Thermal applicability of two-phase thermosyphons in ... - LEPTEN

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720 A.K. da Silva, M.B.H. Mantelli / Applied Thermal Engineering 24 (2004) 717–733In the present work, we proposed to investigate the behavior of thermosyphons exposed to realconditions in cooking chambers. For that, an experimental prototype, which simulates the crosssection of the commercial oven, was built. Four vertical thermosyphons were installed inside theprototype. The experimental measurements were compared with the results generated by a theoreticallumped model, which takes into account the convective and radiative effects inside thecooking chamber.2. Theoretical modelIn the present model, a transient heat transfer balance between the internal surfaces of acooking chamber and the enclosed air is performed. The physical model described in Fig. 1 isbased on the experimental setup built by NCTS, later in this study. The interaction among thefour internal walls is taken into account. The enclosure is filled with air, which is considered anon-participating gas in the radiation net. The radiation scattering is neglected and the forcedconvection flow in the internal walls is considered well mixed. The relative influence of the wallradiation properties and the forced convection, represented by the Reynolds number (Re ¼ vL=m),are examined, where v represents a characteristic velocity (i.e., the mean flow velocity over areferred plate), L is the characteristic length of the plate and m is the kinematic viscosity.This model consists of the heat transfer balance among the air inside the cooking chamber, thetop and bottom horizontal surfaces, and two vertical lateral surfaces. The air temperature wasnamed T air , and the temperature of the top and bottom surfaces were named T 2 and T 4 respectively.The vertical walls surfaces temperatures, T 1 and T 3 , are considered equal and prescribed,varying according to the experimental data, described later in this study. The conduction heattransfer between the internal walls and the heat losses between the vertical walls and the exteriorenvironment are neglected. On the other hand, heat transfer between the horizontal walls and theoutside environment is considered. The overall heat transfer coefficients between the horizontalLq' U2L2(ToutT2)T 3T 2∂T ∂T = 0= 0∂x∂xT 1yT 4T airT outHxq' U4L4(ToutT4)Fig. 1. Theoretical physical model for the enclosure with transient temperatures.
A.K. da Silva, M.B.H. Mantelli / Applied Thermal Engineering 24 (2004) 717–733 721walls and the environment were named U 2 and U 4 . They are concerned with the top and bottomwalls respectively.The transient heat exchange between the walls and the air happens through convection, whilethe transient heat transfer between the internal walls is through convection and radiation. Theheat balance for the enclosed air is given bydT airq air c p;air V air ¼ 2h 1 A 1 ½T 1 T air Šþh 2 A 2 ½T 2 T air Šþh 4 A 4 ½T 4 T air Š ð1ÞdtIn the above equation, the three right hand side terms represent the energy obtained by forcedconvection from the surfaces 1, 2 and 4 respectively. The convective heat transfer coefficientsbetween the walls and the air, h 1 , h 2 and h 4 , are functions of the respective wallÕs temperature, andwere calculated according to the film temperature of each surface. For surfaces 1 and 3, the filmtemperature is defined as T film;1 ¼ðT 1 T air Þ=2, for surface 2, T film;2 ¼ðT 2 T air Þ=2, and finally forsurface 4, T film;4 ¼ðT 4 T air Þ=2. A 1 , A 2 and A 4 , are the internal surface areas for the vertical, topand bottom walls respectively. The three left hand side parameters (q air ; c p;air and V air ) are thedensity, the specific heat and the volume of the air inside the enclosure.Another balance given by Eq. (2), evaluates the temperature variation of surface 2 consideringthree effects. On the right hand side, the first term represents the convective heat transfer betweenthis surface and the inside air, the second term determines the heat losses to the outside environment,and the third term represents the liquid radiation heat flux reaching this surface. Asimilar energy balance is obtained for surface 4, and it is given by Eq. (3), where the same threeterms described for Eq. (2) can be found. Eqs. (1)–(3) form a non-linear and non-homogeneoussystem of differential equations.q 2 c P;2 V 2dT 2dt¼ h 2 A 2 ðT air T 2 ÞþU 2 A 2 ðT out T 2 Þþ X4i¼1A 2 e 2 rG 2 i T 4iT 4 2ð2Þq 4 c P;4 V 4dT 4dt¼ h 4 A 4 ðT air T 4 ÞþU 4 A 4 ðT out T 4 Þþ X4i¼1A 4 e 4 rG 4 i T 4iT 4 4ð3ÞIn Eqs. (2) and (3), the two overall coefficients, U 2 and U 4 , take into account the heat transferthrough the internal metal sheet, the prototype insulation layer, the external metal sheet and theoutside convection heat transfer. Figure 2 gives a detailed view of the top surface. These overallcoefficients are defined in Eqs. (4) and (5):q' U2L2(ToutT2)InsulationMetal SheetbmsbICooking ChamberFig. 2. Top surface insulation detail.
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Thermal applicability of two-phase thermosyphons in ... - LEPTEN

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