Experimental and Numerical Investigation of Natural Convection Heat Transfer in an Inclined, Outer Cylinder Heated Concentric Annulus

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1 Experimental and Numerical Investigation of Natural Convection Heat Transfer in an Inclined, Outer Cylinder Heated Concentric Annulus Yasin K. Salman, Department of Energy Engineering, University of Baghdad, Iraq Mustafa Z. Gheni, Department of Energy Engineering, University of Baghdad, Iraq Abstract-Natural convection heat transfer in an open inclined concentric annulus with the outer cylinder subjected to a constant heat flux while the inner cylinder unheated was investigated experimentally and numerically. For the steady state condition, the investigation focuses on the effect of annulus inclination angle and the outer cylinder heat flux on heat transfer process. Heat transfer results are given for inclination angles of 0 o (horizontal), 30 o,45 o, 60 o and 90 o using concentric annulus with diameter ratio of 1.8, length 500 mm and heat fluxes varied from 70 W/m 2 to 600W/m 2. The mathematical model was solved numerically using finite element software (COMSOL Multi Physics 4.0 b), with the same annulus geometrical dimension and boundary conditions which have been covered by experimental work. After finding the numerical results, the validation between experimental and numerical results has been verified. A good agreement has been found between the experimental and the numerical results. The results showed that the local and average Nusselt number increase as the heat flux increase and when angle of inclination changed from 0o to 90o. Empirical correlations of average Nusselt number as a function of average Rayleigh number were deduced. Key words : Heat transfer, Natural convection, inclined annulus, Empirical correlations Nomenclature symbols Description` units A 2 As Cp Cylinder surface area Specific heat at constant pressure m KJ/kg. 0 K D 1, D 2 Inner and outer annulus diameters mm R 1, R 2 Inner and outer annulus radius mm Dh Hydraulic diameter, 2(R2-R1) mm F1-2 View factor between the inner and outer cylinder g Gravitational acceleration m/s 2 hx Local heat transfer coefficient W/m 2.K hl Average heat transfer coefficient W/m 2.K I Heater current Amp K Thermal conductivity W/m.K L Axial length of annulus mm QC Heat transfer by convection W QCond Heat transfer by conduction W Qcr Heat transfer by convection and radiation W Qt Total heat input W qc Convection heat flux W/m 2 qcr Convection radiation heat flux W/m 2 qr Radiation heat flux W/m 2 Tb L Average bulk air temperature o K 1

2 Ts1 x Ts1 L r V z,, Local surface temperature of annulus inner and outer cylinders Average surface temperature of annulus inner and outer cylinders Radial direction Heater voltage Axial direction o K o K mm volt mm Greek symbols symbol description units β s 1 Coefficient for volumetric thermal expansion o K - ε Emissivity; inner surface and outer surface µ Fluid viscosity kg/m.s v Kinematics viscosity m 2 /s 3 ρ Fluid density kg/m 4 σ Stefan-Boltzman constant W/m 2.K θ Annulus inclination angle degree Φ Fluid rotation angle degree Dimensionless group Group description GrL Mean Grashof number g βd h 3 (t sl t bl ) NuL Mean Nusselt number H L.D h /K Nux Local Nusselt number H x.d h /K Pr Prandtl number µ. Cp/k RaL Mean Rayleigh number GrL.Pr X* Dimensionless axial distance x/dh v 2 1. Introduction Natural convection heat transfer in the annular passage between two concentric cylinders is an important research topic due to its encountered in many industrial applications. Applications are found in energy conversion, storage and transmission systems. Examples of using annulus geometry include solar collectors, phase change of material around pipes in thermal storage systems and nuclear reactor design. Many experimental and theoretical investigations have been conducted in recent years due to the wide range of applications as mentioned above. Kuehm and Goldstein [1] presented numerical and experimental results for natural convection in horizontal annulus over a wide range of Ra L, Pr, and D 1/D 2. They obtained correlation equations for heat transfer by natural convection using a conduction boundary layer model. Their results showed that the heat transfer correlation is similar to that of heat transfer from a single horizontal cylinder as the outer cylinder diameter tends to infinity and correlation is similar to heat transfer to the fluid within a horizontal cylinder as the inner cylinder diameter approaches zero. Takata et-al. [2] studied natural convection analytically and experimentally in an inclined cylindrical annulus enclosed in heated inner and cooled outer cylinders. The three- 2

3 dimensional structure of the fluid flow, temperature distribution and Nu for different angles of inclination was investigated. Results showed that the Nu slightly increased as the annulus inclination angle changed from the horizontal for the case of D 2/D 1 = 2.0. Rao et-al. [3] investigated experimentally and theoretically the natural convection flow and temperature distribution in horizontal cylindrical annuli. They compared the predicted results with the experimental results for the temperature and stream function distributions and determined the dominant flow pattern at a given Ra and D2/D1. Hamad [4] investigated the natural convection heat transfer in an inclined annulus. An empirical correlation for Nu has been given for Pr = 0.7, D 2/D 1=1.636 and Ra L Results showed that the Ra and angle of inclination had a very small effect on the heat transfer coefficient through the annulus. Vafai and Ettefagh [5] carried out natural convection between two horizontal, concentric cylinders open at both ends. The axial velocity was found to decrease away from the open end and a core region was observed inside the annulus where the flow field was almost two-dimensional. Mohammed [6] carried out experimental study to find the local and average heat transfer by natural convection in a vertical concentric cylindrical annulus. The experimental setup consists of an annulus has a radius ratio of and inner cylinder with a heated length 1.2m subjected to the constant heat flux while the outer cylinder is subjected to the ambient temperature. The investigation covers heat flux range from 58.2 W/m 2 to W/m 2. Results show an increase in the natural convection as heat flux increases leads to improve the heat transfer process. Malik et-al. [7] studied the buoyancy driven flow within bottom-heated vertical concentric cylindrical enclosure. Experimental and numerical study of the axial temperature gradient and the heat transfer mechanism within the enclosure were performed. The numerical simulations were validated by comparing the numerical results with experimentally measured axial temperature. Gheni and Salman [8] carried out experimental and numerical study of laminar natural convection inside inclined open annulus passage heated from both inner and outer surfaces to find the local and average heat transfer. The experimental setup consists of an annulus has a radius ratio of 1.8 and inner and outer cylinders with a heated length 500 mm both subjected to the constant heat flux. The investigation covers heat flux range from 70 W/m 2 to 600 W/m 2. Results show an improvement in the natural convection as heat flux increases and as annulus inclination angle increases. Those two variables lead to improve the heat transfer process. 2- Experimental Apparatus A schematic diagram and photograph of the experimental setup of the apparatus are shown in figure (1) and figure (2-a), respectively. It consists essentially of outer and inner aluminum cylinders constitute the concentric annulus passage. The outer cylinder has 46 mm internal diameter while the inner cylinder has 26 mm external diameter and both cylinders have 500 mm in length. The inner cylinders mounted in the passage entrance on a Teflon piece (A) which has the same outer diameter for the inner cylinder. A well designed Teflon bell mouth (B) was fitted on the outer cylinder at the passage entrance region. The bell mouth inner diameter has the same inside diameter of the outer cylinder. Both Teflon pieces (A and B) are equal to 120 mm in length. Another two cylindrical Teflon pieces (C and D) with the same lengths and diameters of (A) and (B) are fitted on the passage exit section of both inner and outer cylinders. Teflon was chosen because of its low thermal conductivity in order to reduce the heat loss from the cylinders ends. The cylinders are held by cross plate (M) tied together with the cylinders components by four threaded rods and nuts and fixed firmly on the rotating wooden board (W). The inner cylinder Teflon piece fitted on a cross plate that connected to the four threaded rods which spanning through the wooding board and to be inside the wooden settling chamber under the board. The board can rotated around a horizontal spindle therefore, the inclination angle of the test section can thus be adjusted as required. The outer cylinder surface is electrically heated by means of nickel chromium wire (main heater) of 0.3 mm in diameter and 5 Ω per meter resistance. The wire is electrically insulated by means of ceramic beads and is wound uniformly along the cylinder length with an asbestos rope of 5mm thickness in order to give a uniform heat flux. As seen in figure (3) The main heater is covered by 30 mm thick asbestos ropes on which three pairs of thermocouples (A1/A2, B1/B2, C1/C2) are fitted at an aluminum plates with 10 mm thickness asbestos rope between it and 10 mm thickness asbestos rope was wounded on it where an electric (guard-heater) is uniformly wounded Malik and Shah [7], Gheni and Salman [8] and D. Subramanyam et.al [9]. 3

4 Figure (1): Schematic diagram of experimental apparatus. (A) Inner cylinder lower Teflon piece ; (B) Outer cylinder lower Teflon piece(bell mouth); (C) Upper Teflon piece for inner cylinder; (D)Upper Teflon piece for outer tube; (E)Thermocouples of the outlet hole; (F)Inner cylinder stand;(g)guard heater;(h)fiber glass layer; (I) Outer cylinder heater; (M) Inner cylinder support plate (R)Asbestos layer; (K)Wooden box; (W) Wooden board;(n) Thermocouple of the inlet hole (a) (b) Figure (2): Photographic of: a- Test apparatus, b- instruments used in the test 4

5 Figure (3): apparatus Cross-sectional view: (1) the inner tube; (2) thermocouples of the outer cylinder; (3) outer cylinder heater with 5 mm (thickness) asbestos rope ; (4) 30 mm (thickness) asbestos rope; (5) 10 mm (thickness) asbestos rope; (6) 10 mm (thickness) asbestos rope; (7) Guard Heater; (8) 10 mm (thickness) asbestos rope (9)7 mm (thickness) fiber glass layer For a certain main heater input the guard-heater input could be adjusted until so that the thermocouples pairs in the outer cylinder insulation layers registered the same temperature to ensure that all heat generated by the main heater flows to the inner surface of the outer cylinder.an asbestos rope of 10 mm thickness covered the guard- heater and serves as an additional insulation layer. A fiber-glass layer of 7 mm thick is used as an outside cover for the outer cylinder heating system. The axial temperature distribution of the inner and outer annulus surfaces have been measured by using 34 Type K (chromel alumel) Teflon insulated thermocouples of mm in diameter. 17 thermocouples are fixed on both the inner and outer surfaces at equal distances along the axis of the annulus; all of the thermocouples are fixed with Defcon adhesive. Three additional thermocouples were fixed at the midpoint of the annular passage and around the annulus outer cylinder surface with 90o spaced, to measure the temperature variation on the outer cylinder circumferential direction. The temperature difference was found negligible in the circumferential direction, hence the inner and outer cylinder was assumed to be circumferentially isothermal. To measure the axial lagging heat losses two thermocouples are fitted with uniform distance in the inner and outer cylinders Teflon piece. One thermocouple is fixed in the test section entrance to measure the inlet air temperature and another three thermocouples are fixed in the passage exit to measure the outlet bulk air temperature. All thermocouples used with leads and the thermocouples with and without lead were calibrated against the melting point of ice made from distilled water and the boiling points of several pure chemical substances. Figure (2) b shows the photographs of instruments used in the test. The power consumed by the heater was measured by an ammeter and voltmeter. Two variac units was used to control the power supplied to the heaters by controlling the voltage across the heaters, a data logger Pico- (Tc-008) was used to record the thermocouple outputs to accuracy within 0.03 mv. 5

6 3- Experimental Procedure The experiments on the annular passage were conducted at different at different orientation and outer cylinder heat flux. As the test run takes so long time to reach the steady state condition, the test procedure followed daily keeping annulus orientation constant and changing the surface heat flux to get at least two test run per day. The following procedures were followed: A. The test apparatus prepared to insure the well performance of all components. B. Adjusting the required inclined angle. C. The supply power to the electric elements was switched on, and it was adjusted by variac to obtain the required constant heat flux, then it was left in operation action for a period until the surface temperature of the cylinders reached to steady state after about (6 hours) during this time the guard heater thermocouples have been monitored and the guard heater input power adjusted accordingly to get zero temperature difference in the three guard heater thermocouples pairs. D. During each experiment, at all the temperatures have been monitored and recorded by the data logger for 15 minutes interval time, together with the input voltage and current until the steady state condition achieved. 4- Experimental data reduction The experimental apparatus described in section two has been used to provide the experimental data for heat transfer calculations through the annulus. The outer cylinder was subjected to the uniform heat flux. The total power supplied to the outer cylinder heater was calculated as follows: Q t = V I.. (1) The convection and radiation heat transfer rate from the inner surface of the outer cylinder are: Qcr=Qt-Qcond... (2) Where Qcond is the axial conduction heat loss which was found experimentally about 3% of the input power. The convection and radiation heat flux can be represented by: qcr=(qcr)/as (3) Where (As = 2πR1L) for the inner cylinder and (AS = 2πR2L) for the outer tube. The convection heat flux which is used to calculate the local heat transfer coefficient is obtained after deduce the radiation heat flux from qcr value. The local radiation heat flux can be calculated as follows: qr = F1-2σε((T s )4 - (T s )4 ). (4) Where: F 1 2 F Hence the convection heat flux at any position is: q c=qcr-qr (5) The local heat transfer coefficient can be obtained as: q c (h x) = (6) (T s ) x (T b ) x All the air properties were evaluated at the mean film air temperature: (T f) x= (T s) x +(T b ) x 2.. (7) 6

7 Where: (T f) x is the local mean film air temperature at(t s ) x. The local Nusselt number for the inner cylinder (Nu x) then can be determine as: (Nu x)= (h x) Dh k = 1 L (T s) x dx T s x=l x=0.. (8).... (9) = 1 L (T b) x dx T b x=l x=0.. (10) = T s T f +T b 2 (11) The average heat transfer coefficient and the average Nusselt number (Nu L) based on the calculation of the average cylinder surface temperature and the average bulk air temperature Ozoe [10], were calculated as follows: h L = 1 x=l h L x dx x=0. (12) Nu x = h L D h k. (13) Gr = g βd h 3 (T T s ) b. (14) v 2 Where β = 1 (273+ ) T f Pr = µ C p k. (15) Ra L=Gr L.Pr (16) All the air physical properties ρ, µ, v and k were evaluated at the average mean film temperature (T f ) Holman [11]. 3.1 Experimental Uncertainty Generally the accuracy of experimental results depends upon the accuracy of the individual measuring instruments and the manufacturing accuracy of the circular cylinder. 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 Kline and McClintock differential approximation method reported by Holman [12]. For a typical experiment, see table (1), the total uncertainty in measuring the heater input power, temperature difference (Ts-Tb), the heat transfer rate and the circular cylinder surface area were 0.38%, 0.48%, 2.6, and1.3% 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. 7

8 Independent variables (v) uncertainty interval (w) Surface to bulk air temperature ± 0.16 C Voltage of the heater ± 0.03 volt Current of the heater ± Amp Hydraulic diameter ± m Average lagging surface temperature ± 0.11 C Table (1): Experimental errors that may happen in the used variables 4. Numerical Analysis The software COMSOL [13] Multi Physics 4.3b was used to solve the governing continuity, momentum and energy Cattani and Corradi [14]. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in terms of dimensional variables for the defined geometry and associated boundary conditions. The domain was defined in the global coordinate frame in which the solver carries out the calculations. Laminar flow of an incompressible Newtonian fluid under the Boussinesq approximation is used. The generalized transport equations solved are given below, Takata et-al. [2], Al-Jabair and Habeeb [15]: The continuity equation: 1 r. d dr (ρ ref r V r ) + 1 r. d d (ρ ref V ) + d dz (ρ ref V z ) = 0... (17) Where: ρ ref = air density at the reference temperature. V r,v andv z are the flow velocities components in the r, and z direction respectively. The momentum equation: r-component dv r ρ ref (V r dr + V r = dp dr dv r d + V dv r z d + µ [( d dr (1 (rv r dr r)) + 1 Where : g r = g cos sinθ -component dv ρ ref (V r dr + V r = dp d 2 dz V r ) d 2 V r r 2 d 2 dv d + v dv z dz V rv r ) + µ [( d dr (1 d (rv r dr )) + 1 d 2 V r 2 d 2 + d2 V r dz r 2 dv d ]+ρg r... (18) + d2 V dz r 2 dv d ] +ρg (19) Where: g = g cos sinθ 8

9 z-component ρ ref (V r dv z dr + V r = dp dz + µ [( d dr (1 r dv z d + V dv z z dz V zdv z dz ) d dr (dv z dr )) + 1 d 2 V z r 2 d 2 + d2 V z dz 2 ] +ρg z... (20) Where: g z = g sinθ The energy equation: ρ ref C p (V r dt + V dt dr r dt + V d z ) = k dz [1 r d dr (r dt dr ) + 1 r 2 d 2 T + d2 T d 2 dz 2] (21) Applying the Boussinesq approximation, the density in the body force term is given by: ρ = ρ ref [1 β(t T ref )] (22) 4.1 Boundary conditions Figure (3) a shows the configuration of the system under study. The boundary conditions assumed no-slip conditions for velocity, constant heat flux on the outer wall Sakar et-al [16], Malik et-al [7]. The reference temperature (Tref) was taken as the arithmetic mean along the axis of the cylinders between the inlet and the outlet temperatures. V r =V = V z = 0 (r=r 1, r=r 2). (23) dv r = V d = dvz = 0 ( = d 00, ). (24) dt dr = constant (r=r2), ( = 00 < < ). (25) dt dr = 0 (r=r1), (00 < < )... (26) 4.2 Mesh and solver details In order to resolve accurately the rapid velocity and temperature variations near the wall, the meshes here were made much finer relative to those in the core region. The unstructured mesh option was used which involves prismatic elements near the wall and tetrahedral elements in the core. Since the geometry shows asymmetric construction only one half of the annulus passage has been simulated figure (3)b, Takata et-al. [2], Brangeon [17], using tetrahedral elements throughout would have entailed prohibitively fine meshes for the required accuracy. Flat hexahedra wedge shaped elements were placed close to the walls Kassem [18], Andreozzi [19].An inflation parameter of two layers with a geometric expansion factor of 1.3 was chosen. This arranged the hexahedra elements from the wall surface in a sequence of two layers. These ensured an adequate number of elements near the wall and avoided a sudden jump in mesh size. 9

10 (a) (b) Figure (3): a- The geometry under the computational mesh, b- Configuration of the system under study 5. Results and Discussion 5.1 Temperature Variation The variation of annulus outer cylinder surface temperature for different heat fluxes and for angles of inclination θ = 0 (horizontal), 30 o, 45 o 60, and 90 is shown in figure (4). It is obvious from this figure that the surface temperature increases as heat flux increases because of faster increasing of the thermal boundary layer as heat flux increases. It can be seen that at θ = 0 o, the outer cylinder surface temperature have no obvious change with the axial distance except at the end of the tubes due the conduction end loses. This behavior explained that there is no flow in the axial direction so the bouncy effect is just in the radial direction.for θ= 30 o,45 o, 60,and 90, the distribution of the surface temperature (T s) with cylinders axial distance for different heat fluxes have the same general shape. As we can see from isothermal counters in figure (5) that at θ=90 0 the isothermal lines are constant in values along the axial direction and they are parallel. So the conduction heat transfer is more effective due to high temperature gradient at the wall. As the angle of inclination moves from vertical to horizontal, the isothermal lines move towards the outer cylinder wall of upper part of the circular annular passage, and these lines are deformed from their conductive pattern and becoming curvilinear. This deformation increases with the decreasing of the inclination angle. This behavior can be attributed to the fact that as the heated air near the heated side diluted the difference between air density near the wall and the annulus flow center causes a circulation which displaces the wall air in a direction upward parallel to the gravity vector. For the horizontal cylinder, the warmer air moves upward along the side walls, and by continuity the heavier air near the unheated inner cylinder outer surface flows downward. As a result, a two symmetrical spiral, like motion is formed along the annular passage. The circulation is driven by radial temperature variation, and at the same time it reduces this temperature variation. These two spiral vortex intensity reduces as the angle of inclination moves from horizontal to vertical position to be faster near the heated outer cylinder inner surface and the flow would be totally in the axial direction in the vertical position. A reverse flow may be expected occur on the inner cylinder outer surface for the high heat flux situation and especially at the passage exit. Therefore; it is expected that the convection heat transfer process in vertical position is better than that in other positions. 10

11 . Figure (4): Variation of surface temperature with the axial distance for different heat fluxes. θ = 90 O θ = 45 O θ = 0 O Figure (5): Middle isothermal contours section for different inclination angles, q=70 W/m 2 11

12 5.2 Velocity variation Figures (6) and (7) show the peripheral velocity density contour in (r- ) plane at mid-section and velocity density contours with velocity vectors along the passage respectively. The velocity density concentrate at the outer wall due to the heat transfer process. As expected for all inclination angles the velocity density movement towards the center and rotate about point near the annulus center for all (X*,θ), this movement is due the circulation of convective flow inside the domain owing to buoyancy forces effect. θ = 0 o θ = 45 O θ = 90 O Figure (6): Middle section of Peripheral velocity density contours and velocity vectors for different inclination angles, q=70 w/m 2 12

13 θ = 90 o θ = 30 o θ = 45 o θ = 60 o Figure (7): velocity density contours and velocity vectors along the passage for different inclination angles, q=200 W/m Local Nusselt number Generally, it is obvious from figure (8) that the local Nusselt number values increase as the heat flux increases because of increasing natural convection currents which improves the heat transfer process. 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, in the vertical position two upward currents flow along the side s walls, where for the horizontal case the flow near the cylinders walls would be in the radial direction depending on the small temperature difference between the walls caused by inner and outer cylinder surface shape. For inclined positions the flow will be combined of the axial and radial direction and by continuity, the fluid near the annular center flows downstream. 13

14 θ = 0 o θ = 45 o θ=60 o θ = 90 o Figure (8): 3D Nusselt number graph, q =200 W/m Average Nusselt number Figure (9) show the experimental results correlated as the logarithmic of mean Nusselt number versus logarithmic Rayleigh number for outer cylinder heat flux varies from q = 70 W/m 2 to 600 W/m 2 and for annular passage inclination angle varies from θ = 0 (horizontal), 30, 60, and 90. Table (2) shows the correlations of average Nusselt number which have been deduced by the experimental and numerical results. 14

15 θ = 0 o θ = 30 o θ = 60 o θ = 90 o Figure (9): Logarithm Average Nusselt Number (NuL) Versus log(ra L). Experimental correlations Numerical correlations θ NuL = RaL 0 NuL= RaL 0 NuL L = RaL 0 Nu = RaL 30 NuL L = RaL 0 Nu = RaL 45 NuL L = RaL 0 Nu = RaL 60 NuL L = RaL 0 Nu = RaL 90 Table (2): correlations of average Nusslt number 15

16 6. Conclusion Free convection heat transfer inside a uniformly heated the outer cylinder of an inclined concentric annular passage have been investigated experimentally and numerically. The following conclusions can be drawn: - The heat transfer process improves when the heat flux increase at the same angle of inclination. - The heat transfer process improves when angles of inclination moves from horizontal to vertical position. - Maximum heat transfer enhancement occurs at θ = Maximum surface temperatures occurs at θ = The average Nusselt number increase with the increasing of the heat flux and with the increasing of the inclination angles. - The isothermal lines are parallel and smooth at low heat fluxes and they become curvilinear with the increasing angle of inclination and heat flux. - Maximum axial velocity accurse at θ = REFERENCES [1] Kuehm, T. H. and Goldstein, R. J., An experimental and theoretical study of natural convection in an annulus between horizontal concentric cylinders. J. Fluid Mech., Vol. 74. (1976). [2] Takata, Y., Iwashige, K., Fukuda, K. and Hasegawa, S., Three-dimensional natural convection in an inclined cylindrical annulus. Int J. Heat Mass Transfer vol. 27, pp (1984). [3] Rao, Y. F., Miki, Y., Fukuda, K., Takata, Y. and Hasegawa, S., Flow patterns of natural convection in horizontal cylindrical annuli. Int. J. Heat Mass Transfer, Vol.28 (1985). [4] Hamad, F. A., Experimental study of natural convection heat transfer in inclined cylindrical annulus. Solar and Wind Technology Vol.6 (1989). [5] Vafai, K. and Ettefagh, J. An investigation of transient three dimensional buoyancy driven flow and heat transfer in a closed horizontal annulus. Int J. Heat Mass Transfer vol. 34, pp (1991). [6] Mohammed, A. A. Natural convection heat transfer in a vertical concentric annulus J. of Engineering, a scientific Refereed Journal Published by college of Engineering University of Baghdad, Vol. 13 pp1-14 ( 2007). [7] Malik, A. H, Khushnood S. and Shah, A. Experimental and numerical study of buoyancy driven flow within a bottom heated vertical concentric cylindrical enclosure, Natural Science vol.5, No.7, pp (2013). [8] Gheni, M. Z. and Salman, Y. K. 'Natural convection heat transfer in inclined open annulus passage heated from two sides International journal of mechanical engineering and technology(ijmet),vol. 5, Issue 11, November pp (2014). [9] Subramanyam, D., Chandrasekhar, M., and Lokanadham, R. Experimental Analysis of Natural Convection over A Vertical Cylinder at Uniform Temperature International Journal of Mechanical Engineering & Technology (IJMET), Vol. 4, Issue 3, pp , ISSN Print: , ISSN Online: (2013). [10] Ozoe, H., Shibata, T. Churchill, S.W."Natural convection in an inclined circular cylindrical annulus heated and cooled on its end plates". Int. J. Heat Mass Transfer vol. 24 pp , (1981) [11] Holman, J. P., Heat transfer, 10th edition, McGraw-Hill Series in Mechanical Engineering (2010). [12] Holman, J. P., Experimental methods for engineers, 8th ed. McGraw-Hill Series in Mechanical Engineering (2011). [13] COMSOL MultiphysicsFinite Element Analysis Software, user guide (5.0), (2014). [14] Cattani, L. and Corradi, C. estimation of local heat-transfer coefficient in coiled tubes with corrugated wall. UIT Heat Transfer Conference, vol 32, pp.12-22, (2012). [15] Al-Jabair, S. and Habeeb, L. J. Simulation of Natural Convection in Concentric Annuli between an Outer Inclined Square Enclosure and an Inner Horizontal Cylinder. World Academy of Science, Engineering and Technology,vol. 69,pp (2012). [16] Sakr R.Y., Berbish N.S., Abd-Alziz A.A. and Hanafi A.S., Experimental and Numerical Investigation of Natural Convection Heat Transfer in horizontal Elliptic Annuli. Journal of Applied Sciences Research, Vol.4, pp , (2008). [17] Brangeon, B., Joubert, P. and Bastide, A. Numerical investigation of natural convection in inclined channel chimney system vol. 13 pp (2013). [18] Kassem, T. Numerical study of the natural convection process in the parabolic cylindrical solar collector. The Ninth Arab International Conference on Solar Energy (AICSE-9), vol. 209, pp , (2007). 16

17 [19] Andreozzi, A., Buonomo, B., and Manca, O. Numerical investigation on natural convection in asymmetric channel-chimney systems. In WIT Transactions on Modelling and Simulation, vol.46, pp , (2007). [20] Omar Mohammed Ali and Ghalib Younis Kahwaji, Numerical Investigation of Natural Convection Heat Transfer From Circular Cylinder Inside An Enclosure Using Different Types of Nanofluids International Journal of Mechanical Engineering & Technology (IJMET), Volume 5, Issue 5pp , ISSN Print: , ISSN Online: ,(2014). [21] Gheni, M. Z. Natural Convection Heat Transfer in The Annulus Passages (An Experimental and Numerical Investigation) LAP LAMBERT Academic publishing ISBN: (2016). 17