. Sunday Albert LAWAL,. Benjamin Iyenagbe UGHEOKE DEVELOPMENT AND PERFORMANCE EVALUATION OF THERMAL CONDUCTIVITY EQUIPMENT FOR LABORATORY USES. DEPARTMENT OF MECHANICAL ENGINEERING, FEDERAL UNIVERSITY OF TECHNOLOGY, P.M.B. 65, MINNA, NIGERIA. DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF ABUJA, P.M.B. 7, ABUJA, NIGERIA ABSTRACT: In tis study, termal conductivity test equipment was designed and fabricated for te determination of termal conductivity values of non metallic materials only. Te energy balance equation for te equipment was based on te transient metod analysis. Tree specimens, cut to uniform area of 0.00m were used for te experiment, to validate te performance of te test equipment. Tese materials were cork, cardboard and asbestos. Te following values of termal conductivity 0.088, 0.0 and 0. w/m o k were obtained respectively for tem. Te values were compared to teir respective reference values and a correcting factor of 0.0 was obtained. KEYWORDS: conductivity, material, temperature, termal INTRODUCTION Our world is filled wit vast assortment of bot natural and artificial temperature differences. Tus an immerse variety of eat transfer equipment as been created to deal wit tese differences: boiler, condensers, solar collectors, radiators, insulators, refrigerators stores te list is almost endless (Frank, 99). Tis temperature difference can best be explained under te subject eat transfer wic cuts across many disciplines, from metallurgy, cemical processes to nuclear fusion. Te problem posed in designing eat transfer related equipment is te ability of designer to judge rigtly te material to be selected for a given design. For instance, wen te required temperature in a particular design for a specific condition is required to be ig and sould be maintained as suc, te material selected for te design sould provide suc effect. If owever, practical result of te design sow a low temperature record, te design is said to ave failed. Te inside temperature of a boiler in an industry will reac an equilibrium temperature wit its surrounding, if wrong judgment of material selection was made during material selection process. In te selection of material for eat transfer applications, te amount of eat conducted troug te material wit respect to time is considered very important as it is a determinant factor. For example, eat excanger plates, insulators etc are selected based on teir termal conductivity value. Knowing te termal conductivity of a material can be a key to obtaining te optimum performance of a particular design or can lead to an accurate measurement of its overall termo pysical properties. Tis termal conductivity value is a numerical value tat gives te designer te idea of te eat conduction of a material wic in oter words, will enable te designer select appropriately material tat will fit into a particular purpose and condition. Hence, it is important to ave a data bank of te termal conductivity values of materials as tey are developed and to do tis requires some equipment tat is not easy to come by most especially in developing countries like Nigeria. It is in a bid to address tis sort coming tat te termal conductivity equipment was designed and fabricated locally for laboratory use. So many types ave been developed for example, eat flow meter, guarded eat flow meters, guarded ot plate instrument, flas diffusivity metods etc ( Jurgen, 004). But te need for local availability of termal conductivity meter as submitted by Igodalo and Okoebor (996) will provide for more researc into local materials development and various uses tat suc materials can be put into. It was terefore, te need to make tis termal conductivity equipment available locally tat tis work was carried out. DESIGN ANALYSIS AND CALCULATION Termal conductivity meter is laboratory test equipment based on te principle of eat conduction. Te early development of eat conduction is largely due to te effort of a Frenc Matematical pysicist, Josep Fourier (8), wo first proposed te law tat is known today as Fourier s Law of Heat Conduction, wic is expressed in equation () copyrigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 49
KAΔT Qx = () Δx were K is te termal conductivity and as a unit w/m o k. Te step by step design of eac components of te termal conductivity is detailed below. Boiler Design: Te boiler eater was designed to boil a minimum water of 4 litres capacity in 0 minutes and te eat output of te electric eater (coil) was calculated from Q Q = (watt) () τ were Q = MCΔT, eat output from eater (76000J), Q = eat transfer rate (960W), M= mass of water (kg), C = specific eat capacity of water (KJ/kg o K), t = time (s) and Δ T = temperature difference ( o C). Te eat capacity adopted for te design was 000W Condensation Rate: Te average condensation rate of steam during te eating period was calculated from equation (3), ( Nortcroft and Barber, 979) M C ΔT q = (kg / s) ( 3) Hfg H 3600 were m = mass of water eated (kg), C = specific eat capacity of water (KJ/kg 0 C), H = recovery time 0 (our) Δ T = temperature rise (T T ) C, H fg = specific entalpy of evaporation of steam at working pressure (KJ/kg). Condensation rate, (q) =.89 x 0 4 (kg/s), Volume of Boiler: Te volume of boiler was calculated from equations (4a & 4b) m V w = (4a) ρ V T = Vw + Vgx (4b) But VT = πr were V T = total volume, V w = volume of water, V gx = volume of steam, ρ = density of water. Te eigt obtained was 34.34mm, but 36mm was adopted Boiler Sell Design: Te circumferential stress value was adopted for design of boiler sell, because it as a iger value for pressure vessel aving closed ends as bot longitudinal and circumference t stresses were induced (Kurmi and Gupta, 003). σ pd = t (5a); [ σ ] d but σ = L f pd t = (5b), σ pd Figure : Boiler sell td = + mm (5c) σ were σ = circumferential stress (allowable stress), [ σ ] = Yield stress of boiler material, f = factor of safety, d = internal diameter of te pressure, t = tickness of te boiler material, design tickness ( t D ) =.697mm but.5mm was adopted. Cover Plate Design: Te cover plate was a circular flat plate wit uniformly distributed load and te tickness of te plate is determined from p t = K.d (6) σ were K is a value wic depends upon te material of te plate and te metod of olding te edges, p = pressure, d = diameter and σ = allowable stress. t =.74mm but t = 4mm was adopted. Bolt Requirement: Te upward force acting on te cylinder used was given by F = πrp (7a) Te resisting force offered by number of bolts was given by Tome X (Year 0). Fascicule. ISSN 584 665
.5di π F = ( dc ) σ tb n 4 (7b) From equations 7a and 7b, equation (8) was obtained D π π rp = F = ( dc ) σ tb n 4 (8) were r = radius of cylinder, = eigt of cylinder, p = pressure of cylinder, d = diameter of ole, σ tb = minimum yield strengt of.5di bolt. Te number of bolts obtained was 6.87 and 8 was used. Te volume of plate material for insulation surface was obtained using Figure : Bolt Arrangement equation 9 V = πr (9), but r = r3, were r = radius of te insulation surface, = eigt of cylinder. Boiler Insulation Tickness: Te minimum tickness Insulation Surface Material Insulation Material required for insulation was r r as sown in equation Boiler Material 0. Q π ( Tl T3 ) = (0) L r r 3 T 3 ln ln r r + T k a k b r were T = temperature of steam inside te vessel, T = r temperature of boiler material, T 3 = temperature of te r3 insulator surface, K a = coefficient of termal conductivity Figure 3: Boiler Insulation Tickness of boiler material, K b = coefficient of termal conductivity Q of insulator, eat transfer rate per unit lengt. Te value of T3 = 39.7 o C, sows tat te assumed value L for r was satisfactory. Steam Pipe Design at an Inclined Angle: According to Croft, Davison and Hargreaves (995), using te relation opp x tan θ = = () adj y and z can be determined from Pytagoras teorem z = x + y were, θ = pipe angle(69.5 o T L = W + Z () ),W = eigtofpipefromboiler, w l L = boilereigt,i = boilereigt,t L = 06mm i Pipe Volume: Te pipe volume was obtained k using equation (3) ((Kurmi and Gupta, x 003) V = πrl T (3) Figure 4: Pipe Inclination Angle were r = radius of pipe, V = volume of pipe (333366.mm ). Pipe Pressure: Using Boyle s law (Rogers & Mayew, 99), te pipe pressure was calculated P V = P V (4) were P = boiler pressure (atmosperic pressure), V = total volume of boiler, V = volume of pipe. P = pressure in pipe, (.6N/mm ) Pipe Insulation: Te pipe was treated as a composite ollow cylinder and like te boiler unit, equation 0 olds according to Rajput (003) Te Size of Insulator Surface Material (Plate) Required: Te size of insulator surface for plate as sown in figure5 was obtained using equation (5) ø z y copyrigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 5
L Steam Figure 5: Size of Insulator Surface Material d 0 ANNALS OF FACULTY ENGINEERING HUNEDOARA International Journal Of Engineering Size of plate (area) = π d 0 L (5) But d 0 = r3, were d 0 = diameter of te pipe + te insulation, L = lengt of pipe. Te size obtained was 0.08 x 06 Heat Excanger Unit (Steam Jacket Design): Te pressure in steam jacket was determined using Boyle s law P V = P (6a) 3V3 P V P 3 = (6b) V3 were V 3 = volume of steam jacket, P 3 = pressure in steam jacket (0.03N/mm ), Te steam jacket sell design value obtained from te boiler design was adopted and te steam jacket L R insulation size was equally adopted to for te design. Test Section Design: Te sell, cover plate tickness C were obtained as in equations 5c and 6 Design of Volume of Test Section: According to L s Antony and Martin (995) and using equation 7, L m wen = Lm + Ls + clr (7) d V = πr (8) Figure 6: Design of Volume of Test Section were V = volume of test section (585.7mm 3 ), = eigt of test section, L m = Tickness of metal seet (mild steel), L s = Tickness of specimen, L R = tolerance, C = eigt of conical flask FABRICATION AND PERFORMANCE EVALUATION Te numerical values obtained from te design procedure were used in fabrication of te termal conductivity equipment. Cutting process using acksaw and welding process were some production processes tat were involved in te fabrication of te equipment. Table 3 sow all te materials involved in Plate. Termal Conductivity Test Equipment te fabrication of te equipment. Plate sows te potograp of te fabricated conductivity test equipment. Te performance of te test equipment was obtained by comparing values of termal conductivities obtained from te test equipment wit te documented termal conductivity values as sown in table. Tis was acieved by using te equipment to carry out experiment using tree specimens of non metallic materials i.e. cork, cardboard and asbestos. Eac of tese specimens was cut to an area of 0.00m and was placed in te test section at a position wic it fit into. A conical flask containing ml of water was placed directly on te specimen and a cork aving a termometer passing troug it was used to cork te conical flask. Te termometer measured te temperature canges of te water in te flask. Cotton wool was used to insulate te specimen and te conical flask. Te test section was ten closed and te initial water temperature was noted. A second termometer was inserted into te steam outlet pipe wit te aid of a cork to monitor te steam temperature so as to ensure tat a base temperature of 00 o C was maintained. Te boiler water outlet valve was closed and ten te water inlet cover was opened. Five litres of water was filled into te boiler, wile te steam inlet valve, outlet valve and condensate outlet valve were all closed. Wit te boiler water inlet cover remaining open, te boiler was switced on. Immediately te water started boiling, te boiler water inlet cover was closed, wile te steam inlet valve was fully opened wit all oter valves remaining closed. Timing commenced wit te aid of stop watc immediately te steam inlet valve was opened. Te experiment was timed in eac case for 0 minutes. Temperature and time records were taken. Eac specimen was experimented twice and mean temperature values were obtained as sown in table. 5 Tome X (Year 0). Fascicule. ISSN 584 665
S/No 3 S/No 3 Material Cork Cardboard Asbestos Material Cork Cardboard Asbestos Table : Result Obtained Compared wit Reference Calculated Termal Conductivity Kc (w/m 0 k) Reference Termal conductivity Kr (w/m o k) 0. 0. 0.6 Tickness (m) l 0.009 0.003 0.003 0.088 0.0 0. Difference ( Kr Kc) 0.0 0.0 0.038 Table : Experimental Result Mean initial Mean Final Temp (T o i C) Temp (T o 4 C) 45 48 40 59 4 54 Corrected Termal conductivity Kc (w/m o k) 0.08 0. 0.4 T T i (0i o C) 55 60 58 T T 4 (0 o C) 5 4 46 At te end of eac experiment te steam outlet valve was opened to release steam. Te water in te boiler was also topped to maintain te five litres. Te termal conductivity of te material was determined by adopting te energy balance equation using te lumped eat capacity approac of te transient state using Fourier s law as sown in equation (9) (Rajput, 003).303MCL θ log θ A K = (9) τ were K = termal conductivity of material to be determined; T = temperature of steam; T i = initial water temperature in conical flask; θ ;θ, temperature differences at te beginning and at te end of te experiment; time (s), A = specimen area; M= mass of water in conical, C = specific eat capacity of water in conical flask, L = tickness of specimen. MATERIALS AND COST ESTIMATE Galvanized steel was used for te fabrication of te boiler sell based on its properties like melting point of o C, a moderate termal conductivity value of.w/m o C and ig density 78kg/m 3, wic meet te condition of service required for boiler. was used for cover plate, steam pipe and bolts, wile insulation material used was cotton wool of 0.063w/m 0 C. Te material cost was based on te cost of materials used for te construction of te termal conductivity equipment under current market price and te factors considered in costing are as follows (a) material cost, (b) labour cost and (c) Overead cost. Labour cost was determined by assuming a direct labour cost of 0% of te material cost, wile Overead cost wic includes oter expenses incurred apart from direct material and direct labour cost was determined by assuming a 0% of te cost of material and te total cost is te sum of material, labour and overead costs (Jonson, 98). Te cost of production of te termal conductivity equipment was NGN, 65:00. (Were NGN stand for Naira, wic is Nigeria currency). Table 3 sow te materials cost and specification. Table 3: Material Cost and Specification S/No Component s Name Material Dimension Qty Standard price Total cost / unit (NGN) (NGN). Boiler / eat excanger Galvanized steel 4 x 4mm 7 7 Cover plate. Stand x 8mm 000 000 3. Heater x 0mm 800 800 4. Welding 000W 400 400 5. Insulator bar 000 000 6. 7. 8. 9 0 3 4 5 6 7 Insulator surface cover Steam pipe Coupler Nipples Plunge / socket Gate valves Termometer Bolts & nuts Screws Paint Conical flask Total cost Oxy acetylene Cotton Aluminum Galvanized steel Galvanized steel Galvanized steel Cast iron Brass Mercury in glass Aluminum colour Pyrex glass 4kg x 4mm OD(5mm) OD(5mm) OD(5mm) OD(5mm) OD(5mm) 30cm M4 sort M4 sort litre ml 4 8 8 00 000 80 600 80 60 30 300 0 00 000 00 60 000 00 60 480 40 300 0,030 copyrigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 53
RESULTS AND CONCLUSION Te termal conductivity test equipment for te determination of te co efficient of termal conductivity of non metallic materials as been successfully designed and fabricated. Te equipment performance was evaluated during te experiment conducted on te tree samples of cork, cardboard and asbestos. Te termal conductivity co efficient for eac sample was discovered to ave a correcting factor of 0.0 wen compared wit te documented value. Te cost of producing te equipment locally is not too ig compared to imported equipment. Terefore, wit tis equipment, researc institution laboratories can use it to study te termal conductivity values of non metallic. REFERENCES [.] Antony C, Robert D and Martins H (995), Introduction to Engineering Matematics, Addison Wesley Longman, England. [.] Frank M.W (99) Heat and Mass Transfer. Addison Wesley, Longman England [3.] Igodalo O.A and Okoebor W.J (996) Termal Conductivity of Some Local Waste Materials: Rice Husk, Palm Kernel sells and Wood Savings. NSE Tecnical Transactions Vol. 3 No 3 PP 68 73 [4.] Jonson D.T (98) A Guide to Business Management in te Tropics, st Edition, Macmillan Press Ibadan, Nigeria [5.] Jurden B. (004) Termal Conductivity Equipment ( infor@netzsc net) [6.] Kurmi R.S and Gupta J.K (003) A text Book of Macine Design, S. Cand and Company Ltd, New Deli [7.] Norctcroft L.G and Bareber W.M (979) Steam Trapping and Air Renting 5 t Edition, Hutcinson & Company Publisers Ltd, London [8.] Rajput R.K (003) Heat and Mass Transfer second Edition S. Cand and Company Ltd, New Deli [9.] Rogers G and Mayew Y (99) Engineering Termodynamics (Work & Heat Transfer) 4 t Edition. Addison Wesley Longman ANNALS OF FACULTY ENGINEERING HUNEDOARA INTERNATIONAL JOURNAL OF ENGINEERING copyrigt UNIVERSITY POLITEHNICA TIMISOARA, FACULTY OF ENGINEERING HUNEDOARA, 5, REVOLUTIEI, 338, HUNEDOARA, ROMANIA ttp://annals.fi.upt.ro 54 Tome X (Year 0). Fascicule. ISSN 584 665