I have been trying to model heat transfer and pressure drop for oscillatory flows inside a closed channel flowing past a matrix material. My intuition and experimental results (in journal papers) tend to show that the net heat transfer (measured as the heat transfer coefficient)


$$h= \frac{q^{''}}{(T_{solid}-T_{fluid})A_{ht}}$$ 


NOTE: I provide $T_{solid}$ as a constant input BC and calculate $q^{''},T_{fluid}$ from simulation results. $A_{ht}$ is the known surface area through which Heat transfer occurs from the simulation results


should be enhanced for oscillatory flows when compared to a steady flow.

I am modeling both the flows as turbulent ($k-\epsilon$) in **ANSYS FLUENT**. For oscillating flow I provide the velocity profile as a sinusoidal input as $v = v_{max} \sin(\omega t)$, $t,\omega$ are time and frequency respectively




It turns out that the time average $h$ for both the cases (steady & oscillatory) come out to be quite similar.

For oscillatory flow I use 


$$\bar{h} = \frac{\sum_{i=1}^{N}h_i t_i}{\sum_{i=1}^{N}t_i}$$, where $t_i$ is the size of time-step. $i=1$ to $N$ encompass one time-step.




Is there something wrong in the way I am calculating the average $h$ for oscillatory flows? Particularly, I would like to know if there could be some other approach to calculate the average $h$ or there might be some other explanation for this result.