Volume IV, Issue IX, September 2015 IJLTEMAS ISSN

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1 Volume IV, Iue IX, Setember 15 IJLEMAS ISSN A Comutational Study of A Multi Solid Wall Heat Conduction Made U of Four Different Building Contruction Material Subected to Variou hermal Boundary Condition. [1] [1] Shantanu Dutta NSHM Knowledge Camu, Deartment of Mechanical Engg.Durgaur Abtract: by conduction (alo known a diffuion heat tranfer i the flow of thermal energy within olid and non-flowing fluid, driven by thermal nonequilibrium (i.e. the effect of a non-uniform temerature field, commonly meaured a a heat flux (vector, i.e. the heat flow er unit time (and uually unit normal area at a control urface. Conider a quare building wall which i made u of four different material (refer Fig. 1. he wall i ubected to a hot temerature of 1 C (initial-condition and i then ubected to variou thermal boundary condition and volumetric heat generation; a hown in a table below. By Comutational Fluid dynamic (CFD analyi i.e.finite volume analyi for thi tate of Conduction,we tudy the teady tate temerature contour for the four different cae. We alo analye the heat tranfer (oitive for outward/heat-lo and negative for inward/heat-gain from the different egment of the wall, total heat-gain, total heat-lo and energy balance; for the different cae. Finally we dicu the effect of volumetric heat generation on the reult for the tye [cae C & D] of BC and try to otimize our reult Key word; hermal Boundary, CFD, Conduction, Heat ranfer, Energy Balance. Finite volume method, : Otimization H 1.BRICK 4.LY WOOD.CONCREE 3.GYSUM Fig 1: Multi Solid Wall I. INRODUCION eat conduction i of increaing imortance in variou area, namely in the earth cience, and in many other evolving area of thermal analyi. A common examle of heat conduction i heating an obect in an oven or furnace. he material remain tationary throughout, neglecting thermal exanion, a the heat diffue inward to increae it temerature. he imortance of uch condition lead to analyze the temerature field by emloying ohiticated mathematical and advanced numerical tool. he tudy conider the variou olution methodologie ued to obtain the temerature field. he obective of conduction analyi i to determine the temerature field in a multi body analyi i how the temerature varie within the ortion of the body. he temerature field uually deend on boundary condition, initial condition, material roertie and geometry of the body. Why one need to know temerature field in a multi layered olid body i becaue, we can analye and comute the heat flux at any location, comute thermal tre, exanion, deflection, deign inulation thickne, and imlify heat treatment method and maor deign calculation. he olution of conduction roblem involve the functional deendence of temerature on ace and time coordinate. he term teady imlie no change with time at any oint within the medium, while tranient imlie variation with time or time deendence. Obtaining a olution mean determining a temerature ditribution which i conitent with the condition on the boundarie and alo conitent with any ecified contraint internal to the region. Further ranient heat conduction i encountered in metallurgical indutrie where metal and alloy are ubected to different heat treatment rocee to enhance their hyical and chemical roertie (e.g. annealing. he actual heat treatment roce involve comlex heat tranfer rocee decribed and uch roblem are referentially olved uing numerical method. Numerical heat tranfer i a broad term denoting the rocedure for the olution, on a comuter, of a et of algebraic equation that aroximate the differential (and, occaionally, integral equation decribing conduction, convection and/or radiation heat tranfer. Comared to the exerimental method, numerical analyi rovide a more direct way to enhance/reduce heat tranfer effectively o age 6

2 Volume IV, Iue IX, Setember 15 IJLEMAS ISSN a to imrove the erformance or to otimize the tructure of a thermal device. C a e Boundary Condition Left Bottom Right o A 5 C Inulat ed B Inulat ed q W=15 W/m h=1w/m. K, =3 C 5 C q W=15 W/m h=1w/m. K, =3 C Volum etric Heat Genera tion (W/m 3 Neceary rogram by uing matlab/cilab have been generated to get the reult and we lot the teady tate temerature contour for the different cae. Other arameter like from left, from right, from to, from bottom, otal heat gain,otal heat lo & Energy balance have been alo tudied from the different wall of the late. Finally we dicu the effect of volumetric heat generation on the reult for the tye C&D of BC and try to otimize our reult. ablea: Fig A: FigA: C q W=15 5 C Inulated h=1w/m. W/m K, =3 C 5 D 5 C q W=15 h=1w/m.k, W/m =3 C Inulated 5 H.Baig et. al.[1] have analyed conduction/natural convection by numerical analyi acro multi layer building hey carried out the heat leak for different number of air filled cavitie. homa Bloomberg[] tudied heat conduction in two and three dimenion by numerical method and analyed everal cae of two dimenional heat conduction.filio de Monte, et al. [3] olved two dimenional Carteian unteady heat conduction roblem for mall value of time. Shidfara et al. [4] identified the urface heat flux hitory of a heated conducting body. he nonlinear roblem of a nonhomogeneou heat equation with linear boundary condition i conidered. F. de Monte [5] develoed a new tye of orthogonality relationhi and ued to obtain the final erie olution of one-dimenional multilayered comoite conducting lab ubected to udden variation of the temerature of the urrounding fluid. Arild Gutaven et al.[6] analyed heat tranfer and conduction in window frame with cavitie by CFD method In the reent tudy we have ued the grid deendent tudy and have ued the finite volume aroach method of comutational heat conduction to tudy the CHC tranient heat imulation of multi olid wall of D and ay long (in z-direction having Carteian comutational x-y domain of ize L=1 m and H=1m, for CHC tranient imulation. he multi olid wall (ee fig 1 i made u of four different building contruction material. 1.Brick of denity 19 kg/m3, ecific-heat: 79 J/Kg K, thermalconductivity:.89 W/m-K. Concrete of denity 4 kg/m3, ecific-heat: 84 J/Kg K, thermal-conductivity: 1.4 W/m-K 3.Gyum of denity 8 kg/m3, ecificheat: 19 J/Kg K, thermal-conductivity:.16 W/m-K 4. lywood of denity 54 kg/m3, ecific-heat: 11 J/Kg K, thermal-conductivity:.1 W/m-K reectively. he multi olid wall i ubected to initial temerature of 1 C (initial-condition and i ubected to variou thermal boundary condition and volumetric heat generation(cae C & D; hown in a table A below. Fig B:- II. MAHEMAICAL FORMULAION he General 1 D Heat Conduction Equation i a follow which can be extended to our D model i a follow. age 7

3 Volume IV, Iue IX, Setember 15 IJLEMAS ISSN Aume the denity of the wall i ρ, the ecific heat i C, and the area of the wall normal to the direction of heat tranfer i A. An energy balance on thi thin during a mall time interval t can be exreed a: (Rate of Heat Generation at x-(rate of Heat Conduction at x+dx +(Rate of Heat Generation inide the =(Rate of energy content of the E q q G..(1 x x dx E G q x E tt gv t Et mc ( t t t C Ax( t t t g Ax q g Ax C x dx.(4 Dividing by A x ( ( Ax (3 tt t t give: he baic governing equation i the Lalace' x y equation(g.e.:.(7 he G.E for Heat conduction thu become: C k q.(8 t he governing artial equation are converted to dicretized algebraic equation uing FVM. V C ( dv t V k dv V qdv.(9 he Finite Volume (Exlicit Dicretized Equation i: w e S N f e w, n, ( f f ( y ( y ( x ( x n w e n (1, In thi aer we have ued -D Heat conduction: Solution Algorithm for Exlicit method a it i relatively imle to et u and rogram. q q 1 [ xx x t t t ] g C [ ] A x t (5 aking the limit a x, t and from Fourier law we obtain finally: 1 ( ka g C A x x t III. FINIE VOLUME MEHOD (6 he FV method i a Control volume baed technique of numerical dicretiation. It offer everal advantage (including it conervativene and robutne that make it articularly attractive for ue in both academic and commercial CFD alication. It i alo well uited for invetigating diffuion roblem. It imlement the following comutational te: (ameh generation entailing the diviion of the domain of interet into dicrete control volume, (b Integration of the governing equation on the individual control volume to contruct algebraic equation for the dicrete variable (the unknown uch a reure, velocity, temerature, and conerved calar. (c Linearization of the dicretied equation and olution of the reulting linear ytem of equation to yield udated value of the deendent variable (Niofor, 9 [7], Eymard et. al., [8] and Verteeg and Malalaekara [9], 7. he data of different material wa extracted from hermo Mechanical roertie of Material: by A.V. Marchenko[11] 3.1Solution Algorithm : 1. Enter the inut: material roertie,geometric arameter (l1& l and maximum number of cv in the x and y direction, b.c inut and convergence criteria.. Grid generation: calculate all the geometric arameter of all the cv 3. Set the initialization for t, and dirichlet b.c for temerature,t [i.e.equation variable array]. 4. Aign cell-wie conductivity. 5. Aign cell-wie denity 6. Aign cell-wie ecific heat 7. After chooing the generic boundary condition function we calculate error function. 8. Modify the other (non-dirichlet boundary condition(if neceary. 5. Set told(= t( for all cv. 6. For each face, calculate heat fluxe. 7.Check the harmonic mean of the roertie of interface (See Fig B 7. For each interior and border cv, calculate Q conduction and finally, 8. Check for convergence. rm ( old ( i max X ( max (11 ; rm 9. If not, go to te 3 and continue till convergence i achieved. he geometric arameter of grid are: L1 L x, y ( i max ( max.urface area age 8

4 Volume IV, Iue IX, Setember 15 IJLEMAS ISSN related arameter obtained for different tet cae of D heat Conduction arameter Cae A Cae B Cae C Cae D from left 1.594e e e+4 needed. In heat tranfer, three tye of condition on are encountered: ecified temerature: = w at a boundary, where the wall temerature w i known; thi i called a dirichlet condition. ecified heat flux: λ( / n w = q w, where n i normal to the urface, and the wall heat flux q w i known; thi i called a Neumann condition; from right 1.577e+4 the ecified heat tranfer coefficient α: =λ( / n w = α( w i ; thi i called a mixed condition Here we will be dealing with both dirichlet condition & non- dirichlet condition BC : able B: from to 1.341e e+4 V. RESULS & DISCUSSIONS: from bottom 5.667e e+3 Fig 3(Cae A: otal heat gain 1.5e+3 1.5e+3.65e+4.65e+4 otal heat lo 1.5e+3 1.5e+3.65e+4.65e+4 Fig 4(Cae B: Energy balance e e-4-9.6e e-4 S S y; S S x. e Volume= w V x. y n Note1:FVM UNSEADY ERM:I Level of Aroximation Volume Averaging of rate of change of velocity/temerature in a CV a a value at the centroid of CV i.e. cell center. (II Order. V dv ( avv ( t t t V (1 Note: II Level of Aroximation Dicrete Rereentation of the rate of change (I order Forward Finite Difference : (13 ( t n1 t n Fig 4(Cae B: IV. BOUNDARY CONDIIONS In our roblem there are four tye of Boundary condition. hee equation mut be accomanied by boundary condition aroriate to the articular roblem. For tranient roblem, an initial condition i required, and in all roblem boundary value for all variable are age 9

5 Volume IV, Iue IX, Setember 15 IJLEMAS ISSN Fig 5(Cae C: / Symmetry wall,convective heat lo from wall, Contant heat flux] and alo the initial value of temerature. All the roblem below ha been olved on a coarer grid ize of imax=max=. However on refining the grid to of imax=max=4 alo doe not refine our reult much. Hence to adot a Grid indeendent tudy we can chooe to work with of imax=max=3 to ave comutational time and cot. We have adoted a teady tate convergence criteria of 1-6. In future coure we can ue any other Boundary condition to get a better idea about the behavior & thermal roertie of the building material or any other material. Dicuion Fig 6(Cae D: REFERENCES [1]. H.Baig and M.A.Antar: Conduction/Natural convection analyi of heat tranfer acro multi layer building block. 5 th Euroean hermal Science Conference, Netherland, (8. []. homa Bloomberg, Heat conduction in two and three dimenion. Comuter Modelling of Building hyic Alication, Lund univerity Sweden(1996 [3]. Filio de Monte, Jame V. Black & Donald E Amo :olving two dimenional Carteian unteady heat conduction roblem for mall value of time. International ournal of hermal Science Elevier 6( [4]. A. Shidfara, G.R. Karamalib and J. Damirchia, An invere heat conduction roblem with a nonlinear ource term, Nonlinear Analy 65, (6, [5]. F. de Monte, ranient heat conduction in one-dimenional comoite lab. A `natural' analytic aroach, International Journal of Heat and Ma ranfer, 43, (, [6]. Aril Gutaven,Chritian Kohler, Dariuh Arateh,Dragan Curcia: wo dimenional Comutational fluid dynamic and conduction imulation of heat tranfer in window frame with internal cavitie-m ech hei. [7]. Niofor, M.. (9. ool for numerical dicretiation: finite Volume method for diffuion roblem. Cranfield Univerity, UK. MSc hei. [8]. Finite volume method - Eymard, Galluoët, et al.. [9]. Verteeg, H. K. and Malalaekera, W. (7.An introduction to comutational fluid dynamic: he finite volume method, nd Ed. earon Education, Harlow,England. [1]. hermo Mechanical roertie of Material: Alekey.V. Marchenko, Univerity of Norway. After analyzing the Cae C & cae D lot we come to the concluion that on inulating the right and bottom for cae C & D ha reulted in more heat generation comared to cae A or B. he temerature contour lot obviouly tell u that in cae of C & D higher temerature i achieved in lywood region wherea it i more in the cae of gyum for cae of A & B. If we increaing the value of wall temerature it will reult in more heat generation. he net heat lo i leat for cae A and alo leer for cae B comared to Cae C & D. he Numerical error in energy balance i leat for cae B and even leer when comared to cae C. VI. FINAL CONCLUSION & FUURE WORK: Chooing the material roerty condition for the above tudy hold the firt key to reult. he bet otimiation can only be achieved by changing the nature of Boundary condition i.e. [Contant wall temerature, Inulated wall age 1