Thermal Conductivity Study of South East Nigerian Woods Using Steady State Conditions on the Grain Directions

www.idosr.org Nwankwo et al ©IDOSR Publication International Digital Organization for Scientific Research ISSN: 2579-079X IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019. Thermal Conductivity Study of South East Nigerian Woods Using Steady State Conditions on the grain directions Nwankwo A.M.1, Festus L.Tor2 and Onah T.O.3 3Department of Mechanical Engineering, Caritas University Amorji Nike Enugu, Enugu Nigeria. 2Department of Mechanical Engineering, Kenule Beeson Sari-Wiwa Polytechnics, Bori. Rivers State, Nigeria. 1Department of Mechanical and Production Engineering, Enugu State University of Science and Technology Enugu, Enugu Nigeria. Email: [email protected] ABSTRACT This study investigates the anisotropic property of selected wood sample from rain forest zone (south eastern part) of Nigeria. Using an experimental rig constructed for the purpose which is called modified lee-disc. The experimental investigations of five selected wood samples were done, heating each from longitudinal and at right angle (Radial) to the grain direction of each wood sample. The thermal conductivity value ‘K’ along (Longitudinal direction) grain directions of 0.12 – 0.143w/mk-1 were obtained, while in the perpendicular direction (Radial direction) to the grain values of 0.08 – 0.12w/mk-1 were obtained equally. It is observed that lower conductivity values occur at the perpendicular direction (right angle) to the heat source. Keyword; Steady state, thermal conductivity, Nigerian woods. INTRODUCTION Wood is hard fibrous tissue and organic poor heat conductance of wood is due material found in many plants. Natural to the paucity of free electrons which composite of cellulose fibers -with are media for energy transmission and strong tension capability rooted in a due to the porosity of wood. Wood is a matrix of lignin which repels typical a permeable raw material. Its compressive force. Wood also may be structure is complicated which makes it stated as other plant materials that has a strong anisotropic material in the area equivalent properties, and to any other of drying shrinkage and mechanical material gotten from wood, or wood applications. The complicated panels, chips and fiber. The conduction structures of wood consist of many cell of heat through wood and wood based types which have a cell wall materials has been well understood surrounding a cell lumen in the center. since the time of Fourier. The Also the arrangement of wood cells in conduction of heat across south eastern two main directions, in longitudinal Nigerian woods is less understood, direction as the tree grains direction especially since this phenomenon has and radial-transverse direction- received little attention until perpendicular to the grain direction. It investigations to alternative building is this structure that makes its physical materials starts to develop as a result of and mechanical properties directionally high cost of concrete and iron based dependent- anisotropic nature of wood. materials. Wood and wood-based [1] Thermal conductivity of wood as a materials have many applications in result of changes or differences in a areas that require good insulating grain direction, with defects and also properties. In building construction, with moisture content in the wood in wood as a building material is of special the direction of heat flow. Therefore, to concern because of its low thermal get the thermal conductivity of a conductivity and good strength. The particular wood we have to consider the 7 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019. www.idosr.org Nwankwo et al combination of the variances: the content available. Understanding the thermal conductivity values of the theory behind the wood’s thermal substance in wood, the theoretical conductivity, it makes it possible to models for examining the relationship predict its property changes with of wood structure and the experimental extended range of moisture content of rig and instrumentations to be used. the wood sample. Therefore, theoretical Thermal conductivity of wood is usually model can be step up on dry wood measured by the one-dimensional samples. In the processing of wood like steady state method, two –dimensional kiln-drying, impregnation, hot pressing and transient methods, but this research etc, knowing the thermal conductivity is focusing on the two dimensional of the wood sample is of a very big steady-state method using linear essence as long as the process involves regression method. With the moisture high temperature range. Thermal content available in the wood, insulators are those materials that are equilibrium will take longer time to be poor conductors of heat. Wood is a reached. It is not quite realistic typical example of an insulator (heat). conducting the test with the moisture Figure 1: Three main axes of wood with respect to grain direction and growth ring. Literature/Theoretical Underpinning longitudinal axes. [3] in their work Orthotropic and anisotropic are some of thermal properties of wood and wood wood’s attributes as an engineering panel products for use in buildings still materials [2] They conducted a study on talked about the two major properties the thermal conductivity for uniform affecting the thermal conductivity of density of wood cells Because of the wood - density and moisture content. orientation and property of the wood They also dealt with the percentage fibers and the manner in which a tree water content in a wood. [4] still talked increases in diameter as it grows, about the two major properties affecting properties vary along three mutually the thermal conductivity of wood - perpendicular axes: longitudinal, radial, density and moisture content. They also and tangential Figure1. The longitudinal dealt with the percentage water content axis and grain direction are in parallel, in a wood. In his work another method the radial axis normal to the wood’s of finding thermal conductivity was growth rings and perpendicular to the used. They used what is called cut-bar grain direction and the tangential axis thermal conductivity facility. The main of the wood is tangent to the growth aim was not to get the thermal rings and perpendicular to the grain conductivity, rather to get the contact direction. In comparative analysis, conductance of cylindrical shape inner wood’s properties differ in each of these and outer interfaces [5]. The same direction s and axis, but the main Fourier’s law was used, with known difference is between radial and temperature distribution in the inner 8 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019. www.idosr.org Nwankwo et al 훿푇 and outer cylinders. Another literature At steady state = (3) had their research on thermal properties 훿푋 At steady state and if there are heat of wood, gypsum and insulation at sources into or heat-sink out of the elevated temperature. [6] objective was body: - to support the expansion of fire Then; Energy balance becomes; Energy resistance models concept for wood and in + energy generated/lost = δu + wood panels. There are so many other energy out literatures that were reviewed in the Where δu = change in internal energy. course of this work. Thus: Theory of Heat Equation 훿푇 푄 = −퐾퐴 (4) From a generalized 3-dimensional 훿푋 unsteady state equation we drive Energy generated = 푞퐴훿푥 (5) Fourier steady state equation; ∆푈 = 휌퐶푣훿푇훿푋퐴푑푥 (6) {퐾훿푇 whenever temperature gradient exists Energy out = −퐾퐴훿푇훿푋) = −퐴 + 푥+푑푥 훿푋 in a body or a system, heat will flow 훿 (퐾훿푇/훿푋) (7) from the higher temperature region to 훿푋 푑푥 } 퐾훿푇 the lower temperature region at a rate Thus, 푞 + 훿푥( ) = 휌퐶푣훿푇훿푋 (8) 훿푋 proportional to the temperature 퐾훿2푇 훿푡 From which푞 + = 휌퐶푣 gradient i.e. 훿푋 2 훿푥 푞 훿푇 = 훼 For a 3- dimensional (1) heat flow and with 퐴 훿푋 훿푇 no internally generated heat: 푞 = −퐾퐴 퐾훿2푇 훿푇 (2) 훿푋 = 휌퐶푣 (9) 훿푋 2 훿푋 Figure 2: 3D analysis of heat flow ∆푄 푥 Thus, for 퐾 = (11) 훿2푇 훿2푡 훿2푡 훿푡 퐴∆푡 ∆푇 3D:퐾 + ]′ + = 휌퐶푣 (10) 훿푋 2 훿푦 2 훿푧 2 푑푥 Where ΔQ is the quantity of heat, Δt is 훿2푇 훿2푡 훿2푡 푞 1 the time rate of change through a Or 훿2푇 = + + + = this is 훿푋 2 훿푦 2 훿푧 2 푘 훼훿푡 /훿푥 thickness x, in a direction normal to a the vertical divergence of temperature, surface of area A, per unit area of A. Due with internal heat generation q. Where to a temperature difference ΔT, 푘 훼 = = thermal diffusivity. Having assumptions are: under steady state 휌푐 conditions and heat transfer is reliant generated this equation Fourier’s steady on only on the temperature slope. state equation is chosen since our δt/δx Alternatively, it can be thought of as a =0, therefore the equation (9) after flux of heat (energy per unit area per transformation is given by; 9 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019. www.idosr.org Nwankwo et al unit time) divided by a temperature unit length) gradient (temperature difference per METHODOLOGY In order to evaluate the thermal bears the working drawing of the conductivity of Nigerian woods, through modified lee disc. a triangular interface and pyramid Heat was supplied to the assembly by Q- volume, a known thermal conductivity link manufacturing company with a apparatus was modified - lee disc was triangular shaped 210 x110mm electric re-designed to obtain data over a iron of 1100w capacity, Too avoid heat temperature range of Nigerian wood loss; the wood samples were cut in the samples and under some certain same shape with the electric iron of thermal conditions. The primary triangular shape and coated with fiber influence of the modified lee disc (as it glass heat insulator, with a little was called after re-design) is that the dimensional difference. The heat materials are locally sourced. These source is from mains of supposedly materials are readily available at the 240v.

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