10. Forced Convection

\[h = f(D,v,\rho,\mu,k,C_P)\] These 7 variables with totally 4 basic dimensions of \(M,L,t,T\) shall be written as 3 dimensionless groups.

Variable Symbol Unit Dimensions
heat transfer coefficient \(h\) W/(m\(^2\).K) \(Mt^{-3}T^{-1}\)
thermal conductivity \(k\) W/(m.K) \(MLt^{-3}T^{-1}\)
specific heat \(C_P\) J/(kg.K) \(L^2t^{-2}T^{-1}\)
diameter \(D\) m \(L\)
velocity \(v\) m/s \(Lt^{-1}\)
density \(\rho\) kg/m\(^3\) \(ML^{-3}\)
viscosity \(\mu\) kg/(m.s) \(ML^{-1}t^{-1}\)