Numerical calculation of a generalized thermal model of radio-electronic apparatus

A method is proposed for numerical calculation of the temperature field of a generalized model of electronic equipment with high component density.Notation x,y,z,x,y spatial coordinates, m - time, sec - L_x, L_v, L_z dimensions of heated zone, m - _x, _y, _z effective thermal-conductivity coefficients of heated zone, W/m·deg - ₂ thermal conductivity of chassis, W/m·deg - a _z thermal diffusivity of heated zone along z axis, m²/sec - c₁ effective specific heat of heated zone, J/kg·deg - ₁ effective density of heated zone, kg/m³ - c₃, ₃, c₂, ₂ thermophysical characteristics of cooling agent and chassis, J/kg·deg·kg/m³ - q_v(x, ), q(x, y) volume heat-source distribution, W/m³ - q_s (x) surface heat-source distribution, W/m² - p number of cooling agent channels - Fo Fourier number - Bi Biot number - Uⁱ coolant velocity in i-th channel, m/sec - T₁(x, ), T₂(x, ), T₃(x, ) temperature distribution of heated zone, chassis, and coolant, °K - T₃₀, T₁₀(x), T₂₀(x) initial temperatures, °K - T_3in coolant temperature at input to channel, °K - T_T(x) effective temperature distribution of heat loss elements, °K - T_C temperature of external medium, °K - dimensionless heated zone temperature - _v(x) local volume heat exchange coefficient, W/m³·deg - ₁₂(x), _1C(x), _1T(x) heat liberation coefficients - W/m²·sec; ₂₁(x, y), _2c(x, y), _2T(x, y) volume heat-exchange coefficients of chassis with heated zone, medium, and cooling elements, W/m³·deg Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 876–882, May, 1981.