Application of Net Radiation Transfer Method for Optimization and Calculation of Reduction Heat Transfer, Using Spherical Radiation Shields

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1 Wld Applied Sciences Junal (4: , 00 ISSN IDOSI Publicatins, 00 Applicatin f Net Radiatin Tansfe Methd f Optimizatin and Calculatin f Reductin Heat Tansfe, Using Spheical Radiatin Shields Seyflah Saeddin, Mhsen Tabi, Jalal Mghimi Kandelusi and Nima Maghsdl Depatment f Mechanical Engineeing, Faculty f Engineeing, Semnan Univesity, Semnan, Ian Depatment f Mechanical Engineeing, Faculty f Engineeing, Islamic Azad Univesity, Semnan, Ian Abstact: Analytical slutins play a vey imptant le in all mdes f heat tansfe. In this wk a simplifying appach f calculating the adiant enegy is achieved using the cncept f net adiatin tansfe and pvides an easy way f slving a vaiety f situatins. T be me pecise, the bjective f this pape is t calculate the net adiatin heat tansfe between tw cncentic sphees with and withut adiatin shield between them. Meve, using this methd the pecentage eductin in heat tansfe between tw sufaces was calculated and theefe ptimizatin was dne. It is cncluded that when tw adiatin shields with diffeent mateials have been applied t educe heat tansfe, the shield with lwe emissivity shuld be clse t the suface with highe tempeatue t incease eductin in heat tansfe. Meve, it is fund fm these calculatins that, ne adiatin shield with lwe emissivity can educe the net heat tansfe even bette than tw adiatin shields with highe emissivity. Key wds: Radiatin shield Net adiatin methd Cncentic sphees Emissivity INTRODUCTION intactable pblems in heat tanspt by adiatin can be easily slved using the cncept f net adiatin tansfe. Heat tanspt by adiatin is nt just a Use f netwk epesentatins was fist suggested by theetical pblem, since undestanding and Oppenheim [3]. This methd pvides a useful tl f pedicting the adiant enegy becmes cucial in many visualizing adiatin exchange between plates in the pactical situatins. In high-pefmance insulating enclsue and may be used as the basis f pedicting mateials it is cmmn t limit the effects f this exchange. This subject is als applicable t the cnductive and cnvective heat tansfe by design f multi-cveplate sla cllects. Indeed, in [4] evacuating the space between tw sufaces. This leaves the sla-adiatin tansmittance thugh a multi-plate themal adiatin as the dminant heat lss mde. plana windw is calculated and a matix-methd Thee ae many influential ways t minimize heat deivatin f the fmulae is pesented. Meve, lsses when adiatin heat tansfe is egnant mde. Micc and Alda [5] genealized the methd f net On way f educing adiant heat tansfe between tw tansmittance t spheical and cylindical symmety. paticula sufaces is t use mateials which ae highly But, they used nly ne adiatin shield between tw eflective. Using adiatin shield between the heat main sufaces. exchange sufaces is the pssibility that is pen t We d nt state t be iginal since the net adiatin scientists []. These shields d nt delive emve any methd can be fund in the liteatue [6]. Hweve, in heat fm the veall system; they nly place anthe this wk, the geneal fmulatin has been investigated esistance in the heat-flw path s that the veall heat t calculate net heat tansfe between tw cncentic tansfe is etaded. Radiatin shields cnstucted fm sphees. Applying N adiatin shields, afementined lw emissivity mateials can be used t educe the net fmulatin will be genealized t calculate eductin heat adiatin tansfe between tw sufaces. Nte that the tansfe between thse sufaces and accdingly sme + emissivity assciated with ne side ( n may diffe fm pblems wee slved. T the best f auths knwledge - that assciated with the ppsite side ( n f the shield these fmulatins and pblems cannt fund in the []. Ou gal cnsists in shwing hw appaently pevius liteatues. Cespnding Auth: Depatment f Mechanical Engineeing, Faculty f Engineeing, Semnan Univesity, Semnan, Ian. Tel: , Fax: , Tabi_mech@yah.cm. 457

2 Wld Appl. Sci. J., (4: , 00 Analysis: F the analysis, the fllwing simplifying assumptins ae made: R tt Sufaces ae diffuse and gay. Space between sphees is evacuated. Cnductin esistance f adiatin shield is negligible. The tempeatue f the heat-tansfe sufaces ae maintained the same in bth cases. The tw cncentic sphees and all the shields ae in adiant balance. Radiatin is ne-dimensinal. The emissivity assciated with the inne and ute sufaces f the shield ae the same. Using the abve assumptins, the adiatin heat tansfe equatins can be investigated by fllwing pcedues: The basic cncepts elated t heat tanspt by adiatin ae vey well knwn. F an ideal gey suface the emitted themal adiatin leaving a suface, pe unit time and unit aea, is given by i E bi i + + A AF A i i i i 4 E b T ( The net adiatin heat tansfe between any tw f the cncentic sufaces is then When E R tt b bi b i E E ( T T Mst eal sufaces exhibit a selective emissin, in the sense that the emissivity is diffeent f diffeent wavelengths. In geneal can be a functin f the wavelength and the suface tempeatue, i.e. (,T. A special type f nn-black suface, called a gey bdy, is defined as ne f which the emissivity is independent f the wavelength [7]. F simplicity we will estict u study t gey bdies. In additin, we will cnside that emissin is diffuse, s the intensity leaving a suface is independent f diectin. Using the net adiatin methd the ttal esistance between tw sufaces can be btained by: Theefe, the net heat tansfe between inne and ute sufaces is: ( (3 (4 i withut shield i withut shield i withut shield i sn i T ( T i + + A AF A i i i i Recgnizing F, it fllws that: i i T ( T + A A i i And finally the net heat tansfe between inne and ute sufaces can be btained by: i i i T A( T i i Ts A( T i i with shield i A ( T T Asn( Tsn T sn sn T have gd cmpaisn between the amunt f heat tansfe with and withut adiatin shields, it is must t find a functin as the amunt f heat tansfe with N adiatin shields between inne and ute sufaces; when N is the numbe f shields. As cited befe, the shields d nt delive emve heat fm the system and theefe the heat tansfe between each tw adjacent sphees can be btained as fllws: Ai( Ti T N i sn i + + i n sn sn (5 (6 (7... ( (8 i sn i with shield Whee, and ae as fllws: i sn (9 (0 ( Adding all these equatins, eliminates all the unknwn shield tempeatues and afte slving f the net heat tansfe, we btain ( [( ( ] ( 458

3 Wld Appl. Sci. J., (4: , 00 Fig. : Tw cncentic sphees (a withut adiatin shield (b with ne adiatin shield (c with tw adiatin shields Fig. : Nmal emissivity as a functin f tempeatue [] Equatin ( nt fund in pevius liteatues and epesents the net heat tansfe between tw cncentic sphees when N shields have been applied t educe the amunt f heat lss. Applicatin: As mentined befe the emissivity is a functin f tempeatue. Because emissivity and tempeatue f each shield is unknwn, Fig.. has been emplyed f slving Eqs. (9-( at the same time. Nte that all the calculatins have been pefmed f all thee mateials in Fig.. Example : Cnside tw cncentic sphees as shwn in Fig.. (a. The inne sphee has tempeatue K, adius 50 cm and emissivity f 0.8. The ute sphee has tempeatue 330 K, adius 00 cm and emissivity f 0.3. If ne shield has been applied at adius 75 cm t educe heat tansfe between inne and ute sphees (Fig.. (b, the pecentage eductin in heat tansfe, tempeatue and emissivity f the adiatin shield can be calculated as fllws: ( w i with shield F Aluminum Oxide Shield: Using Fig.. and slving Eqs. (9 and ( tgethe: ( w i with shield T K, And the pecentage eductin in heat tansfe is: ( i withut shield ( i with shield i withut shield % 459

4 Wld Appl. Sci. J., (4: , 00 Similaly f silicn cabide shield: ( w ( w T K, i with shield T K, T K, i with shield And the pecentage eductin in heat tansfe is: % And the pecentage eductin in heat tansfe is: % Finally f tungsten shield: ( w i with shield T K, And the pecentage eductin in heat tansfe is: % ( i withut shield ( i with shield i withut shield % Finally f tungsten shield: ( i with shield w % Example : Cnside the tw cncentic sphees f example. If tw shields with same mateials have been It can be easily seen that, ne adiatin shield with applied at adius and cm t educe heat lwe emissivity (shield with tungsten mateial in tansfe between inne and ute sphees (Fig.. (c, the example. can educe the net heat tansfe even bette pecentage eductin in heat tansfe, tempeatue and than tw adiatin shields with highe emissivity emissivity f the adiatin shields can be calculated as (shields with aluminum xide and silicn cabide mateials fllws: in example.. ( i with shield w Example 3: Cnside the tw cncentic sphees f example. If tw shields with diffeent mateials have F aluminum xide shield: been applied at adius and cm t educe heat Using Fig.. and slving Eqs. (9, (0 and ( tgethe: tansfe between inne and ute sphees (Fig.. (c, the pecentage eductin in heat tansfe, tempeatue and ( i with shield w emissivity f the adiatin shields can be calculated by fllwing the same pcedues as Example. T 7.34 K, Table. pesents the tempeatues, emissivities, net heat tansfe and pecentage eductin in heat tansfe in T K, all six pssible mdels. As it can be peceived fm Table. mdel N. 5 And the pecentage eductin in heat tansfe is: is the best mdel f educing heat tansfe between tw cncentic sphees, if we want t use tw adiatin Similaly f silicn cabide shield: T K, T K, And the pecentage eductin in heat tansfe is: shields with diffeent mateials. It is inteesting that, althugh the adiatin shields tempeatue in mdel N. 6 is less than mdel N. 5, but in the wake f highe emissivity in secnd adiatin shield in mdel N. 6, the net adiatin heat tansfe and pecentage eductin in 460

5 Wld Appl. Sci. J., (4: , 00 Table : The pecentage eductin in heat tansfe, tempeatue and emissivity f tw adiatin shields with diffeent mateials Shield at adius cm Shield at adius cm Pecentage eductin Mdel Mateial Tempeatue K Emissivity Mateial Tempeatue K Emissivity ( w in heat tansfe % i with shield N.. Aluminum xide Silicn cabide N.. Aluminum xide Tungsten N. 3. Silicn cabide Aluminum xide N. 4. Silicn cabide Tungsten N. 5. Tungsten Aluminum xide N. 6. Tungsten Silicn cabide Nmenclatue Geek symbls A Suface aea Emissivity Eb Blackbdy emissive pwe Wavelength F Shape fact The Stefan Bltzmann cnstant, N Numbe f shields Subscipts Net heat tansfe i Inne sphee Radius f sphee Oute sphee Rtt Ttal esistance sn nth adiatin shield T Abslute tempeatue Supescipts - Oute suface + Inne suface heat tansfe ae smalle than mdel N. 5. It can be REFERENCES deduced fm this Table that, if we want t chse the best cmbinatin f tw adiatin shields with diffeent. Hlman, J.P., 009. Heat tansfe. McGaw-Hill. mateials, it is bette t use the shield with lwe. Incpea, F.P., D.P. DeWitt, T.L. Begman and emissivity clse t the suface with highe tempeatue. A.S. Lavine, 006. Fundamentals f Heat and Mass Tansfe. Jhn Wiley & Sns. CONCLUSIONS 3. Oppenheim, A.K., 956. Radiatin Analysis by the Netwk Methd. Tans. ASME, 7(4: In this wk an equatin f calculating heat tansfe 4. Shucliff, W.A., 974. Tansmittance and eflectin between tw sphees was investigated. Thanks t net lss f multi-plate plana windw f a sla-adiatin adiatin methd the pecentage eductin in heat cllect: Fmulas and tabulatins f esults f the tansfe, tempeatue and emissivity f the adiatin shield case n 5. Sla Enegy, 6(3-4: wee calculated. It is fund that, when tw shields with 5. Micc, C.D. and C.M. Alda, 003. On the net same mateials applied f educing heat tansfe, the ne adiatin methd f heat tansfe. Eupean J. with lwe emissivity bette educes net heat tansfe. Physics, 4: Als it was cncluded that when tw adiatin shields 6. Siegel, R. and J.R. Hwell, 99. Themal Radiatin with diffeent mateials have been applied t educe heat Heat Tansfe. Tayl and Fancis. tansfe, the shield with lwe emissivity shuld be clse 7. Mdest, M.F., 003. Radiative Heat Tansfe. t the suface with highe tempeatue t incease Academic Pess. eductin in heat tansfe. ACKNOWLEDGEMENT The auths gatefully acknwledge the suppt f the talented ffice f Semnan Univesity f funding the cuent eseach gant. 46