THEORETICAL ANALYSIS OF TRANSIENT LAMINAR FORCED CONVECTION IN SIMULTANEOUSLY DEVELOPING FLOW IN PARALLEL-PLATE CHANNEL

An analytical study of transient laminar forced convection in parallel plate channel for simultaneously developing flow is performed. A general boundary condition of the fifth kind at the duct walls, that accounts for both external convection and wall heat capacitance effects is used. The flow is subjected to a periodic variation of the inlet temperature. The thermal response of the system for inlet periodic perturbations is sought after the initial transient has completely disappeared. The generalized integral transform technique is used to provide a hybrid analytical-numerical solution. The periodic analysis is performed by using two similar coupled problems for the real and imaginary parts of the solution. The coupled transformed equations are simultaneously solved through well-established algorithms for stiff initial value problems. Numerical results are presented in graphical and tabular format and compared against previously published works.