空気中におかれた加熱鉛直平板の自然対流 : 物質特性値の温度による変化の影響

概要

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Previously Pohlhausen and recently Ostrach calculated the velocity and temperature distributions about a heated flat plate which is placed vertically in air, neglecting the variation of property values depending on temperature except the buoyancy term. There exists some discrepancy between their theoretical values and the experimental results which were measured by Schmidt and Beckmann. The author solved momentum and energy equations taking into account the variation of properties depending on temperature, by perturbation theory using Pohlhausen's solution as 0 approximation. It is assumed that (1) Prandtl number is 0.733 ; (2) specific heat is constant ; and (3) viscosity and thermal conductivity vary in proportion to T^<0-76> where T is absolute temperature. Agreement between the velocity and temperature distributions obtained here and those measured by Schmidt and Beckmann is good. Calculated value of Nusselt number can be expressed as follows : Nu_1=0.359 G^<1/4>_<γ_1>(1-0.055T_0-T_1/(T_1)) where T_0 and T_1 denote the absolute temperatures of the flat plate and of the undisturbed air, respectively and N_<u1> and G_<r1> are respectively Nusselt and Grashof numbers evaluated at undisturbed condition.
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