Transient conjugated heat transfer from a rectangular hot film

Abstract

A numerical calculation is carried out for the transient response of a flush-mounted hot-film sensor in a gas flow heated by a step change in the hot-film output flux. The numerical method used is called the unsteady surface element method. This calculation is part of a study of unsteady behavior of hot-film anemometers that involve substrate effects. The numerical results show that the early-time film temperature agrees well with an analytical solution, and the steady-state Nusselt number agrees with an existing numerical solution. The spatial average film temperature vs time is presented for several values of the rectangular hot-film aspect ratio. Nomenclature a = streamwise half-length of the hot film, m b = span wise half-length of the hot film, m K = thermal conductivity, W/(mK) — streamwise length of the yth surface element, m = spanwise length of the yth surface element, m M = number of time steps N = number of surface elements Np = flow parameter, Eq. (16) Nu = Nusselt number P = hot-film output flux, W/m2 Pe = Peclet number, p(2a)2/af q = heat flux, W/m2 qQ = hot-film output, W/m2 T = temperature Tav = spatial average hot-film temperature TQ = initial temperature T- = (T - TQ)l(qQalKs) t+ = ast/a2 x = streamwise coordinate x+ = x/a Xj = center of the yth surface element y = spanwise coordinate y+ = yla yj = center of the ;th surface element z = coordinate normal to the interface a = thermal diffusivity, m2/s /3 = velocity gradient, s1 F( ) = gamma function Ai/r = influence function, Eq. (13) TJ = dummy space variable in the spanwise direction A = dummy time variable //,( ) = unit step function f = dummy space variable in the streamwise direction $ = fundamental solution, defined in Appendix A