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International Journal of Research and Innovation (IJRI)

International Journal of Research and Innovation (IJRI) 1401-1402

THERMAL ANALYSIS OF DOUBLE PIPE HEAT EXCHANGER USING CFD

Lakamana Satyabhaskar1, K.koteswara Rao2,Y Dhana Shekar3 1 Research Scholar,Department Of Thermal Engineering, Kits, Peddapuram(M) Tirupathi Village, Divili 533-433,Eg Dt,AP, India. 2 Associate Professor,Department Of Thermal Engineering, Kits, Peddapuram(M) Tirupathi Village, Divili 533-433,Eg Dt,AP, India. 3 Assistant Professor , Department Of Thermal Engineering, Kits, Peddapuram(M) Tirupathi Village, Divili 533-433,Eg Dt,AP, India.

Abstract Heat transfer equipment is defined by the function it fulfills in a process. On the similar path, Heat exchangers are the equipment used in industrial processes to recover heat between two process fluids. They are widely used in space heating, refrigeration, air conditioning, power plants, chemical plants, petrochemical plants, petroleum refineries, and natural gas processing. The operating efficiency of these exchangers plays a very key role in the overall running cost of a plant. So the designers are on a trend of developing heat exchangers which are highly efficient, compact, and cost effective. A common problem in industries is to extract maximum heat from a utility stream coming out of a particular process, and to heat a process stream. Therefore the objective of present work involves study of refinery process and applies phenomena of heat transfer to a double pipe heat exchanger.

*Corresponding Author: Lakamana Satyabhaskar Research Scholar,Department Of Thermal Engineering, Kits, Peddapuram(M) Tirupathi Village, Divili 533-433,Eg Dt, Andhra Pradesh, India. Published: January 02, 2015 Review Type: peer reviewed Volume: II, Issue : I

Citation: Lakamana Satyabhaskar, Thermal Analysis Of Double Pipe Heat Exchanger Using CFD

transfer surface, and ideally they do not mix or leak. Such exchangers are referred to as direct transfer type, or simply recuperators. In contrast, exchangers in which there is intermittent heat exchange between the hot and cold fluids—via thermal energy storage and release through the exchanger surface or matrix are referred to as indirect transfer type, or simply regenerators. Such exchangers usually have fluid leakage from one fluid stream to the other due to pressure differences and matrix rotation/valve switching. Classifications of heat exchangers:

INTRODUCTION A heat exchanger is a device that is used to transfer thermal energy (enthalpy) between two or more fluids, between a solid surface and a fluid, or between solid particulates and a fluid, at different temperatures and in thermal contact. In heat exchangers, there are usually no external heat and work interactions. Typical applications involve heating or cooling of a fluid stream and evaporation or condensation of single- or multicomponent fluid streams. In other applications, the objective may be to recover or reject heat, or sterilize, pasteurize, fractionate, distill, concentrate, crystallize, or control a process fluid. In a few heat exchangers, the fluids exchanging heat are in direct contact. In most heat exchangers, heat transfer between fluids takes place through a separating wall or into and out of a wall in a transient manner. In many heat exchangers, the fluids are separated by a heat

There are a number exchanger types based on the type of flow configuration, method of heat transfer and constructional features. The process designer has to select the best suitable type that meets the performance and operational requirements. Following is the list of heat transfer equipment. Based on Principles of Operation (Transfer process): Recuperative Type (Direct Transfer): Cold and hot fluids flow simultaneously. Heat is transferred through a wall separating the fluids. Eg: Steam boilers, Heaters, Condensers etc. Regenerative type (Storage): One and the same heating surface is alternatively exposed to the cold and hot fluids. Heat carried by the hot fluid is taken away and stored in the walls of the apparatus and then transferred to the cold fluid Eg: Open hearth and glass melting furnaces, Air heaters of blast furnaces. 21


International Journal of Research and Innovation (IJRI)

Fluidized Bed Type:

Based on application:

It is a direct transfer type used to transfer heat between a fluid and finally divided particles of a sold material Eg: used in chemical industry, Coal fired boilers for waste heat recovery.

Condenser, Cooler, Chiller, Evaporator, Vaporizer, Recoiled heater, Waste heat boiler etc.

Based on Fluid Flow Arrangement: Counter flow: Parallel flow: Cross Flow: Single Pass Shell and Tube:

Scrubber condenser Froth- cooled heat exchanger Plastic tube exchanger Carbon block exchanger Scrapped surface exchanger

The tube bundle, or stack, is inserted inside the shell. Tube sheets hold the tubes in place and form a barrier to prevent the tube-side fluid from mixing with the shell-side fluid. A series of baffles directs the flow of cooling fluid back and forth across the tube bundle.

Materials And Manufacturing Process

Based on Method of Heat Transfer and Constructional Features Shell and Tube Heat Exchanger: Fixed tube heat exchanger U- tube exchanger Floating head exchanger Single Tube Heat Exchanger: Double pipe exchanger Trombone cooler Coils in vessel Parallel Plate Heat Exchanger: Gasketed Plate exchanger Spiral plate exchanger Lamella exchanger Plate evaporator. External Heating Type: Jacketed Vessel Steam Tracing Heat Transfer without Surfaces: Flash evaporation Direct contact condensers Cooling towers Heat transfer fluids Direct heating Direct use of steam Submerged combustion Extended Surfaces: Air cooled exchanger Plate fin exchanger Tank heating with finned tubes Solids heating with a bank of longitudinally finned tubes. Air heater

Special Types:

The selection of materials of construction is a very important aspect to be considered before undertaking the design of heat exchangers. In each individual case, the choice of proper material shall be made, bearing in mind the specific requirements which are normally as follows: 1. Mechanical resistance i.e. strength and sufficient toughness at operating temperatures. 2. Chemical resistance under operating conditions with regard to corrosive media, concentration, temperature, foreign substances, flow behavior etc. the rate of corrosion must be negligible over a prolonged period of time and the material must be resistant against other corrosion phenomenon. 3. No detrimental interference by the material on the process or on the products. 4. Easy supply of material within time permitted and in the time required. 5. Good workability. 6. Lowest possible costs. Descriptions of some of the material and their specifications: SA20 : Specification for general requirements for steel plates for pressure vessels. SA480: Specification for general requirements for delivery of flat rolled stainless Steel, stainless and heat resisting steel plates, sheet and strip. SA530: Specification general requirements for specialized carbon and alloy steel pipe. SA450: Specification for general requirements for carbon, feritic alloy and austenitic alloys steel tubes. SA203: Nickel alloy steel plated for pressure vessels. SA204: Molybdenum alloys steel plates for pressure vessels. SA240: Chromium and Chromium nickel, stainless steel plates, sheet and strip for fusion welded unfired pressure vessels. SA264: Stainless, Chromium, Nickel steel, clad plate, sheet and strip. SA285: Low and intermediate tensile strength carbon steel plates for pressure vessels. SA299: Carbon manganese, Silicon steel plates for pressure vessels. SA575: Carbon Steel plates for pressure vessels for intermediate and high temp Service SA577: High strength alloy steel plates, quenched 22


International Journal of Research and Innovation (IJRI)

and tempered for pressure Vessels SA537: Carbon magnesia, silicon steel plates, heat treated for pressure vessels. SA105: Forgings, carbon steel for piping components. SA181: Forgings carbon steel for general purpose piping. SA182: Forged or rolled alloy steel pipe flanges, forged fittings and valves. SA234: Pipe fitting of wrought carbon steel and alloy to moderate and elevated temperature services. SA350: Forgings, Carbon and low alloy steel requiring notch toughness, testing for piping components. SA420: Pipe fittings of wrought carbon and alloy steels for low temperature service SA336: Alloy steel forgings for seamless drum heads and other pressure vessels SA106: Seamless carbon steel pipe for high temperature service (343ยบC to 427ยบC) SA312: Seamless and welded austenitic stainless steel pipe. SA333: Seamless and welded steel pipe for low temperature eservice.

temperatures, the temperature gradually reduces towards the top, so that each tray is a little cooler than the one below. The crude needs to be heated up before entering the fractionation column and this is done at first in a series of heat exchangers where heat is taken from other process streams which require cooling before being sent to rundown. Heat is also exchanged against condensing streams from the main column. Typically, the crude will be heated up in this way up to a temperature of 200 - 280 0C, before entering a furnace. As the raw crude oil arriving contains quite a bit of water and salt, it is normally sent for salt removing first, in a piece of equipment called a desalter. Upstream the desalter, the crude is mixed with a water stream, typically about 4 - 6% on feed. Intense mixing takes place over a mixing valve and (optionally) as static mixer. The desalter, a large liquid full vessel, uses an electric field to separate the crude from the water droplets.

Problem description The present work is based on industrial requirement. In the petroleum refinery, after distillation, different grades of oil come out at different high temperature which comes in to a pump and supplied at required level. The aim is to design a double pipe heat exchanger for an already existing suction pool of pump in which hot hydrocarbons are passing after distillation. The heat recovered from high temperature hydrocarbons is utilized to increase the temperature of crude oil up to required limit. The pool data, drawings, temperature of hydrocarbon and required temperature rise of crude oil were given by industry. Refinery Process Description Introduction: Every refinery begins with the separation of crude oil into different fractions by distillation. The fractions are further treated to convert them into mixtures of more useful saleable products by various methods such as cracking, reforming, alkylation, polymerization and isomerization. These mixtures of new compounds are then separated using methods such as fractionation and solvent extraction. Impurities are removed by various methods, e.G. Dehydration, desalting, sulphur removal and hydrotreating. Refinery processes have developed in response to changing market demands for certain products. With the advent of the internal combustion engine, the main task of refineries became the production of petrol. Distillation is the first step in the processing of crude oil and it takes place in a tall steel tower called a fractionation column. The inside of the column is divided at intervals by horizontal trays. The column is kept very hot at the bottom (the column is insulated) but as different hydrocarbons boil at different

Distillation (Fractionation): Because crude oil is a mixture of hydrocarbons with different boiling temperatures, it can be separated by distillation into groups of hydrocarbons that boil between two specified boiling points. Two types of distillation are performed: atmospheric and vacuum. Design Aspects of Present Heat Exchanger The thermal design is based upon a certain process parameters, the thermal and physical properties of the process fluids and the basic governing equations. Conventionally design method of heat exchanger is largely based on the use of empirical equations as well as experimental data which is available mostly in the form of graphs and chart. Salient Features of Heat Exchanger The heat exchanger considered for analysis here has the following parameters. Shell side. Type of fluid: crude oil. Inlet temperature =313K Outlet temperature =553K. Mass flow rate=0.320kg/s. Diameter of shell=0.3m. 23


International Journal of Research and Innovation (IJRI)

Tube side Type of fluid: diesel oil. Inlet temperature =618K Outlet temperature =?. Mass flow rate=145.6kg/s. Specific gravity=0.874 Tube inside diameter =0.2027m. Tube outside diameter=0.2191m The properties of fluid are not available so with the help of the specific gravity mentioned for the hot fluid, obtained by API gravity equation 3.1. The petroleum refining is a major industry, petroleum products are an important fuel for power industry, and petroleum derivates are starting point for many syntheses in the chemical industry. Therefore given common names or denoting the refinery operations by which they were produced, and specific gravities are defined by a scale established by the American Petroleum Institute and termed either degrees API or oAPI. The oAPI is related to the specific gravity by

For counter flow LMTD

After obtaining API gravity from table hot fluid is identified as diesel. As cold fluid is crude oil. Design of double pipe heat exchanger: Thermal design calculations For this the following data are required Hot side(tube side) Inlet temperature Thi=618 K Outlet temperature Tho=? Mass flow rate Mh=145.6kg/s Specific heat Cph=3277.3J/kg K Density =874kg/m3 Thermal conductivity k=0.1107 w/m K

Flow area of fin Consider as 10% fin cut so the area of cut is calculated by the following

µ =4.5 ×10-3 Ns/m 2 (or) pa-s

Viscosity Thickness of fin

t=0.002 m s=0.142 m

Fin pitch

N f = 34

Number of fins

cold side(shell side) Inlet temperature Outlet temperature Mass flow rate Specific heat Density Thermal conductivity Viscosity

Tci=313 K Tco=553 K Mc=0.320kg/s Cpc=2491J/kg K =698kg/m3 k=0.130 w/m K

µ =0.75 ×10-3 Ns/m 2 (or) pa-s 24


International Journal of Research and Innovation (IJRI)

Hence it is turbulent flow Friction factor

Area of fin

Colburn factor

Bare area (or) unfin area

Prenatal number

Total fin area

Pressure drop

Perimeter

Equivalent diameter Geometry

Velocity

The designed geometry under consideration in this thesis is a double pipe heat exchanger type or concentric tube heat exchanger with a circular fins or baffles the domain is sub divided in to two sections with a shell and tube channels. Figures 3.2 show schematic two-dimensional views of the heat exchanger to be analyzed. This type of heat exchanger has been designed to recovery of heat from hot source (hot fluid) which is flowing through the tube and the shell side fluid is cold the flow is counter flow. The heat exchanger is one shell pass and one tube pass based on these conditions the heat exchanger is designed.

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International Journal of Research and Innovation (IJRI)

CFD ANALYSIS OF PLAIN TUBE

Results and Discussion Over view

Heat exchanger without mesh

Heat Exchanger with mesh

The present work involves the numerical analysis of the heat exchanger with different materials with varying fin thickness and by changing the mass flow rates for cold fluid. Initially the simulation is carried out with mass flow rate 0.320 Kg/s and shifted to 0.220 And 0.120 Kg/s. The analysis was carried out for steel, aluminum, and copper material for different thickness range of 0.002M to 0.005M in the interval of 0.001M and the simulations and results are discussed. These simulations are done as an attempt for analysis of heat transfer and flow phenomena in the shell side and tube side. The steady state and unsteady simulations are done with inlet conditions using turbulence model. The domain in the present study is quite a complex 3-d geometry, so it is quite diligent to present the flow physics in the whole domain for discussion. The 2-d planes are taken in the geometry for the discussion. The plane and line along with the whole geometry and the coordinate axes are shown in fig 6.1. The plane and line are taken along the length of the heat exchanger in the x-y planes of constant z-coordinate. Plane is taken in the centre of tubular section and a line is at 0.220M from an outlet of the section. The details of fin materials along with different thickness for comparison are presented in table 6.1. Material/fin thickness

Steel

Aluminum

Copper

Temperature variation on plane along the heat exchanger

t1

0.002

0.002

0.002

t2

0.003

0.003

0.003

t3

0.004

0.004

0.004

Numerical Simulation Procedure

t4

0.005

0.005

0.005

Details of Comparative Study

The Plane and position of line in the flow domain.

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International Journal of Research and Innovation (IJRI)

Material Steel

Temperature variation on plane along the heat exchanger.

Temperature variation across Outlet for varying Fin thickness. Comparison of materials

Temperature variation across Outlet for varying Fin thickness

Material Aluminum

Temperature variation on fin along the heat exchanger. Temperature variations on plane along the heat exchanger

Temperature variation across Outlet for varying Fin thickness. Material copper.

Temperature variations on plane along the heat exchanger.

Variation of Heat Transfer with varying fin thickness. The above graph shows the relation between the heat transfer and fin thickness with different materials. As the fin thickness increases the value of heat transfer is increasing. For copper heat transfer is maximum value when compared to other materials and steel is having the least value of heat Transfer.

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International Journal of Research and Innovation (IJRI)

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International Journal of Research and Innovation (IJRI)

(a) Varition of Friction factor with Reynolds number (b) Varition of Heat Transfer Coefficient with Reynolds number Summary of results Mass flow rates 0.320kg/s Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

604.47

37.65

0.14

88704

2

0.003

605.12

38

0.14

88896

3

0.004

605.59

38

0.14

89088

4

0.005

605.96

38

0.14

89232

Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

609.17

37.65

0.14

90208

2

0.003

609.47

38

0.14

90272

3

0.004

609.59

38

0.14

90304

4

0.005

609.69

38

0.14

90320

Variation of properties with different thickness (a) Steel (b) Aluminum (c) Copper Mass flow rates 0.220kg/s

Velocity (m/s)

Heat transfer (W)

1

0.002

526.65

37.65

0.14

167265.66

2

0.003

528.38

38

0.14

168600.05

3

0.004

529.72

38

0.14

169622.3

4

0.005

530.72

38

0.14

170435.08

Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

538.39

37.7

0.14

176473.69

2

0.003

539.76

38

0.14

177524.04

3

0.004

540.55

38

0.14

178145.21

4

0.005

541.07

38

0.14

178549.9

Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

540.46

38

0.14

178074.16

2

0.003

541.39

37.8

0.14

178820.6

3

0.004

541.88

38

0.14

179189.36

4

0.005

542.21

37.8

0.14

179464.3

Variation of properties with different thickness (a) Steel (b) Aluminum (c) Copper Mass flow rates 0.120kg/s Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

604.47

37.65

0.14

88704

2

0.003

605.12

38

0.14

88896

3

0.004

605.59

38

0.14

89088

4

0.005

605.96

38

0.14

89232

Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

604.47

37.65

0.14

134432

2

0.003

605.12

38

0.14

135200

3

0.004

605.59

38

0.14

135744

4

0.005

605.96

38

0.14

136192

Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

565.17

37.65

0.14

139648

2

0.003

575.88

38

0.14

140224

3

0.004

576.52

38

0.14

140560

4

0.005

576.93

38

0.14

140768

Sr no

Thickness of fin (m)

Temperature (k)

Pressure (Pascal)

Velocity (m/s)

Heat transfer (W)

1

0.002

576.44

37.65

0.14

140512

2

0.003

577.18

38

0.14

140912

3

0.004

577.58

38

0.14

141136

4

0.005

577.83

38

0.14

141232

Variation of properties with different thickness (a) Steel (b) Aluminum (c) Copper Conclusions 1. As we increase the fin thickness the temperature of the cold fluid at the outlet of the heat exchanger increases. 2. We get high temperature profile at outlet in case of Aluminum and copper compared to steel material. 3. There is very minor changes occur in the pressure and velocity profile with increase of fin thickness as well as change of material that is pressure and velocity doesn’t get much affected by thickness of fin and material of fin. 29


International Journal of Research and Innovation (IJRI)

4. The simulated outlet temperature is 543k which is very near to design outlet temperature 553k. There is less than 3% variation occurs than design value. 5. By decreasing the mass flow rate for there is increasing the value of temperature up to 609k and 577k. 6. After 5min there is no variation in temperature with respect to time.

flow passages, ASME Journal of Heat Transfer 114 (1992), pp. 373–382. 10.D Q kern design of process heat transfer.D.Q. Kern, Process Heat Transfer, McGraw-Hill, New York, 1950.

Future Scope

11.Ebru Kavak Akpinar Evaluation of heat transfer and exergy loss in a concentric double pipe exchanger equipped with helical wires. Energy Conversion and Management 47 (2006). 3473- 3486.

1. Optimization of fin thickness and material for a heat exchanger 2. Experimentation thermal analysis of double pipe heat exchanger. 3. Numerical analysis of double pipe heat exchanger using augmentation devices.

12.e. r. g. eckert, r. j. goldstein, w. e. ibele, s. v. patankar, t. w. simon, n. a. decker, s. l. girshick, p. j. strykowski, k. k. tamma, a. bar-cohen, j. v. r. heberlein and d. l. hofeldt Heat transfer-a review of 1990 literature Int.J Heat Mass Trans. Vol. 34, No. 12, pp. 2931-3010, 1991.

References

13.Edited by Chang S. Hsu Exxon Mobil Research and Engineering Company Baton Rouge, Louisiana, And Paul R. Robinson PQ Optimization Services Katy, Texas, USA Practical Advances in Petroleum Processing Volume 2

1.A.Behzadmehr, N. Galanis and A. Laneville, Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux, International Journal of Heat and Mass Transfer 46 (2003), pp. 4823–4833. 2.A. E. Bergles and W. J. Marner Augmentation of Highly Viscous Laminar Heat Transfer Inside Tubes with Constant Wall Temperature, Experimental Thermal and Fluid Science 1989; 2:252-267. 3.A.E. Saad, A.E. Sayed, E.A. Mohamed, M.S. Mohamed, Experimental study of turbulent flow inside a circular tube with longitudinal interrupted fins in the stream wise direction, Experimental Thermal Fluid Science 15 (1) (1997) 1–15. 4.Alam, P.S. Ghoshdastidar, A study of heat transfer effectiveness of circular tubes with internal longitudinal fins having tapered lateral profiles, International Journal of Heat and Mass Transfer 45 (6) (2002) 1371–1376. 5.Bergles, A. E., and Joshi, S. D., Augmentation Techniques for Low Reynolds Number In-Tube Flow, in Low Reynolds Number Flow Heat Exchangers, S. Kakac, R. K. Shah, and A. E. Bergles, Eds. Hemisphere, Washington, D.C., pp. 695-720, 1983. 6.B.Yu, J.H. Nie, Q.W. Wang, W.Q. Tao, Experimental study on the pressure drop and heat transfer characteristics of tubes with internal wave-like longitudinal fins, Heat Mass Transfer 35 (1999) 65–73. 7.C.P.Kothandaraman.S.Subramanyan. Heat and Mass transfer Data book New age international publisher sixth edition. 8.C.R. Friedrich, S.W. Kang, Micro heat exchangers fabricated by diamond machining, Precision Engineering 16 (1994) 56–59. 9.D.A. Olson, Heat transfer in thin, compact heat exchangers with circular, rectangular, or pin-fin

14.G. Fabbri, A genetic algorithm for fin profile optimization, Int. J. Heat Mass Transfer 40 (9) (1997) 2165–2172. 15.G. Fabbri, Heat transfer optimization in internally finned tubes under laminar flow conditions, Int. J. Heat Mass Transfer 41 (10) (1998) 1243–1253. 16.John H. Lienhard IV / John H. Lienhard V.A heat transfer textbook third edition. 17.Kuehn, T. H. and Goldstein, R. J. An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders. Journal of Fluid Mechanics, 1976, 74, 695719. 18.Lai, F. C., Improving effectiveness of pipe insulation by using radial baffles to suppress natural convection. International Journal of Heat and Mass Tranffer, 1993, 36, 899-906. 19.Monheit, M., Experimental Evaluation of the Convective Characteristics of Tubes with Twisted Tape Inserts, in Advances in Enhanced Heat Transfer--1987, M. K. Jensen and V. P. Carey, Eds., HTDVol. 68, ASME, New York, pp. 11-18, 1987. 20.N. Queipo, R. Devarakonda, J.A.C. Humphrey, Genetic algorithms for thermo sciences research: application to the optimized cooling of electronic components, Int. J. Heat Mass Transfer 37 (6) (1994) 893–908. 21.O. Zeitoun and A.S. Hegazy, Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature, Heat Mass Transfer 40 (2004), pp. 253–259.

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International Journal of Research and Innovation (IJRI)

22.P chattopadhyay Heat and mass transfer through theory and problems. Khanna publishers 23.Q.W. Dong , Y.Q. Wang and M.S. Liu Numerical and experimental investigation of shell side characteristics for RODbaffle heat exchanger. Applied Thermal Engineering Volume 28, Issue 7, May 2008, Pages 651-660 24.R. Kumar, Three-dimensional natural convective flow in a vertical annulus with longitudinal fins, International Journal of Heat and Mass Transfer 40 (14) (1997) 3323–3334.

K.koteswara Rao. Assistant professor Kits, Peddapuram(M) Tirupathi Village, Divili 533-433, Eg Dt,Andhra Pradesh,India.

25.Sarkhi, E.A. Nada, Characteristics of forced convection heat transfer in vertical internally finned tube, International Communications in Heat and Mass Transfer 32 (2005) 557–564 Authors

Y Dhana Shekar, Assistant Professor , Kits, Peddapuram(M) Tirupathi Village, Divili 533-433, Eg Dt,Andhra Pradesh, India

Lakamana Satyabhaskar Research Scholar (mtech in Thermal Engineering) Kits, Peddapuram(M) Tirupathi Village, Divili 533-433, Eg Dt,Andhra Pradesh,India.

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