Laminar forced and mixed convection heat transfer from a plane vertical isothermal surface to near-critical carbon dioxide

Numerical predictions are made for laminar forced and mixed convection heat transfer from a plane vertical isothermal surface to near critical carbon dioxide. The variation of all the thermo-physical properties with temperature has been taken into consideration. The governing equations are integrated using the Patankar–Spalding implicit finite difference scheme. Computations are made for three pressures,viz., 75 bar (P/Pcr = 1.015), 80 bar (P/Pcr = 1.083), and 100 bar (P/Pcr = 1.354), for different values of ΔT ranging from 2 K to 30 K. Three free stream velocities and two values of T∞, T∞ < T∗ and T∞ = T∗ are chosen so as to give Reynolds numbers, Re∞ ranging from 103 to 4 × 105 for forced flow and Gr∞/Re∞2 from 0.004 to 3.4 for mixed convection flows. Based on the results obtained, correlations have been proposed to evaluate the Nusselt numbers both for aiding flow and for opposing flow. The form of the proposed correlation takes into account the variation of the fluid properties in the near-critical region. The Nusselt numbers obtained from the proposed correlations deviate from the numerical predictions within ±10% in the case of forced flow, ±11% in the case of opposing flow and ±15% in the case of aiding flow. The deviation is found to be maximum for pressures close to critical pressure and for those cases for which the surface temperature, Tw is close to the pseudo-critical temperature, T∗ (pseudo-critical temperature is the temperature at which the maximum value of Cp occurs). The predictions also indicate that whenever the property variations are severe, the velocity and temperature profiles deviate considerably from those for constant property cases. However, when the pseudo – critical temperature lies within the boundary layer, the velocity profiles for mixed convection exhibit peaks and there is distortion of the temperature profiles at a location close to the point at which the maximum value of Cp occurs.