rho_oil 870[kg/m^3] Oil Density mu_oil 1e-2[Pa*s] Oil Viscosity Cp_oil 2000[J/kg/K] Oil Heat Capacity k_oil 0.1[W/m/K] Oil Thermal conductivity gamma_oil 1 Ratio of specific heats v_air 5[m/s] Air Velocity outside pipe T_in 25[degC] Inlet temperature T_ext -10[degC] External temperature d_wall 2[cm] Thickness of pipe wall k_wall 45[W/m/K] Thermal conductivity of pipe wall d_ins 3[cm] Thickness of insulation layer k_ins 0.025[W/m/K] Thermal conductivity of insulation oil_rate 2500[m^3/h] Oil volumetric flow rate