EFFECTS OF PRESSURE ON NATURAL CONVECTION FROM

The" board of examiners hereby recommends to the Department of Mechanical Engineering, BOOT, Dhaka, acceptance of the thesis, "Effects of pressure on natural convection from an inclined isothermal cylinder in" an inert environment", submitted by A. Ahsan Mian, in partial compliance with the requirements for the degree of Master of Science in Mechanical Engineering. This is to certify that the work presented in this thesis is the outcome of the investigations carried out by the candidate under the guidance of Dr.

The author appreciates the cooperation of the university staff during the drafting and preparation of the dissertation. From the experimental results, correlations are developed in terms of Nusselt number, Rayleigh number and cylinder slope. 'Heat Transfer' estimates the rate at which heat is transferred across system boundaries, subject to specific temperature differences, and the temperature distribution of the system during the process.

All of the above equipment requires the application of the first law of thermodynamics, material data, and heat transfer relationships appropriate to the specific system.

1.3 . Heat Transfer from Cylinders

Horizontal Cylinders
Vertical Cylinders
Inclined Cylinders
Basis of Tile Present Work Selection
Objectives of the Present work

Heat transfer from hot radiators, cooling coils, transmission lines, electrical transformers, electrical heating elements and electronic equipment are typical examples. The necessity of studies of the heat transfer behavior at ambient pressure other than atmospheric lies in the availability of pressure and vacuum producing equipment and the vacuum processes in food, pharmaceutical, metallurgical and other industries. Inclined pipes and pipes carrying steam, hot or cold chemicals are common examples of heat transfer from or to the inclined cylindrical surface.

Many studies have been conducted on natural convection heat transfer from the outer surface of a vertical or horizontal pipe at constant temperature and constant heat flux at atmospheric pressure. In addition, almost very little research has been done on the behavior of heat transfer in a fluid other than air and at higher or lower atmospheric pressures. Experimental studies are therefore essential to observe changes in heat transfer due to the above physical or environmental changes.

Design of an experimental procedure to determine the average heat transfer coefficient for various inclined cylinders including horizontal and vertical cylinders.

Chapter - II

Literature Review

General
Vertical Plates
Horizontal Plates
Inclinded Plates
Vertical Cylinder
Horizontal Cylinders
Inclined Cylinders
At Pressures other than Atmospheric
Variable Fluid Properties

Bayazitoglu and Ozisik reported that Mc Adams had proposed the following simple correlation for heat transfer by free convection on a vertical wall of height L maintained at a uniform temperature. Hyman has established a simpler equation for heat transfer from horizontal cylinders to liquid metals. AI-Arabi and Salman developed correlating equations based on experimental data for convective heat transfer in the laminar range.

Heat transfer was determined by measuring the cooling rate of the cylinders from 100 to 90.C. The average heat transfer was found to increase with trend and the results can be related in terms of NuD/(GrD sin )1/4 versus (LID) tane. For the same length and slope of the cylinder, the average heat transfer coefficient decreases as the diameter increases.

For the same length and diameter of the cylinder, the average coefficient of thermal conductivity hL increases by wi!!' ~inclination angle e, for larger lengths. Based on the average heat transfer, the critical transition point from the laminar region to the turbulent region is independent of the cylinder diameter. For the same heat flux, both the local and average heat transfer coefficients increase with slope.

Chapter - III

Mathematical Modeling of the Problem

General
Description of the problem
Similarity Analysis
Modification of the Similarity Equations for the Present Problem

Heat was transferred from the sample to the ambient atmosphere of the vessel by natural convection. This procedure was repeated 14 times to obtain 14 sets of readings at each cylinder tilt. The same sequence was followed for different cylinder inclinations and different ambient gases.

The exact solution of the equations mentioned in Article 3.1 is very complicated, but the parameters on which the flow and transport characteristics depend can be found using the similarity technique. The quantity Gr = gj3L3!J.t/v' is called the Grashof number and is a measure of the force of the induced flow, as indicated by D. The Grashof number is essentially the ratio between the relative quantities of the viscous force and the convection of momentum terms.

The Prandtl number Pr = ~CpIk, appears in the energy equation and indicates the steepness of the temperature gradients in the flow field. The additional amount Ec=gj3L/Cp arises as an indication of the relative importance of viscous dissipation. In the above NusseIt number equation, the viscous dissipation factor Eckert number is almost constant as changes in 13 and Cp are negligible for the present situation.

In the present case physical dimensions remain the same while the changes in density (other properties remaining the same) are brought about by changing the pressure. Now for surfaces other than vertical, the slope 8 can be included in the Nusselt number equation 3.8. Since the slope of the cylinder 8 tends to zero, D/2 becomes Cosec8 L and UJ-/v becomes -VGrLas was discussed earlier.

For cylindrical surfaces, the theoretical analysis is quite complicated and is not available in the literature. Thus, instead of deriving separate differential equations, the flat plate similarity solution will be applied to cylindrical surfaces to correlate dimensionless parameters based on experimental data.

Chapter - IV

General Description

4.2 Test Specimen

Temperature Measuring Devices

The temperature of the cylinder and surrounding liquid was measured directly by two independent digital thermometers, equipped with radiation and convection heat transfer equipment. Since the air outside the vessel was steady and both the outside air and interior gas were in equilibrium with the vessel, the vessel temperature could be taken as that of the undisturbed interior ambient fluid. At steady state, the heat generated by the heater in the test cylinder was equal to the heat conducted through the vessel wall to the outside air before significant rise in the interior fluid temperature was noted.

Pressure Measuring and Control Devices

Input Heat Tvi.cilsunng Devices

Chapter - V

Test Procedure

Measurement of Temperature

5.2 !Estima~on of Emissivity

Measurement of Pressure
Setting of Inclination of specimen
Determination of Heat Transfer Coefficient

Measurement of Input Power
Estimation of Conduction Loss
Estimation of Radiation from the Cylinder

Test Procedure

The top cover plate of the spherical container is attached to the container with twelve bolts fixed on it. To set a given inclination of the test cylinder, the cover plate was opened and the supporting flexible wire length was adjusted. For 30°, 45° and 60° inclinations, one supporting wire length was kept fixed and the other wire length was reduced by Lcos8 from the length of the wire in the horizontal position.

The electrical energy introduced into the test cylinder was transferred partly to the sealed container by radiation, partly to the thermocouples and supporting wires by conduction, and the rest to the ambient fluid by convection. After obtaining the convective heat transfer rate, the convective heat transfer coefficient was determined by dividing the convective heat transfer rate by the area product of. To get the power input to the test cylinder a special wattmeter was used to measure the actual power consumed by it.

Since thermocouples were attached to the surface of the test cylinder, part of the energy generated in it was conducted through the thermocouples and holding wires to the surrounding fluid. A significant portion of the heat input to the cylinder was transferred by radiation to the container enclosure. Five orientations of the test cylinder with inclination angles of and 90' to the vertical were investigated at a constant surface temperature of 91.5'C.

The two ends of the test cylinder were connected to supporting wires hanging vertically down from the inside of the cover plate. The thermocouple attached to the midpoint of the cylinder was connected to the digital configuration indicator. The heater line plates were bolted to the cover plate.

To align the cylinder with a 30° tilt, one of the supporting flexible wire lengths was kept fixed (160 mm) and the other wire length was reduced by an estimated amount of Lcos30°. To perform the experiment in the vertical position of the test cylinder, one length of carrier wire was released while the other wire length was kept at 160 mm.

Chapter - VI

Results And Discussions

Similar nature of the graph was found for all the other trends and hence they are not presented. This shows that the variations of the observed heat transfer coefficients with pressure are logarithmic. At low pressure, the density of the gas decreases and therefore the extent of convection decreases with almost constant radiation.

It is seen that with the increase of slope with vertical, the heat transfer rate increases. As the slope decreases, the thickness of the boundary layer on the cylinder surface increases. The pattern of heat transfer from the upper surface of the cylinder is unaffected by tilt except at vertical, but the pattern of the lower surface is greatly affected.

From the lower half of the cylinder, the liquid particles cannot move directly upwards, they must overcome. As the plume travel increases, it has been analytically shown in the literature that the heat transfer coefficient decreases. That is, as the extent to which fluid particles remain in contact with the solid along the direction of flow increases, so does the thickness of the boundary layer.

There are five curves in the figure corresponding to five slopes of the test cylinder. Just like the heat transfer coefficient as in Figure 2, the Nusselt number also increases with the increase in slope and with the increase in pressure. Here the variation of conductivity k is almost insignificant and therefore the heat transfer coefficient will be almost proportional to the I Nusselt number if the length of the cylinder is the same.

Despite the skewness of the data, linear curve fitting for log-log plots yields correlation coefficients of 0.99 or better. Rayleigh number obtained from Arabi and Salman data". The nature is similar to the plot of the present work.

Chapter - VII

Conclusions And Recommendations

Conclusions

Recommendations

Syful: Study of the Effects of Pressure on Natural Convepion Heat transfer, I from an Inclined cylinder placed in an Inert Atmosphere, M. Oosthuizen, P.H.: Experimental study of free convection Heat Transfer fron inclined cylinders, Journal of Heat Transfer, 1989, pp. Warner, c.Y., and Arpachi, V.S., “An experimental investigation of turbulent natural convection in air at low pressure along a vertical heated flat plate,.

White, D.H.: "An Experimental Investigation of Natural Convection HT from vertical flat plates in Mercury", Ph.D.

Appendix - A

Correction Factors

Appendix B

Emissivity Estimation