Analytical and Numerical Design Analysis of Concentric Tube Heat Exchangers A Review

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1 IOP Confeence Seies: Mateials Science and Engineeing PAPER OPEN ACCESS Analytical and Numeical Design Analysis of Concentic Tube Heat Exchanges A Review To cite this aticle: Kathik Silaipillayaputhu et al 207 IOP Conf. Se.: Mate. Sci. Eng View the aticle online fo updates and enhancements. Related content - Plate flat finned tubes heat exchange: Heat tansfe and pessue dop modeling M Bououd, O Hachchadi and A Mechaqane - Exegy analysis of double tube heat exchange fo paallel flow aangement. Saif Nawaz Ahmad, Neeaj Piyadashi, Akash Kuma Bhoi et al. - A Numeical Analysis on a Compact Heat Exchange in Aluminum Foam B Buonomo, D Ecole, O Manca et al. This content was downloaded fom IP addess on 06/09/208 at 20:4

2 Analytical and Numeical Design Analysis of Concentic Tube Heat Exchanges A Review Kathik Silaipillayaputhu, Tawfiq Al Mughanam, Abdulaziz Al Mojil and Mohammed Al Dhmoush King Faisal Univesity, Saudi Aabia Abstact. This pape consides an analytical and a numeical appoach in the design of a concentic tube heat exchange. Sensible heat tansfe is consideed in the analysis and the heat exchange is developed fo actual opeating conditions in a chemical plant. The heat exchange is a concentic tube heat exchange whee hot oil exchanges heat with hot wate. Hot oil is in the inne pipe and the heating medium, hot wate, is in the oute pipe (annula side) of the heat exchange. An analytical model employing effectiveness-numbe of tansfe units (ɛ-ntu) appoach and log mean tempeatue diffeence (LMTD) appoach wee employed in the design of the concentic tube heat exchange. In the design pocess, pefomance chats wee developed fo concentic tube heat exchange. Pefomance chats descibe the pefomance of the heat exchange in tems of cucial dimensionless paametes. Pefomance chats help to select the ight numbe of tansfe units (NTU) fo the given heat exchange. Both paallel and counte flow configuations wee consideed fo the design analysis. Likewise, a numeical model was also consideed in the design of the heat exchange. The esults fom the analysis ae pesented and compaed. Fom the esults it can be seen that both numeical and analytical appoaches poduce the exact same esults. The designe cetainly has the flexibility to choose an appopiate design methodology based on the available inputs and equiements.. Intoduction Heat exchanges (HX) ae used in all pocess and manufactuing industies woldwide. Heat exchange equipment tansfes heat fom a hot fluid to a cold fluid. Heein both fluids ae sepaated by means of a solid wall. Typically, most heat exchanges ae two-fluid heat exchanges though theefluid heat exchanges ae becoming popula. Heat exchanges can be classified in tems of flow and constuction. In tems of flow, heat exchanges can be classified as paallel flow, counte flow and coss flow. In tems of constuction, they can be classified as shell and tube, concentic tube and finned tube heat exchanges. The choice of a heat exchange fo a given application is dependent on the application itself, available esouces, space, existing connections in the field, etc. Whateve may be the choice of a heat exchange, it is vey essential that a heat exchange be designed such that it delives the equied heat tansfe while occupying less space, being light weight, and yet be piced competitively. In this poject, a concentic tube heat exchange is designed fo heating hot oil. Hot oil is used fo a cetain pocess heating application and hot wate is the heating medium. The heat exchange will be designed such that the hot oil shall flow though the inne pipe and hot wate though the oute pipe (annula side) of the heat exchange. A conventional ε-ntu appoach, LMTD appoach and a numeical appoach ae employed in design the concentic tube heat exchange. Both paallel and counte flow configuations ae consideed in the Content fom this wok may be used unde the tems of the Ceative Commons Attibution 3.0 licence. Any futhe distibution of this wok must maintain attibution to the autho(s) and the title of the wok, jounal citation and DOI. Published unde licence by Ltd

3 design analysis. Heein, pefomance chats wee developed to aid the design pocess. Pefomance chats descibe the vaiation of heat exchange effectiveness with espect to capacity ate atio and numbe of tansfe units (NTU). Since all paametes in pefomance chats ae expessed in dimensionless basis, the developed pefomance chats ae applicable fo any system of units, inlet fluid tempeatues, fluid flow ates, mateials of constuction and size. Each design appoach has unique chaacteistics and these aspects ae discussed in the subsequent sections of the pape. Thee ae numeous efeences available in the liteatue petaining to heat exchange pefomance modelling, and only the most petinent ae discussed. Kays and London [] and Rohsenow [2] descibed both the logaithmic mean tempeatue diffeence and the methods in ode to size and pedict the pefomance of a heat exchange. Domingos [3] pesented a geneal method of calculating oveall pefomance and intemediate tempeatues of complex cossflow heat exchanges using the concept of effectiveness and a local enegy balance. Pignotti and Shah [4] and Shah and Pignotti [5] discussed the tools developed peviously (such as Domingos method, the Pignotti chain ule, etc.,) to detemine the elationship fo highly complex heat exchange flow aangements. As compaed with the pesent investigation, these studies petained to quite diffeent geometies such as coss flow and shell and tube heat exchanges. Futhemoe, they did not addess the design of optimal heat exchanges, which achieve the equied task at the lowest cost while satisfying imposed constaints. Mott and Mills [6] and Genic et al. [7] ae among those eseaches who descibed optimization analysis based pimaily on minimizing enegy costs elated to pumping of a fluid. Kovaik [8] descibed a technique to optimize a coss flow heat exchange. The objective function which was employed included cost factos elated to the heat exchange size and pumping powe, as well as the equied heat tansfe ate. Similaly Rao et al. [9] and Caputo et al. [0] poposed methods to minimize capital and opeating costs fo shell-and-tube heat exchanges while satisfying the equied heat tansfe duty. Silaipillayaputhu and Idem [] consideed a numeical appoach in the design and optimization of a double pipe heat exchange. Theein, the heat exchange was optimized such that the capital cost and opeation cost of the heat exchange wee minimized. 2. Nomenclatue Symbol Name A o Heat exchange suface aea (m 2 ) C min C max C C p D H Minimum capacity ate fluid (W/K) Maximum capacity ate fluid (W/K) Capacity ate atio (dimensionless) Specific heat (J/kgK) Tube hydaulic diamete (m) d in d out Tube inside diamete (m) Tube outside diamete (m) h i Intenal heat tansfe coefficient (W/m 2 K) h o Extenal heat tansfe coefficient (W/m 2 K) m Mass flow ate (kg/s) 2

4 K L Nu NTU P Q Re T Themal conductivity (W/mK) Tube length (m) Nusselt Numbe (dimensionless) Numbe of tansfe units (dimensionless) Pandtl Numbe (dimensionless) Rate of heat tansfe (W) Reynolds numbe (dimensionless) Tempeatue (K) T m log mean tempeatue diffeence (K) V Velocity (m/s) R f f f Fouling facto Dacy fiction facto Function, dimensionless U o Oveall heat tansfe coefficient (W/m 2 K) Geek Symbols Heat exchange effectiveness ε Suface oughness of pipe, m Dynamic Viscosity (Ns/m 2 ) ΔT ΔP Density (kg/m3) Tempeatue Diffeence (K) Pessue dop in pipe (Pa) 3. Analytical Appoach This poject consides the design of a concentic tube heat exchange wheein the hot oil is in the inne pipe of the heat exchange and hot wate is in the oute pipe (annula side) of the heat exchange. The hot oil is used fo a cetain heating application in the pocess plant. It is poposed to pe-heat the oil using the available waste hot wate in the facility. It is desied to aise the tempeatue of 400 lbm/h of hot oil fom 90 F to 00 F by employing hot wate that is available at 5000 lbm/h at 50 F. The hot oil employed in the study is a heat tansfe fluid, ated fo open systems, having a viscosity gade of ISO 46. The themophysical popeties of the fluids employed in the heat exchange ae descibed in Tables and 2 espectively. 3

5 Table. Hot Oil Themal Popeties. (kg/m 3 ) m (kg / s) C P (J/kg- o C) k (W/m- o C) (N-s/m 2 ) Table 2. Hot Wate Themal Popeties. (kg/m 3 ) m (kg / s) C P (J/kg- o C) k (W/m- o C) (N-s/m 2 ) The design constaints fo the poject ae descibed in Table 3. The design constaints ae heat tansfe duty, heat exchange diamete, and length. An additional design constaint, allowable pessue dop, will be consideed while employing the numeical model. Employing this constaint in the conventional ε-ntu appoach and LMTD appoach will make the design pocess a little tedious. Theefoe, in pactical applications, this constaint is examined in tems of flow velocity. In eal life applications, to keep the pessue dop within easonable limits, it is a common accepted pactice to keep the velocity of flow in the pipe to be aound 3 m/s. Table 3. Design Constaints. Design Constaints Paamete Condition Dischage oil tempeatue 37ºC Max. heat exchange extenal diamete 75 mm (2.5 in NPS) Max. heat exchange length.2 m (4 ft) Allowable pessue dop, oil side* 500 Pa * - fo Numeical design analysis The assumptions employed in the analysis ae that the heat excahnge is opeating at steady state, the popeties of the fluids and the heat exchange wall emains constant, and the heat exchange is opeating adiabatically. The ate of heat tansfe o the heat tansfe duty, being one of the design constaint can be detemined as follows [2] Q mc pt () Hee, the tem ΔT efes to the absolute tempeatue diffeence between the fluid at inlet and at exit of the heat exchange. Assuming the concentic tube heat exchange to be well insulated it can be assumed that the ate of heat gained by the hot oil will be equal to ate of heat lost by the hot wate such that 4

6 Q (2) Q oil Q hotwate The aveage specific heat and the mass flow ate of both the fluids ates ae known. The equied dischage tempeatue of the hot oil is known as well. Theefoe, the ate of heat tansfe and the dischage tempeatue of hot wate can be eadily detemined by employing Equations () and (2). The capacity ate atio fo the given aangement may be given as [2] C C (m c ) min p oil (3) Cmax (m cp ) hotwate Hee, C min coesponds to the capacity ate of minimum capacity ate fluid, which is hot oil and C max coesponds to the capacity ate of maximum capacity ate fluid, which is hot wate. The values fo C min and C max can be eadily computed as the petinent infomation ae available. The heat exchange effectiveness may then be detemined by employing the following equation [2] Q Q max C min T Q (4) Hotwate,inlet T oil,inlet Hee, the ate of heat tansfe Q is given by Equation (). Fo a concentic tube heat exchange subjected to paallel flow, the heat exchange effectiveness may also be given as [2] exp NTU( C ) C (5) Likewise, fo a concentic tube heat exchange subjected to counte flow, the heat exchange effectiveness may also be given as [2] ) exp NTU( C ) (6) C exp NTU( C Numbe of tansfe units (NTU) is a dimensionless paamete that is widely used by pocess enginees and heat exchange designes. NTU is a physically significant dimensionless paamete as it encompasses mateial chaacteistics, fluid chaacteistics, flow chaacteistics, heat exchange size, fouling, etc. Using Equation (5) and (6), fo a ange of NTU vaying between 0. and 0, and capacity ate atios vaying between 0 and the heat exchange effectiveness can be eadily plotted and pefomance chats can be developed fo the concentic tube heat exchange. The following figues and 2 descibe the pefomance chats fo concentic tube heat exchange. Using the pefomance chats, the equied NTU fo the heat tansfe duty can be detemined. 5

7 Effictivness Effictivness ICMMM 207 Concentic Tube HX - Paallel Flow C = 0.0 C = 0.25 C = 0.5 C = 0.75 C = NTU Figue. Pefomance of concentic tube heat exchange subjected to paallel flow. Concentic Tube HX - Counte Flow C = 0.0 C = 0.25 C = 0.5 C = 0.75 C = NTU Figue 2. Pefomance of concentic tube heat exchange subjected to counte flow. NTU is a dimensionless paamete that accounts fo mateial chaacteistics, flow chaacteistics, size, constuction, fouling, etc. Theefoe, NTU is a physically significant dimensionless paamete that is used by enginees duing the design phase of the heat exchange. Likewise, it must be ecognized that highe the NTU, the moe would the aea, mateial, size, weight and cost. In keeping up with the competition, it is impotant to design the equipment such that it is compact, less weight, low cost and yet delive the equied heat tansfe. Pefomance chats descibed in Figues and 2 shall help in optimizing the heat exchange duing the development phase. In addition, it is a common belief that inceasing the suface aea enhances the ate of heat tansfe. Howeve, this is tue only until a theshold limit and inceasing the suface aea (i.e., NTU) beyond that limit, adds unnecessay weight 6

8 and cost. Figues and 2 is cetainly helpful in choosing the ight suface aea (i.e., NTU) fo the given application. The detemination of intenal and extenal heat tansfe coefficients ae descibed extensively in [] and [2] and theefoe they ae not discussed heein. Consideing the fouling esistances, and conduction esistances, the oveall heat tansfe coefficient may be given as [2] U o in,out in,out in,out in,out R fo ln R fi (7) h o k pipemateial,in in,in in,in in,in h i Recall that the equied NTU fo the heat exchange was detemined using pefomance chats. The NTU of a heat exchange can also be descibed as [2] NTU UA (8) C min Hence, fom Equation (8), the equied suface aea of the heat exchange can be eadily detemined. The suface aea of the heat exchange can be descibed as A d L in, out (9) Fom Equation (9) the equied length fo the concentic tube heat exchange can be detemined. If log mean tempeatue diffeence (LMTD) appoach wee to be used, the ate of heat tansfe may be descibed as [2] Q U A T (0) o o lm The computation of log mean tempeatue diffeence descibed in detail in [2] and theefoe not included heein. T m fo paallel and counte flows ae Fo LMTD appoach, the equied heat tansfe suface aea is detemined by employing Equation (0) and the equied length of the concentic tube heat exchange can be detemined by employing Equation (9). Using the equations descibed in this section a MATLAB model was developed to design the concentic tube heat exchange. 4. Numeical Appoach This section of the document descibes the govening equations equied to design the heat exchange using numeical appoach. Only the hot oil side is consideed in the analysis, as heating up of hot oil is the pimay focus in the poject. The dimensions of the inne pipe and the flow velocity of oil ae detemined such that the equied heat tansfe duty is satisfied fo a given mass flow ate and fo an allowable pessue dop. Fom Equation (), fo the given conditions, the tempeatue diffeence in the hot wate between the inlet and dischage was found to be negligible. This means that the hot wate tempeatue emains appoximately a constant while flowing though the concentic tube heat 7

9 exchange. Hence, it is easonable to assume that the heat exchange wall is at constant tempeatue duing the steady state opeation of the heat exchange. Consideing the heat exchange to opeate adiabatically, an oveall enegy balance yields the heat tansfeed fom the tube wall to the hot oil [, 2] p, T,out T, in πdh,inne LhiΔT m Q m c () The log-mean tempeatue diffeence is the mean tempeatue diffeence between the tube wall and the hot oil [, 2] T m T T T T w,in T n T w w T T w,in,out,out The empiical Dittus-Boelte coelation fo tubulent convection heating can be given as [, 2] Nu h D i H,inne Re P (3) k The Dacy fiction facto epesents the dimensionless pessue loss pe unit length in a pipe and can be expessed in tems of the mean oil velocity [, 2, 6] ΔP L f (4) 2 2 ρv D H,inne An expession fom Haaland [, 3, 5, 6] povides an explicit elation between the fiction facto, pipe elative oughness, and the Reynolds numbe (2) f ε.8log D 3.7 H,inne. 6.9 Re (5) The Reynolds numbe may be defined as [, 2] Re V H,inne (6) D The mean oil velocity in the pipe is detemined fom the continuity equation [, 6] V 4m 2 H,inne D (7) Upon eaanging, the enegy consevation can be expessed in dimensionless as follows [] 8

10 0.8 m c cp, VD H,inne p f 0.023, k L k Tw T,in ln Tw T,out (8) Upon eaanging Equations (4) and (5), the following dimensionless equation can be obtained [] f 2. V L DH,inne.8 log pd H,inne 3.7 (9) VDH,inne 2 Upon eaanging Equation (7), the following dimensionless equation can be obtained [] f V D 2 H,inne 4 3 m 0 (20) The quantities f, f 2, and f 3 epesent simultaneous nonlinea algebaic equations whose numeical oots ae to be detemined by employing techniques such as Newton Raphson method, Secant method, etc. MATLAB softwae has an inbuilt solve fo solving simultaneous nonlinea algebaic equations. By solving the thee simultaneous non linea equations, the thee unknowns, namely, the pipe diamete, length and pipe velocity can be detemined. 5. Results Based on the analytical (ɛ-ntu and LMTD) appoach and numeical appoach as discussed in the sections 3 & 4 espectivily, Matlab models wee developed to design the concentic tube heat exchange. The heat exchange was subjected to the input conditions as descibed in section 3 and the design constaints as descibed in Table 3. The esults fom both models fo paallel and counte flow concentic tube heat exchange ae descibed in Table 4. Table 4. Desciption of Concentic Tube Heat Exchange. Item Inne Side Annula Side Fluid Hot Oil Hot Wate Inlet Temp ( C) Dischage Temp ( C) Mass flow ate (kg/s) Heat Tansfe (W) Pessue dop, oil side (Pa)* 250 NA Mateial Cabon Steel, SMLS A53B Cabon Steel, ERW A 53B Diamete (in) - Analytical /2 /4 Diamete (in) - Numeical /2 NA Length (m) - (ɛ-ntu) appoach, paallel flow Length (m) - (ɛ-ntu) appoach, counte flow Length (m) - LMTD appoach, paallel flow Length (m) - LMTD appoach, counte flow Length (m) - Numeical appoach * - fo numeical design analysis Design of Concentic Tube Heat Exchange 9

11 It can be clealy seen that both the analytical and numeical appoach delive the same esults fo the pescibed conditions. Though fom pefomance chats, it can be clealy seen that the counteflow heat exchanges pefom significantly bette than the paallel flow heat exchanges, fo the given application, thee is absolutely no diffeence in the esults between counte and paallel flow configuations. This is due to the pevailing unifom tempeatue of the hot fluid in the heat exchange. The mateial selection fo the heat exchange was based on DuPont Engineeing Standads as pescibed in [4]. 6. Conclusions This pape eviews the analytical and numeical appoach in the design of a concentic tube heat exchange. Theein, both paallel and counte flow configuations ae analyzed. In the design pocess, pefomance chats wee developed fo concentic tube heat exchange. Pefomance chats help the enginees to quickly detemine the pefomance of the heat exchange without pefoming tedious calculations. Likewise, pefomance chats help the enginees to detemine the equied NTU fo the heat exchange. NTU accounts fo the physical chaacteistics of the heat exchange, fluid and themal popeties, type of heat exchange and fouling. Since NTU accounts fo all the petinent paametes, optimizing NTU is an essential item in the design of the heat exchange. An ove sized exchange (having highe NTU) will cetainly incu highe capital and opeational costs and while an unde sized heat exchange (having lowe NTU) shall cetainly not delive the equied heat tansfe. Pefomance chats developed in this pape will help the designes and enginees by poviding this cucial infomation. In addition, both analytical and numeical appoaches ae eviewed in this pape. Numeical appoach accounts fo tube side pessue dop and the heat exchange can be designed such that this design citeion is satisfied. Analytical appoach consisting of ε-ntu and LMTD methods do not explicitly satisfy this citeion. Likewise, employing the analytical appoach can help to optimize the heat exchange by choosing the ight NTU fo the given application. Howeve, if the equied dischage tempeatues ae unknown, it is quite tedious to model using LMTD method as the design pocess shall be iteative. Theefoe, based on the available infomation and the equied specifications, the designes can choose an appopiate method fo the design of a concentic tube heat exchange. 7. Refeences [] Kays, W. M., and London A. L., Compact Heat Exchanges, 3 d Ed., McGaw-Hill, New Yok, 984. [2] Rohsenow, W. M., Heat Exchanges Basic Methods, in Heat Exchanges Themal-Hydaulic Fundamentals and Design, Hemisphee Publishing Copoation, Washington D.C., 982. [3] Domingos, J. D., Analysis of Complex Assemblies of Heat Exchanges, Int. J. Heat Mass Tansfe, Vol. 2, pp , 969. [4] Pignotti, A. and Shah, R. K., Effectiveness-numbe of tansfe units elationships fo heat exchange complex flow aangements, Int. J. Heat Mass Tansfe, Vol. 35, No. 5, pp , 992. [5] Shah, R. K. and Pignotti, A., Themal Analysis of Complex Cossflow Exchanges in Tems of Standad Configuations, J. Heat Tansfe, Vol. 5, pp , 993. [6] Mott, J. E. and Mills, R. R., Computeized Design of a Minimum Cost Heat Exchange, ASME Pape 72-HT-26, 972. [7] Genic, S. B., Jacimovic, B. M., and Genic, V. B., Economic optimization of pipe diamete fo complete tubulence, Enegy and Buildings, Vol. 45, pp , 202. [8] Kovaic, M., Optimal Heat Exchanges, J. Heat Tansfe, Vol., pp ,

12 [9] Ramananda Rao, K., Shinivasa, U., and Sinivasan, J., Synthesis of Cost-Optimal Shell-and Tube Heat Exchanges, Heat Tansfe Engineeing, Vol. 2, No. 3, pp , 99. [0] Caputo, A. C., Pelagagge, M. P., and Salini, P., Heat Exchange Design Based on Economic Optimization, Pape CIT , ENCIT ABCM, Cuitiba, Bazil, [] Silaipillayaputhu, K., Idem, S., Design of a single tube fuel oil peheate, Heat Tansfe Engineeing, Volume 38, Issue 6, page , Taylo and Fancis, USA. [2] Begman, T. L., Lavine, A. S., Incopea, F. P., and DeWitt, D. P., Fundamentals of Heat and Mass Tansfe, 7 th Ed., John Wiley, Hoboken, NJ, 20. [3] Haaland, S. E., Simple and Explicit Expessions fo the Fiction Facto in Tubulent Pipe Flow, Jounal of Fluids Engineeing, vol. 05, pp , 983. [4] DuPont Technology Consulting; E.I. du Pont Nemous Company; Engg Standads; 2002 evision. [5] Douglas, J. M., Conceptual Design of Chemical Pocesses, pp , McGaw Hill, New Yok, 988. [6] Janna, W. S., Design of Fluid Themal Systems, 2 nd Ed., pp , PWS Publishing Company, Boston, 998.