Analysis of unsteady forced convection in channels by integral transform technique and experiments

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Sadik Kakac, Committee Chair


A theoretical and experimental study of unsteady forced convection between parallel plates channels is presented. A general boundary condition of the fifth kind that accounts for both external convection and wall thermal capacitance effects is imposed. Axial conduction, free convection, the effect of temperature dependent fluid properties and viscous dissipation are disregarded.The first problem proposed is a periodic laminar hydrodynamic developed, thermally developing flow, where the thermal entrance region is studied through the so-called generalized integral transform technique in conjunction with the Mathematica software system employed to construct hybrid numerical-analytical solution. Therefore, each required analytical step is done by symbolic computations. The results are presented in form of 3-D plots which give information about the temperature amplitudes and phase lags. The relevant parameters that are varied in the analysis are the Biot number, the fluid-to-wall thermal capacitance ratio a*, and the dimensionless inlet frequency O.The second problem proposed here is an extension of the first problem, for a periodic laminar simultaneously developing flow. Again, the hybrid numerical-analytical approach given by the generalized integral transform technique is employed to handle the steady two-dimensional Navier-Stokes equations in stream function formulation. A filtering formulation is employed in order to enhance convergence. The relevant parameters, such as the Reynolds number, the Biot number, the dimensionless inlet frequency O, and the fluid-to-wall thermal capacitance ratio a*, are varied in order to study their influence on the solution.The third problem proposed here is a periodic turbulent forced convection flow problem for the thermal entrance region of a duct simulating a parallel plates channel. For this case, only experimental analysis is performed. The experimental analysis is divided into three cases, the smooth duct case, the asymmetric rough duct case, and the symmetric rough duct case. The roughness is simulated by attaching small blocks inside the duct in order to be direct applicable to electronic cooling. For each case, two Reynolds number and four inlet frequency beta are used in order to predict their influence on the solution.For each problem studied, results and comparisons are presented in the form of graphs and/or tables. Discussions about the results are presented for each case, and then, a general discussion is done about all the problems proposed in the present dissertation.


Engineering, Mechanical

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