stationary fluid accelerates under the action of gravity and eventually reaches a terminal velocity. The descriptive equation for the acceleration of the sphere is a first order, non-linear, ordinary differential equation, which can be solved using a finite difference scheme. In this study, we present a method (obtained from boundary layer methods) of generating a velocity—time equation to obtain an alternative solution. The method is used to solve a specific example and the results are compared to those obtained with the numerical solution. The comparison yields a small error, and so the polynomial approximation method can be used as an alternative technique to describing the motion of an accelerating sphere. The accelerating sphere problem is usually encountered in a study of flow past immersed objects. Boundary layer methods are usually taught at the graduate level. The advantage of the method presented here is that boundary layer methods can be introduced to undergraduates in a first or second course in fluid mechanics.