Achieving uniform heat transfer coefficient in coaxial pulsating jet

The main aim of the present paper is to investigate the inverse design of uniform distribution of heat transfer coefficient on the target plate by employing coaxial jet in the steady and pulsating state. The objective function is defined as the root-mean-square of the deviation of the local Nusselt number on the target plate in computational fluid dynamics simulation from the desired Nusselt number. The heat transfer search method minimizes the objective function. The geometric and fluid parameters are taken into account as design variables. Firstly, optimization in the steady state for the target Nusselt numbers 7, 10 and 13 is carried out and the values of the objective function in the optimal state are found to be 0.51, 0.18 and 0.314, respectively. The range of design variables in the steady and pulsating state is similar, while the heat transfer rate of the pulsating state is higher than that of the steady state. The variations of velocity in the inner and outer nozzles with time are considered to have a sine–sine, cosine–sine and constant–sine behavior. Optimization is carried out in the pulsating state for the Nusselt numbers 33, 44, 55 and 57. The objective function for these numbers in the optimal state is less than 0.02. By employing the conjugate gradient method with adjoint equation and the optimal value of design variables, the distribution of Nusselt number on the target plate in the steady and pulsating state for the constant–sine velocity case is experimentally estimated. The difference between experimental results and the value of the target Nusselt number is about 4–14%, indicating a good agreement between the two approaches.