NUMERICAL SIMULATION OF TURBULENT HEAT TRANSFER IN A ROTATING DISK AT ARBITRARY DISTRIBUTION OF THE WALL TEMPERATURE I. V. Shevchuk UDC 536.24 Turbulent heat transfer in a freely rotating disk with an arbitrary change in the wall temperature is investi- gated. With the aid of the integral method developed previously, numerical simulation for the cases of posi- tive, approximately constant, and negative radial temperature gradients of the disk is carried out. Unlike the known Dorfman method, the results of the calculations performed agree well with experimental data. Based on the data obtained, conclusions are drawn about relatively optimum parameters of the model for the con- ditions under consideration. Investigation of different aspects of turbulent heat transfer in a rotating disk is a topical problem as applied to the systems of air cooling of the rotors of gas turbines, hard disks of computers, etc. It is well known that an ana- lytical solution of the problem [1–5] obtained by the integral method with power-law radial distribution of the disk temperature is as follows: T w - T ∞ = c 0 r n * , (1) Nu = K 1 Re ϕ n R x m x , (2) where n R = (n + 1)/(3n + 1), K 1 , c 0 , and n * are constants. The quantity n is an exponent of the power approximation of the velocity and temperature profiles. The constant m x in formula (2) acquires a value of m x = 1 + m at condition (1). In the case of turbulent flow, n = 1/5–1/10 and m = (1 – n)/(3n + 1); in the case of laminar flow, n = 1 and m = 0. At an arbitrary value of m x , in [6] a more general analytical solution is obtained for the wall temperature T w that includes relation (1) as a particular case. Analysis has shown that the solution of the problem obtained by the author of [4–6] is the most exact one, while in a number of cases the calculations by the Dorfman formula [1–3] sub- stantially exceed the reliable experimental and calculated data obtained by other authors. However, under real conditions often the wall temperature distribution cannot be described by the analytical dependences mentioned above. In these cases, use is made of a numerical version of the integral method and the dis- tribution of T w is approximated by some other dependence. In [7, 8], the Dorfman method at a fixed value of n = 1/7 was employed for numerical simulation of the conditions observed in experiments. As in the case of the analytical ver- sion of the Dorfman method, the calculated results for a Nusselt number [7, 8] markedly exceeded the experimental data at dT w ∕ dr 0 and dT w ∕ dr < 0. The calculated and experimental results agreed well at dT w ∕ dr > 0, with the ex- ception of the cases of high Re ϕ numbers at which the calculated data were lower than the experimental values. The authors of [9] simulated the experimental conditions of [7, 8] by solving numerically the differential equations for a boundary layer with use of the known Cebeci–Smith model of turbulent viscosity [10]. The agreement of the calculations with the experiments turned to be good. This is indicative of the reliability of the experimental data of [7, 8], while the substantial error of the Dorfman method at dT w ∕ dr ≤ 0 is responsible for the disagreement of the calculated [7, 8] and experimental results. Journal of Engineering Physics and Thermophysics, Vol. 75, No. 4, 2002 Institute of Engineering Thermal Physics, National Academy of Sciences of Ukraine, Kiev; email: ivshevch@ i.com.ua. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 75, No. 4, pp. 94–97, July–August, 2002. Original arti- cle submitted March 28, 2001. 1062-0125/02/7504-0885$27.00 2002 Plenum Publishing Corporation 885