_31-52_ Yasin K. Salman 31 Free Convective Heat Transfer with Different Sections Lengths Placed at the Exit of a Vertical Circular Tube subjected to a Constant Heat Flux Yasin K. Salman Hussein A. Mohammed Baghdad University Baghdad University, College of Engineering College of Engineering Nuclear Eng. Dept., Baghdad- Al-J aderyia , Iraq Baghdad- Al-Jaderyia, Ir aq (Received 24 January 2006; accepted 11 June 2007) Abstract: A free convective heat transfer from the inside surface of a uniformly heated vertical circular tube has been experimentally investigated under a constant wall heat flux boundary condition for laminar air flow in the ranges of RaL from 6.9 × 108 to 5 × 109. The effect of the different sections (restrictions) lengths placed at the exit of the heated tube on the surface temperature distribution, the local and average heat transfer coefficients were examined. The experimental apparatus consists of aluminum circular tube with 900 mm length and 30 mm inside diameter (L/D=30). The exit sections (restrictions) were included circular tubes having the same inside diameter as the heated tube but with different lengths of 600 mm (L/D=20), 900 mm (L/D=30), 1200 mm (L/D=40), 1500 mm (L/D=50), and 1800 mm (L/D=60). It was found that the surface temperature along the tube axial distance would be higher for restriction with length of 1800 mm (L/D=60) and it would be smaller for the restriction with length of 1200 mm (L/D=40). The results show that the local Nux and average Nusselt number Nu were higher values for the restriction with length of 1200 mm (L/D=40) and smaller values for the restriction with length of 1800 mm (L/D=60). The results were correlated with empirical equations and presented as Log LNu against Log LRa for each case investigated and a general empirical equation was proposed for all cases. Keywords: Experimental study; Free Convective; Different sections length; Vertical Circular Tube; Constant Heat Flux. Introduction Free convective heat transfer has always been of particular interest among heat transfer problems. In free convection process, fluid motion is caused by density variations resulting from temperature difference between the fluid and the contacting surface. Many experimental studies have been performed during the last contacting surface. many experimental studies have been performed during the last Al- Khwarizmi Engineering Journal Vol.3 , No3. , pp 31-52(2007) Al- Khwarizmi Engineering Journal Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 32 three decades and interesting results have been presented. The free convection from cylinders or tubes of circular shapes have been receiving growing interest in the last few decades because of its employment in many practical fields in the area of energy conservation, design of solar collectors, heat exchangers, nuclear engineering, cooling of electrical and electronic equipments and many others, Kakac (1987). Heat transfer studies of free convection from circular tubes are necessary for better thermal design of industrial applications. Although some theoretical and experimental investigations have been published it is to be noted that they are far from sufficient. Experiments using different fluids and different values of length to diameter ratio in both the isothermal surface and the constant wall heat flux conditions are still needed to enable a complete investigation of the problem. Therefore, the present work was carried out in an attempt to fill a part of the existing gap and provides experimental data by experimentally investigating free convection heat transfer from the heated inside surface of a vertical tube to air at constant heat flux. The available work on free convection from the inside surfaces of vertical tubes open at both ends with restriction at exit is limited. However, most of the available investigations are theoretical and deal with the vertical tube in special cases only. To the authors knowledge limited prior work is available on this case, which studied in the present work. Oliver (1962) investigated experimentally laminar flow of relatively non-viscous Newtonian liquids through a vertical jacketed tube. It was shown that better agreement was obtained when the ratio D/L is omitted from the group and further improvement results from the incorporation of the ratio L/D, all the data being adequately represented by an empirical equation. This equation becomes inaccurate when Gzm < π Nuam and it should be mentioned that the power of L/D is only provisional ( ) 0.14 1/ 34 0.7w m m m mNu 1.75 Gz 5.6 10 (Gr Pr L/ D) β µ µ −   = + ×     (1) Martin (1965) made predictions of the lower limiting conditions of free convection in the vertical open thermosyphon of circular cross-section with uniform wall temperature. The overall heat- transfer rate was independent of tube length but proportional to radius, unless the length- radius ratio is below about 1·8, in which case it depends also on temperature conditions at the closed end. The corresponding Rayleigh number was estimated for non-metallic fluids and for a liquid metal. But, Dyer (1975) presented a theoretical and experimental study of laminar air flow natural convective in heated vertical ducts. The temperature and velocity fields and the relationship between Nu and Ra numbers were obtained by solving the governing equations by a step- by-step numerical technique. The influence of Pr number was discussed. Experiments were conducted for Ra number between 1 to 13000. Three ducts were used of different sizes and these ducts were 19.1, 25.4, and 46.7 mm in internal diameter and were all 1220 mm in long. Comparison between experimental and theoretical studies was carried out and showed good agreement. Kokugan and Kinoshita (1975) performed experimental work in a heated vertical open tube consisting of heated section at constant wall temperature. Correlations between Gr and Re numbers were derived by setting up a mechanical energy balance in the tube. The following equation was proposed: 2 o o H o oGr 6.3 Re 3.2( L L ) /( D. Re )= + + . (2) Where: LH =heated length; Lo= entrance length and subscript (o) denoted to at room temperature. The results were compared with available numerical results. Hess and Miller (1979) carried out experiments using a Laser Doppler Velocimeter (LDV) to measure the Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 33 axial velocity of a fluid contained in a cylinder subject to constant wall heat flux on the side walls. The modified Rayleigh numbers ranged between 4.5×109 to 6.4×1010, which corresponds to the upper limit of the laminar regime. The variations of axial velocity with radius for different heights in the bottom and top parts of the cylinder and inside the thermal boundary layer region and with radius for different time were presented. The variation of radial position of maximum velocity and radial position of zero velocity with Rayleigh number were also depicted. Excellent agreement was obtained with the available numerical solution. Shigeo and Adrian (1980) studied experimentally natural convection in a vertical pipe with different end temperature with (L/D=9). The Rayleigh number was in the range 108 Tb heat is transferred to the fluid and Tb increases with x, if Ts < Tb the opposite is true. For constant heat flux (q) it follows the right hand side of Eq. (4) is a constant independent of the distance (x), hence, bd T q. p dx mCp = & ……………….………… (5) by integrating from x=0, it follows that b b ,i q. p T ( x ) T x mCp = + & ……………….…. (6) Accordingly, the bulk temperature varies linearly with the distance (x) along the tube. Moreover, from s bq h ( T T )= − …………………………..(7) Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 37 The temperature difference (Ts-Tb) varies with the distance (x). The difference is initially small (due to the large value of the heat transfer coefficient at the tube entrance) but increases with increasing the distance (x) due to the decrease in heat transfer coefficient that occurs as the thermal boundary layer develops as has been reported by Incropera and DeWitt (2003). The readings of all thermocouples were taken by a precalibarted digital temperature recorder capable of reading 0.01 °C via a multi-switch. The apparatus was mounted in a closed room with plastic transparent shields (2) as shown in Fig. 1a to prevent currents of air, and the measuring instruments were mounted outside of this room. The input electric power to the heater was controlled and changed by the AC variac at each experiment and measured by a digital wattmeter with a resolution of 0.01 W. The steady state condition for each run was achieved after 4 approximately hours. The steady state was considered to be achieved when the temperature reading of each thermocouple did not change by more than 0.5 °C within 20 minutes. When the steady state condition was established, the readings of all thermocouples, the input power and the inlet and outlet bulk temperatures were recorded. Experimental Uncertainty Generally the accuracy of experimental results depends upon the accuracy of the individual measuring instruments and the manufacturing accuracy of the circular tube. The accuracy of an instrument is also limited by its minimum division (its sensitivity). In the present work, the uncertainties in heat transfer coefficient (Nusselt number) and Rayleigh number were estimated following the differential approximation method reported by Holman (2001). For a typical experiment, the total uncertainty in measuring the heater input power, temperature difference (Ts-Ta), the heat transfer rate and the circular tube surface area were 0.38%, 0.48%, 2.6, and 1.3% respectively. These were combined to give a maximum error of 2.43% in heat transfer coefficient (Nusselt number) and maximum error of 2.36% in Rayleigh number. Data Reduction In the present work the following steps were used to analyze the natural convection heat transfer process for air flow in a vertical circular tube when its surface was subjected to a constant wall heat flux boundary condition. The total input power supplied to the heated tube can be calculated: 2 tQ I R = × ……………………………..(8) The convection heat transferred from the heated tube surface: conv. t cond .Q Q - Q= ……………………. (9) Where: Qcond. is the total conduction heat losses (lagging and ends losses) and its calculated from ( )cond . thQ T / R∆= Where: fiberglass layer asbestos layerT T T∆ = − and Rth is the thermal resistance of the insulations o i th insulations ln( r / r ) R 2 k Lπ = Where: ro is the outer radius of the heated tube and ri is the inner radius of the heated tube. It was found that the conduction heat losses from the heated section are approximately about 4% of the total input power. The convection heat flux can be represented by: Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 38 conv . conv . s Q q A = ………………….. (10) Where: As= π × D× L The convection heat flux, which is used to calculate the local and average heat transfer coefficient as follows: conv. x sx bx q h T T = − ……………..……. (11) Where: Tsx is the local surface temperature, and Tbx is the local bulk air temperature. All the air properties were evaluated at the mean film temperature as reported in Cengel (2004). sx bx fx T T T 2 + = ……………… .. (12) Where: Tfx is the local mean film air temperature. The local Nusselt number (NuL) can be determined as: x L h .L Nu k = …………………….. (13) The average values of Nusselt number L( Nu ) can be calculated based on the average heat transfer coefficient as follows: x L L x x 0 1 h h dx L = ∫ = = …………………. ….. (14) L L h . L Nu k = ……………………… (15) The average values of the surface temperature, bulk air temperature and mean film temperature can be evaluated as follows: x L s sx x 0 1 T T dx L = ∫ = = ………………….. …. (16) x L a bx x 0 1 T T dx L = ∫ = = …….. ……… (17) s a f T T T 2 + = ………………………..…(18) . The Grashof and the Rayleigh numbers can be determined as follows: 3 s a L 2 g L ( T T ) Gr β ν − = ……….…….(19) L LRa Gr Pr= × …………………………. (20) Where: f1 /( 273 T )β = + , All the air physical properties ( , ,ρ µ ν and κ ) were evaluated at the average mean film temperature ( fT ), but it was observed in most of the previous work investigations that the physical properties were taken at the mean film temperature which is based on ambient temperature at tube entrance and given by [ Tmf = (Tms+ Ti) /2] . Results and discussion Free convection of air was experimentally studied in a vertical circular tube of different sections (restrictions) lengths placed at the exit of the heated tube. The heated tube was subjected to constant wall heat flux boundary conditions. The effects of the restriction length and Ra number on the heat transfer results were discussed in this section. The results presented in this paper include the surface temperature distribution of the heated tube, local Nu number and average Nu number. The present experimental data covered a total of 40 test runs for five restrictions with different lengths of 600 mm (L/D=20), 900 Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 39 mm (L/D=30), 1200 mm (L/D=40), 1500 mm (L/D=50), and 1800 mm (L/D=60) with the range of heat flux from 249 W/m2 to 1260 W/m2. Surface temperature The distribution of the surface temperature along the tube axial distance may be affected by many variables such as the heat flux, and the restriction length. The surface temperature distribution for selected runs is plotted and shown in Figs.2-6. The distribution of the surface temperature (Ts) with tube axial distance for different heat fluxes and for all restriction lengths have the same general shape. The surface temperature distribution exhibits the following trend: the surface temperature gradually increases with the axial distance until a certain limit to reach a maximum value at approximately (X/D=5.84) beyond which it begins to decrease. This phenomenon, which can be explained as follows: at the entrance to the tube the thickness of the thermal boundary layer is zero. Then, it gradually increases until the boundary layer fills the tube. From the entrance of tube to maximum point the heat transfer gradually decreases and (Ts) gradually increases due to the laminarization effect in the near wall region (buoyancy effect) and due to the upstream axial conduction in the solid walls preheating the air in the restriction section and due to tube end losses. Beyond the maximum point one would surmise that the surface temperature decreases along the axial distance. However, as the air is heated along the tube, its physical properties gradually change with the increased temperature. The thermal conductivity increases causing less resistance to the flow of heat and the viscosity increases causing radial flow of the hotter layers of air nearer to the surface to the tube center. A gradual increase of the local heat transfer beyond the maximum point must then be appeared. For constant wall heat flux this can only take place if the local differences between the bulk air temperature and the surface temperature decreases as shown in the distribution of (Ts-x). Fig. 2 shows the distribution of the surface temperature along the tube for different heat fluxes, for restriction with length of 600 mm (L/Drest.=20). This figure reveals that the surface temperature increases at tube entrance to reach a maximum value after which the surface temperature decreases. This can also be attributed to the developing of the thermal boundary layer faster due to buoyancy effect as the heat flux increases, and as explained previously. Fig. 3 is similar to Fig. 2 but pertains to a restriction with length of 900 mm (L/Drest.=30). The curves in the two figures show similar trend, but the surface temperature values in Fig. 3 were higher than that observed in Fig. 2 due to the length of restriction tube. Figs. 4-6 were similar in trends to Figs. 2-3 but pertains to restrictions with length of 1200 mm (L/Drest.=40) in Fig. 4, 1500 mm (L/Drest.=50) in Fig. 5 and 1800 mm (L/Drest.=60) in Fig. 6 respectively. Fig. 7 shows the effect of variation of restrictions lengths on the tube surface temperature for high heat flux 1260 W/m2. It is obvious from that the surface temperature increases as the restriction length increases, as the heat flux is kept constant except the restriction section with length of 1200 mm (L/Drest.=40) because it has the lowest surface temperature than other restriction sections. It is necessary to mention that the friction between the inside surface of the restriction length and the air flowing through it caused the temperature at entrance of the heated tube to be higher than the ambient temperature. It was also apparent from Fig.7 that the lower values of the surface temperature take place in (L/Drest.=40) and the higher values occur in Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 40 (L/Drest.=60) since the mass flow rate through the heated tube is the main parameter influencing the heat transfer results, so for the restriction tube with (L/Drest.=40) gives smallest flow resistance and maximal mass flow rate and finally lower surface temperature. local nusselt number (Nux) For free convection from a uniformly heated surface of length (L) exposed directly to the atmosphere, the average heat transfer coefficient for the whole length is calculated from: x L L x x 0 1 h h dx L = ∫ = = …………………….(21) Where: x sx bx q q h T T T∆ = = − ……… (22) (ΔT) in the above equation was taken as the difference between that local surface temperature (Tsx) and the air temperature far away the effect of the surface. Most of the previous workers mentioned in introduction section have calculated the heat transfer coefficient based on the temperature difference between the surface temperature and the fluid temperature at the entrance (Ti) [i.e. (ΔT) = (Tsx-Tbi)]. In the present work, since the heat transfer surface is not exposed to the atmosphere (because the flow is confined). So that, the heat is transferred from the hot surface of the tube to the air flowing in it. Thus, (ΔT)x cannot be taken equal to (Ts-Ti). It should be taken as (Tsx- Tbx) where (Tbx) is the local bulk air temperature in the cylinder. The distribution of the local Nusselt number (Nux) with the dimensionless axial distance (X/D) is plotted for selected runs and shown in Figs. 8-14. Figs. 8-12 show the effect of the heat flux variation on the Nux distribution for the five restrictions lengths under consideration in the present work. It is clear from these figures that at the higher heat flux, the results of Nux were higher than the results of lower heat flux. This may be attributed to the secondary flow effect that increases as the heat flux increases leading to higher heat transfer coefficient. Therefore, as the heat flux increases, the fluid near the wall becomes hotter and lighter than the bulk fluid in the core. As a consequence, two upward currents flow along the sides walls, and by continuity, the fluid near the tube center flows downstream. Figs. 13 & 14 show the effect of the restriction section length variation on the Nux distribution with (X/D), for low heat flux 249 W/m2 and for high heat flux 1260 W/m2. For constant heat flux, the Nux values give higher results for the restriction tube with length of 1200 mm (L/Drest.=40) and the lower values occur in the restriction tube with length of 600 mm (L/Drest.=20). This situation reveals that in (L/Drest.=40) the flow will be faster and then it makes heat transfer enhancement rather than other restriction tubes as a result of density increasing and the buoyancy force decreasing which lead to change in the temperature gradient as well as change the volume of upward gases because of the flow area decreases with the increasing of the velocity of upward gases. In addition, since the velocity profile is fully developed at the entrance of the heated section, so the restriction tube will become as a resistance on the air flow and as the length to diameter ratio (L/D) of the restriction tube was higher, the flow resistance will be higher, so that the surface temperature will be higher, and this leads to lower values of Nux when the restriction tube length increases. Finally, the mass flow rate through heated tube which is the main parameter influencing the heat transfer results, causes the maximum heat Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 41 transfer will be occurred in (L/Drest.=40), which gives smallest flow resistance, maximal mass flow rate and higher heat transfer results. The presented results have shown qualitatively the same trend and behaviors as observed by He et al. (2004). average nusselt number ( Nu ) The distribution of the average Nusselt number with the dimensionless axial distance (X/D) is depicted for selected runs in Figs. 15-16 which show the effect of the heat flux variation on the ( Nu ) for restrictions with lengths of (L/Drest.=20) and (L/Drest.=40) respectively. The ( Nu ) variation for other restriction lengths has similar trend as mentioned for (L/Drest.=20) and (L/Drest.=40). average heat transfer correlation The general correlation obtained from dimensional analysis for heat transfer by free convection available in Incropera and Dewitt (2003): n 1Nu f ( Gr, Pr )= ………………(23) In the case of heat transfer from the inside surface of a vertical tube one expects that there is an effect of both length and diameter. For similarity with flat surface (which a cylinder of infinite diameter) the characteristic linear dimension in Nu and Gr numbers may be taken as the tube length (L) since the heated tube is vertically oriented. Then equation (19) becomes: n L 2 LNu f ( Gr , Pr )= (24) The following correlations were obtained from the present work for each restriction length and a general correlation for all investigated cases was proposed and shown in Fig. 17: 0.23 L LNu 0.88 ( Ra )= For restriction with (L/D rest.=20) (25) 0.23 L LNu 1.024( Ra )= For restriction with (L/D rest.=30) (26) 0.23 L LNu 1.068 ( Ra )= For restriction with (L/D rest.=40) (27) 0.23 L LNu 1.036 ( Ra )= For restriction with (L/D rest.=50) (28) 0.23 L LNu 1.042 ( Ra )= For restriction with (L/D rest.=60) (29) 0.23 L LNu 1.263( Ra )= For all restriction lengths (30) A comparison was made between the present case and with the vertical tube open at both ends without any restriction and with the case of putting the restriction tube at the entry of the heated tube as reported by Salman and Mohammed (2005) and this comparison was shown in Fig. 17, the correlation obtained for the normal case as reported in McAdams (1954) and it has this form: 0.25 L LNu 0.59 ( Ra )= (31) From the comparison, it is apparent that the restriction length and position have a significant effect on the heat transfer results. Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 42 Conclusions Laminar free convection heat transfer from the inside surface of a uniformly heated vertical circular cylinder with different restriction lengths placed at the exit of the heat tube was experimentally performed. The following conclusions can be drawn from this work as: 1. The length of restriction tube provides a measure of the severity. An important finding of this study was that if the restriction exceeds a certain size, laminar upward flow throughout the whole of the heated part of the tube is tends to decrease the heat transfer results. This occurs if the ratio of the unheated length to the diameter of the tube (L/D) exceeds 40. 2. It was observed that the hot air near the heated wall aspirated the layers of hot air from the vertical tube. The uplift pressure and the tendency of the system were reached a balance because the air layers of the similar temperature and density were merged. However, this effect (similar to the movement of the hot air in a chimney) also found to be dependent on the intensity of the heat transfer. 3. The experimental results have revealed that the ratio of the axial length (L) to the diameter (D) affects the average heat transfer rate under the same conditions. Within the range of L/Drest.=20-60, the increase in L/D leads to decrease the heat transfer rate except the case of L/Drest.=40. 4. For the same heat flux, the surface temperature values for restriction with (L/Drest.=40) were lower than that for other restriction lengths. 5. For the same heat flux, the Nux values for (L/Drest.=40) were higher than that for other restriction lengths. 6. Empirical equations in the form of Log LNu versus Log LRa were obtained for each restriction length, Eqs. 25-29, and a general correlation for all cases restriction lengths was proposed (Eq. 30). 7. The comparison with the previous work shows that the restriction length and position has a significant effect on the heat transfer results. Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 43 Nomnclature As Tube surface area, (m2) Dimensionless Group Cp Specific heat at constant pressure, (kJ/kg.°C) Gr: Grashof number, g β L3(Ts-Ta)/ν 2 D Tube diameter, (m) Nu: Nusselt number, h.L / k g Gravitational acceleration, (m/s2) Pr: Prandtl number, µ . Cp/k h Heat transfer coefficient, (W/m2.°C) Ra: Rayleigh number, Gr.Pr I Heater current, (ampere) X/D: Dimensionless axial distance K Thermal conductivity, (W/m.°C) L Tube length, (m) Subscript Qcond. Conduction heat loss, (W) a air qconv. Convection heat flux, (W/m2) b bulk Qconv. Convection heat loss, (W) f film Qt Total heat input, (W) i inlet T Temperature, (°C) V Heater voltage, (volt) L m rest. based on tube length mean restriction s surface Greek t total β Thermal expansion coefficient, (1/K) w wall µ Dynamic viscosity, (kg/m.s) x local ν ρ Kinematic viscosity, (m2/s) Air density, (kg/m3). Superscript average Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 44 1. Restriction tube 2. Shields 3. Heated tube 4. teflon connection piece 5. Exit teflon piece 6. Thermocouples 7. Mixing chamber Fig. 1a The layout of experimental apparatus 1. Heated tube 2. Surface thermocouple 3. Electric heater 4. Asbestos layer 5. Fiberglass layer 6. Pair of thermocouples Fig. 1b The heating arrangement Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 45 3 8 13 18 23 280 5 10 15 20 25 30 X/D 60 100 140 180 220 80 120 160 200 T s ( C ) o Lrest.= 900 mm q= 249 W/m^2 q= 389 W/m^2 q= 762 W/m^2 q= 996 W/m^2 q= 1260 W/m^2 Fig.2 Variation of the surface temperature with the axial distance for (L/Drest.=20) Fig. 3 Variation of the surface temperature with the axial distance for (L/Drest.=30) 1. Heated tube 2. Restriction tube 3. Thermocouples 4. Defcon adhesive Fig. 1c The thermocouple locations along the heated tube 3 8 13 18 23 280 5 10 15 20 25 30 X/D 50 70 90 110 130 150 170 190 210 60 80 100 120 140 160 180 200 220 T ( C ) o s Lrest.= 600 mm q = 249 W/m^2 q = 389 W/m^2 q = 762 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 46 3 8 13 18 23 280 5 10 15 20 25 30 X/D 50 70 90 110 130 150 170 190 60 80 100 120 140 160 180 200 T s ( C ) Lrest.= 1200 mm q = 249 W/m^2 q = 389 W/m^2 q = 762 W/m^2 q = 996 W/m^2 q =1260 W/m^2 3 8 13 18 23 280 5 10 15 20 25 30 X/D 40 60 80 100 120 140 160 180 200 220 240 T s ( C ) o Lrest.= 1500 mm q= 249 W/m^2 q= 389 W/m^2 q= 560 W/m^2 q= 762 W/m^2 q= 996 W/m^2 q= 1260 W/m^2 3 8 13 18 23 280 5 10 15 20 25 30 X/D 50 75 100 125 150 175 200 225 250 275 T s ( C ) Lrest. = 1800 mm q = 249 W/m^2 q = 389 W/m^2 q = 762 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 3 8 13 18 23 280 5 10 15 20 25 30 X/D 110 130 150 170 190 210 230 100 120 140 160 180 200 220 240 T s ( C ) o q = 1260 W/m^2 (L/D)rest.= 40 (L/D)rest.= 20 (L/D)rest.= 30 (L/D)rest.= 50 (L/D)rest.= 60 Fig.4 Variation of the surface temperature with the axial distance for (L/Drest.=40) Fig.5 Variation of the surface temperature with the axial distance for (L/Drest.=50) Fig. 6 Variation of the surface temperature with the axial distance for (L/Drest.=60) Fig. 7 Variation of the surface temperature with the axial distance for different restriction lengths Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 47 7 8 9 2 3 4 5 6 7 8 9 2 3 4 1 10 X/D 25 75 125 175 225 275 325 375 0 50 100 150 200 250 300 350 400 N ux Lrest.= 600 mm q = 249 W/m^2 q = 389 W/m^2 q = 762 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 7 8 9 2 3 4 5 6 7 8 9 2 3 4 1 10 X/D 25 75 125 175 225 275 325 375 0 50 100 150 200 250 300 350 400 N ux Lrest.=900 mm q = 249 W/m ^2 q = 389 W/m ^2 q = 762 W/m ^2 q = 996 W/m ^2 q = 1260 W /m ^2 7 8 9 2 3 4 5 6 7 8 9 2 3 4 1 10 X/D 25 75 125 175 225 275 325 375 425 0 50 100 150 200 250 300 350 400 450 N ux Lrest.= 1200 mm q = 249 W/m^2 q = 389 W/m^2 q = 762 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 8 9 2 3 4 5 6 7 8 9 2 3 4 5 1 10 X/D 25 75 125 175 225 275 325 375 0 50 100 150 200 250 300 350 400 N ux Lrest.=1500 mm q = 249 W/m^2 q = 389 W/m^2 q = 560 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 Fig. 8 Variation of the local Nusselt number with the axial distance for (L/Drest. =20) Fig. 9 Variation of the local Nusselt number with the axial distance for (L/Drest. =30) Fig. 10 Variation of the local Nusselt number with the axial distance for (L/Drest. =40) Fig. 11 Variation of the local Nusselt number with the axial distance for (L/Drest. =50) Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 48 8 9 2 3 4 5 6 7 8 9 2 3 4 5 1 10 X/D 0 25 50 75 100 125 150 175 200 225 250 275 300 N ux Lrest.= 1800 mm q = 249 W/m^2 q = 389 W/m^2 q = 762 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 8 9 2 3 4 5 6 7 8 9 2 3 4 1 10 X/D 50 70 90 110 130 150 170 190 40 60 80 100 120 140 160 180 200 N ux q = 249 W/m^2 (L/D)rest.= 20 (L/D)rest.= 30 (L/D)rest.= 60 (L/D)rest.= 50 (L/D)rest.= 40 7 8 9 2 3 4 5 6 7 8 9 2 3 4 1 10 X/D 125 175 225 275 325 375 100 150 200 250 300 350 N ux q = 1260 W/m^2 (L/D)rest.= 60 (L/D)rest.= 50 (L/D)rest.= 30 (L/D)rest.= 20 (L/D)rest.= 40 7 8 9 2 3 4 5 6 7 8 9 2 3 4 1 10 X/D 25 75 125 175 225 275 325 375 0 50 100 150 200 250 300 350 N u Lrest.= 600 mm q = 249 W/m^2 q = 389 W/m^2 q = 560 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 Fig. 12 Variation of the local Nusselt number with the axial distance for (L/Drest. =60) Fig. 13 Variation of the local Nusselt number with the axial distance for different restriction lengths Fig. 14 Variation of the local Nusselt number with the axial distance for different restriction lengths Fig. 15 Variation of the average Nusselt number with the axial distance for (L/Drest. =20) Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 49 7 8 9 2 3 4 5 6 7 8 9 2 3 4 1 10 X/D 25 75 125 175 225 275 325 375 425 0 50 100 150 200 250 300 350 400 N u Lrest.=1200 mm q = 249 W/m^2 q = 389 W/m^2 q = 762 W/m^2 q = 996 W/m^2 q = 1260 W/m^2 9.34 9.38 9.42 9.46 9.50 9.54 9.589.36 9.40 9.44 9.48 9.52 9.56 Log (RaL) 1.00 1.40 1.80 2.20 2.60 3.00 3.40 1.20 1.60 2.00 2.40 2.80 3.20 3.60 L og (N uL ) NuL= 1.289 (RaL)^0.23 - The present work NuL= 1.248 (RaL)^0.23 - (Salman & Mohammed, 2005) NuL= 0.59 (RaL)^0.25 - (McAdams, 1954) References Abd-el-Malek B. M. and Nagwa A. B. (1991)”Group method analysis of steady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder” J. of Computational and Applied Mathematics, Vol.36, No. 2 , pp. 227-238. Al-Arabi M.; Khamis M. and Abd-ul-Aziz, (1991)”Heat Transfer by Natural Convection from the Inside Surface of a Uniformly Heated Vertical Tube”. Int. J.Heat and Mass, Vol.34, No.4/5, pp.1019- 1025. Chang C. J.; Lin T. F. and Yan W. M. (1986) “Natural convection flows in a vertical, open tube resulting from combined buoyancy effects of thermal and mass diffusion” International J. of Heat and Mass Transfer ,Vol.29, No.10, pp.1543-1552. Dyer J.R., (1975)”The Development of Laminar Natural Convective Flow in a Vertical Uniform Heat Flux Duct”. Int. J. Heat and Mass Transfer, Vol.18, pp.1455- 1465. Fukusako S. and Takahashi M. (1991) “Free convection heat transfer of air-water layers in a horizontal cooled circular tube“ Int. J. of Heat and Mass Transfer, Vol. 34, No. 3, pp.693-702 He Y. L.; Tao W. Q.; Qu Z. G. and Chen Z. Q. (2004)“Steady natural convection in a vertical cylindrical envelope with adiabatic lateral wall “Int. J. of Heat and Mass Transfer, Vol. 47, No. 14-16, pp.3131- 3144. Hess C.F. and Miller C.W., (1979)” Natural Convection in a Vertical Cylinder Subject to Constant Heat Flux”. Int. J. Heat and Mass Transfer, Vol.22, No.3, pp.421- 430. Fig. 16 Variation of the average Nusselt number with the axial distance for (L/Drest. =40) Fig. 17 Correlation of the average heat transfer results and compared with available literature Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 50 Holman J.P. (2001) “Experimental Methods for Engineers” 7th Edition, McGraw-Hill International Edition, New York, USA. Incropera F. P. and DeWitt D. P. (2003) “Fundamentals of Heat and Mass Transfer” 5th Edition. John Wiley & Sons Inc, New York. Kakac S. (1987), The Effect of Temperature Dependent Fluid Properties on Convective Heat Transfer, In Handbook of Single-Phase Heat Transfer (edited by Kakac S., Shah R. K. and Aung W.), pp.18.1-18.56. John & Wiley, New York. Kokugan T. and Kinoshita T., (1975) ”Natural Convection Flow Rate in a Heated Vertical Tube”. J. of the Chemical Engineering of Japanese, Vol. 8, No.6, pp.445-450. Kuan-Tzong Lee (October 2000 )“Fully developed laminar natural convection heat and mass transfer in partially heated vertical pipe“ Int. Communications in Heat and Mass Transfer, Vol. 27, No. 7, pp.995- 1001. McAdams, (1954) “Heat Transmission”, McGraw-Hill International Edition, New York, USA. Martin B. W. (1965) “Free convection limits in the open thermosyphon” Int. J. of Heat and Mass Transfer, Vol. 8, No.1, pp.19- 25 Moawed M. (2005) “Experimental investigation of natural convection from vertical and horizontal helicoidal pipes in HVAC applications “ Energy Conversion and Management ,Vol. 46, No.18-19, pp.2996-3013. Oliver D. R. (1962) “The effect of natural convection on viscous-flow heat transfer in horizontal tubes “Chemical Engineering Science ,Vol. 17, No.5, pp.335-350. Popiel C. O. and Wojtkowiak J. (2004) “Experiments on free convective heat transfer from side walls of a vertical square cylinder in air” Experimental Thermal and Fluid Science, Vol.29, No.1 , pp.1-8. Salman Y.K. and Mohammed H.A. (2005) “The effect of restriction shape on laminar natural convection heat transfer in a vertical circular tube” Al-Khawarizmi Engineering Journal, Vol. 1, pp.83-100. Selver R., Kamotani Y., Ostrach S., (1998) “Natural Convection of A Liquid Metal in Vertical Circular Cylinders Heated Locally From the Side” J. of Heat Transfer ASME Transactions, Vol.120, pp. 108-114. Shenoy, A. V. (1984)“Natural convection effects on heat transfer to power-law fluids flowing under turbulent conditions in vertical pipes” Int. Communications in Heat and Mass Transfer ,Vol.11, No.5, pp.467-476. Shigeo K. and Adrian B. (1980)“Experimental study of natural convection in a horizontal cylinder with different end temperatures” Int. J. of Heat and Mass Transfer ,Vol. 23, No.8, pp. 1117- 1126. Vinokurov V. F., Volkov S.V., Martynenko O. G., Khramtsov P. P. and Shikh I. A. (1993) “Some aspects of free-convective heat transfer in eddy flow through a horizontal tube” Int. J. of Heat and Mass Transfer, Vol.36, No.18 , pp.4487- 4491. Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 51 Wojciech T. K. (2000) “Natural convection heat transfer around horizontal tube in vertical slot “ Int. J. of Heat and Mass Transfer ,Vol. 43, No.3 ,pp. 447-455. Yan W. M. and Lin T. F. (1991)“Theoretical and experimental study of natural convection pipe flows at high Rayleigh number” Int. J. of Heat and Mass Transfer, Vol.34, No.1, pp.291-303. Yissu W. (1995) “Laminar Natural Convection in Vertical Tubes with One End Open to a Large Reservoir” Int. J .of Heat Transfer, Vol. 56-06, Section: B, pp.3411. Cengel Y.A. (2004) “Heat Transfer a Practical Approach” McGraw-Hill International, 3rd edition, New York, USA. Yasin K. Salman /Al-khwarizmi Engineering Journal, Vol.3, No.3, pp 31- 52 (2007) 52 انتقال الحرارة بالحمل الحر باستخدام مقاطع مختلفة االطوال وموضوعةعند مخرج انبوب دائري شاقولي معرض لفیض حراري ثابت یاسین خضیر سلمان.د حسین احمد محمد كلیة الھندسةكلیة الھندسة/ / امعة بغداد امعة بغداد جج كلیة الھندسةكلیة الھندسة/ / جامعة بغداد جامعة بغداد كقسم المیكانیك القسم النوويالقسم النووي قسم المیكانی ::الخالصةالخالصة یتن اول البح ث دراس ة عملی ة النتق ال الح رارة بالحم ل الح ر لجری ان الھ واء الطب اقي ف ي داخ ل أنب وب دائ ري ش اقولي صمم الجھاز العمل ي ).ُ 5 10*٩(إلى ) 6.9 108*(من ) RaL(حراري ولمدى تغیر لرقم رایـلي باستخدام شرط ثبوت الفیض ال على درج ة الح رارة , الموضوع في مدخل األنبوب وفي الموقع العلوي ألنبوب التسخین) restriction(إلیجاد تأثیر طول المقید والمع دل ) Nux(الت الي عل ى تغی ر رق م نس لت الم وقعي على طول سطح األنبوب المسخن وكذلك على معام ل انتق ال الح رارة وب )Nu( . الجھ از العمل ي المس تخدم یتك ون م ن أنب وب م ن االلمنی وم مس خن حراری ًا بط ول )900mm ( وبقط ر داخل ي )30mm .( لك ن ب أطوال مقیدات الدخول تتضمن أنبوب دائري أسطواني لھ نفس القط ر ال داخلي ألنب وب التس خین و), 1500 mm, 1200 mm, 900 mm, ,600 mm١٨٠٠ mm( , لقد وجد من خالل النتائج العملیة أن درجة الحرارة عل ى ط ول س طح األنب وب تك ون أعل ى م ا یمك ن للمقی د ال ذي طول ھ )1800 mm ( وتكون اقل ما یمكن للمقید الذي طولھ)1200 mm .( أظھرت النتائج أن قیم رقم نسلت الموقعي)Nux (والمعدل )Nu( تكون أعلى ما یمكن للمقید الذي طولھ)1200 mm ( وتكون اقل ما یمكن في حال ة المقی د ال ذي طول ھ)1800 mm .( لق د LNu(بش كل ) empirical equations(ت م الحص ول عل ى مع ادالت تجریبی ة Log ( ض د) LRa (Log لك ل حال ة م ن .الحاالت المستخدمة في البحث وكذلك تم الحصول على معادلة عامة تربط جمیع الحاالت