Impingement Heat Transfer over a Rotating Disk: Integral Method

Understanding of peculiarities of real jets is frequently based on the solutions of simplified problems. For an axisymmetric laminar jet impinging on a stationary surface at *w = 0, it was shown that a constant-thickness boundary layer develops near the stagnation point, whereas the velocity components at the outer edge of the boundary layer are described by the equations: vr#i = ar, vz,#i = -2az; A = 4/*p or A = 1.5 DT (hj/dj)-0.22. The first of relations is valid for the potential flow of a uniform stream impinging on the disk; in this case dj = d. The second equation (2) is effective for real singular axisymmetric jets over the range hj/dj = 2-6 for high enough values of Rej, whereas A #~ 1 for low values of Rej. For coaxial uniform flow impingement on a rotating disk, works present velocity profiles and friction coefficients in the graphical or tabulated form. Nusselt numbers were calculated for the boundary condition (here c0 is constant) Tw-T#i = c0rn*, only at n* = 0 and 2 for few values of Pr and *k in works. Experimental radial distributions of the Nusselt number are presented in papers. At Vj = 0 the problem reduces to the case of the free rotating disk studied extensively in works. The main objective of the present work consists of the development of an integral method and obtaining an approximate analytical solution of the problem under consideration. This method is based on the exact numerical solution of the Navier-Stokes and energy equations under conditions (1) and (3) at 10 values of n* = -2-4, different Pr = 0.1-1 and *k = 0-#i.