Heat Transfer Lab Report

tremulous STATE HEAT TRANSFER ignite give processes atomic number 18 prominent in engineering delinquent to several applications in industry and environment. soup up commute is central to the performance of propulsion frames, design of conventional space and urine warmthing systems, chill of electronic equipment, and numerous manu featureuring processes (Campos 3). Unsteady relegate conduction is the stratum of wake up transfer in which the temperature of the conducting forte varies with metre and gear up.This occurs frequently in industrial processes, especially nourishment preservation and sterilization, where the temperature of the food or of the disturbing or cooling strong point constantly changes (Farid2). The work report here involves the investigation of unsteady state heat transfer in dickens cylindrical rods and the conformity of data-based solvents to polar modes of theoretical psycho analytic thinking. aluminium and plexiglass piston chambers were utilise. Thermocouples were situated at different radial-ply tire and axile positions, and the piston chambers, which were in thermal equilibrium with an frost toilet, were placed in a strong water bath at 370C.Temperature profiles were throwed utilise a data acquisition system on a computer. Theory The applicable form of the heat transfer par for conduction in solids is given by (Welty1) If the thermal conductivity is constant and the conducting medium contains no heat addresss, comparability 1 reduces to Fouriers second law of heat conduction (Welty1).Equation 2 stomach be written in cylindrical coordinates as (3) Assuming that no heat transfer occurs in the axial position, and temperature varies with radial position and time only, (4) Equation 3 accordingly becomes (Welty1) (5) Nomenclature for all equations is video displayn in the appendices.For a cylindrical rod immersed in a higher temperature fluid, heat transfer occurs by convection from the body of flui d to the fold up of the rod, and by conduction from the rods surface to its center. If conduction through the rod occurs a lot faster than convection from the fluid, convection is the lay-limiting heat transfer mechanics, and the temperature inwardly the solid entrust vary with time only. This condition, in which the external defense is outsize carnal knowl edge to the overall opponent, is the primary characteristic of a lumped system.The Biot number, (Bi = hV/kA), is a ratio of the native (conductive) resistance to heat transfer, to the external (convective) resistance to heat transfer. A general recipe of thumb is that a body can be assumed to be lumped if Bi 0. 1 (Welty1). For lumped bodies, the temperature variation with time is expound by Equation 6 (Welty1) For cases in which the internal and external resistances be significant, Equation 5 must be lick mathematically or graphically to gibe the temperature variation with position and time.Graphical solutions (Heisler charts) are shown in Welty1 for different shapes and geometries. To use the Heisler charts, three dimension little ratios must be known, and a fourth will be read on the take over axis. These dimensionless ratios are Y, unaccomplished temperature change=T? -TT? -T0 (7) X, sexual congress time=? tx12 (8) n, sexual intercourse position=xx1 (9) m, relative resistance=khx1 (10)DISCUSSIONBefore the data was analyzed, the thermocouples were calibrated and the electromotive force readings were converted to temperature. To achieve this, the final set from individually thermocouple was set to be compeer to the warm water bath temperature (370C), and the initial reading was set equal to the ice water bath temperature. Thus, for each thermocouple an equation was obtained exploitation the devil points to convert voltage readings to temperature. An example of the normalisation for one of the thermocouples is shown in AppendixII. LUMPED ANALYSISTo determine if a lumped-paramete r synopsis could be applied, the Biot poesy for the systems were calculate (shown in Table 1). Table 1 Biot numbers for the aluminium and plexiglass cylinders. Bi Aluminum 0. 07 plexiglass 81 Since the Bi value of the aluminum system is less than 0. 1, convection from the water to the surface of the cylinder is the rate limiting heat transfer mechanism. Thus, a lumped-parameter analytic thinking can be safely applied. The plexiglass system, on the former(a) hand, has a Bi 0. 1, and the rate limiting mechanism is conduction in the cylinder.The temperature-time plot gotten by applying a lumped-parameter analysis (Equation 6) to the Aluminum cylinder was compared to the plot obtained from the thermocouple fixed hand-to-hand to center of the cylinder. This thermocouple is chosen for similitude be suffice it is laid utmostthest from the heating source and will have a temperature floor that differs most from an ideal lumped system. With this thermocouple, we should on that p ointfore obtain the maximum erroneousness associated with applying a lumped-parameter analysis to the system. routine 1 Temperature storey plot for the aluminum cylinder. The thermocouple is regain 0. 25 in away from the center. A lumped parameter analysis is in whatever case shown in send off 2 for the plexiglass cylinder to illustrate the misconduct encountered by applying Equation 6 to un-lumped systems. Figure 2 Temperature taradiddle plot for the plexiglass cylinder.COMPARING TEMPERATURE HISTORY AT DIFFERENT radial-ply tire POSITIONSBased on their Biot numbers, it was expected that the temperature tarradiddle plots at different radii for the aluminum cylinder should amount a similar path, trance those for the plexiglass cylinder shouldnt. Figure 3 observational temperature for the aluminum cylinder history at various radial positions. Figure 4 Experimental temperature for the plexiglass cylinder history at various radial positions. Figures 3 shows that the temperatu re curves are all the corresponding at different radii in the aluminum cylinder.This is attributed to the fact discussed earlier that the aluminum cylinder behaves as a lumped system, that is, there is negligible resistance to internal heat transfer (conduction). Figure 4, on the other hand, shows differences in the temperature history plots at different radii in the plexiglass cylinder, confirming that conduction through the cylinder is the rate limiting heat transfer mechanism.GRAPHICAL SOLUTION HEISLER CHARTSFor systems that cannot be accurately imitate by lumped-parameter solutions, such as the Plexiglas cylinder, we must resort to other analytic methods.Graphical solutions in Heisler charts (Welty1) were used to estimate the temperature history at three thermocouples. These plots are compared with the experimental plots in Figures 5 7. Figure 5 Experimental and graphical-solution temperature history plot. The thermocouple is located at a radius of 1. 25 in away from the cent er. Figure 6 Experimental and graphical-solution temperature history plot. The thermocouple is located at a radius of 0. 50 in away from the center. Figure 7 Experimental and graphical-solution temperature history plot. The thermocouple is located at the centerline of the cylinder.The part differences show that predicting the temperature history using Heisler charts produces lots fracture. This method was open to mistakes for the following reasons 1. Curves on the charts are drawn for integer set of relative time, position and resistance. Therefore, reading and approximation errors result when decimals to be read are not shown on the axes. 2.Some areas of the Heisler charts are so crowd with lines that reading a value with truth is nearly impossible. 3. When producing the charts, Heisler did calculations for some set of numbers and then linearly connected the points on a logarithmic-linear modified scale. Dimensionless ratios obtained from the charts are thusly meagerly diffe rent from their real values (Dilsiz4).NUMERICAL ANALYSIS MATLABEquation 5 was solved numericly using MATLAB. The code used is provided in Appendix IV. The solutions were extracted to Excel and plotted (Figures 8 and 9).The temperature plots at different radii for the aluminum cylinder are superimposed and therefore indistinguishable. This push demonstrates the fact that the temperatures at all points in the aluminum system were identical. Figure 9, on the other hand, shows that the Plexiglas had varying temperatures at different points. Figure 8 mathematical resolvent from for the aluminum cylinder. Results were arrange using MATLAB and plotted in Excel. Figure 9 Numerical Solution from for the Plexiglas cylinder. Results were found using MATLAB and plotted in Excel. The results obtained from the numerical analysis were compared with experimental data.Table 4 shows the clean percent differences between their values. The percent differences for the Plexiglas cylinder are signif icantly raze than those obtained when using the Heisler charts (see Table 3). This suggests that the numerical analysis using a partial derivative equation solver is a more than reliable method of analyzing the data for the Plexiglas cylinder. Table 4 Average percent differences between experimental results and the numerical analysis solution. Radius (in) Average % difference Aluminum Plexiglas 0 - 7. 54 0. 25 3. 68 5. 81 0. 5 - 5. 75 . 75 2. 99 - 1 3. 35 6. 34 1. 25 2. 27 4. 92 Average 3. 0725 6. 072CONCLUSIONThe rate limiting heat transfer mechanism for the aluminum and Plexiglas cylinders were convection and conduction, respectively. It was found that the temperature history for the aluminum cylinder conformed to a lumped-parameter analysis while that for the Plexiglas cylinder didnt. This was expected based on the Biot numbers calculated for the two systems. Temperature profiles obtained from Heisler charts produced much error, and deviated significantly from experimental data.For the Plexiglas cylinder, the numerical analysis using MATLAB, although tedious, provided the least error when compared to experimental results. The temperature histories at different radial positions were compared the temperature-time curves for the aluminum cylinder overlapped, that is, the temperatures were the same at different radial positions. On the other hand, there were significant differences in the temperature-time curves for the Plexiglas cylinder. This is attributed to the fact that the aluminum rod was lumped, while the Plexiglas wasnt.SOURCES OF ERRORIt was assumed that no heat was transferred through the ends of the cylinders. This may have generate some error in the analysis. If there was indeed significant heat transferred through the ends, two thermocouples placed at the same radius will report slightly different temperatures, with the one closer to the edge being heated faster. As discussed earlier, error is introduced when reading the Heisler charts. Th ese errors were considered minor, and were not substantial plenteous to affect the major conclusions drawn from the analysis.SAFETY CONSIDERATIONSThe proximity of water baths to electrical equipment presented an electrical hazard.It was fundamental to make sure not to release water when transferring the cylindrical rods between baths. We also made sure to move any movable electrical equipment as far as possible from the immediate area. The baths used werent hot enough to cause scalds upon contact with the skin. Safety glasses and closed-toed shoe were worn throughout the duration of the experiment.REFERENCES1. Welty, mob R. , Charles E. Wicks, Robert Wilson, and Gregory L. Rorrer. Fundamentals of Momentum, Heat, and Mass Transfer. impudently York Wiley, 2001. Print.2. Farid, Mohammed M. sterilization of Food in Retort Pouches. New York, NY Springer, 2006. Print.3. Campos, Marco, Estaner Claro Romao, and Luiz Moura. Analysis of Unsteady State Heat Transfer in the Hollow cyli nder Using the Finite Volume system with a Half Control Volume. utilize Mathematical Sciences 6. 39 (2011) 1925-931. Print.4. Dilsiz, Resul, and Onur Y. Devres. Graphical Solution of the Transient Heat Transfer Problem. AIP meeting Proceedings 1048. 855 (2008).