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

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.