Theoretical and experimental analysis of unsteady forced convection in circular ducts

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Sadik Kakac - Committee Chair


The analysis of forced convective heat transfer with laminar and/or turbulent flow subjected to periodic variations of the fluid inlet temperature usually leads to a nonclassical Sturm-Liouville type eigenvalue problem for which no known solution is presently available. This work reports the findings of two complementary studies (theoretical and experimental, and theoretical and empirical), respectively, on unsteady and steady forced convection of a Newtonian fluid flowing inside the thermal entry region of a circular duct, being subjected to different boundary and inlet conditions. A theoretical approach based on ideas associated with the generalized integral transform technique was developed to alleviate the need for the solution of complex time-dependent eigenvalue problems, while the difficulties associated with other methods overcome through consideration of time-independent auxiliary eigenvalue problems, resulting in a transformed infinite set of coupled, first-order, linear differential equations in the complex domain.In the second phase, accurate computational procedures were developed for obtaining benchmark analytical results of a hybrid nature. For practical purposes, consideration was given to cases of: (a) unsteady thermally developing forced convection with laminar and turbulent air flow inside a circular duct subjected to periodic variations of the fluid inlet temperature while imposing a fifth-kind boundary condition at the internal fluid-solid interface, and (b) thermally developing steady forced convection with turbulent air flow inside a circular duct subjected to a uniform fluid inlet temperature distribution with the first-kind boundary condition imposed at the internal fluid-solid interface. Benchmark results for quantities of practical relevance were obtained in terms of the axial variation in amplitudes and phase lags of centerline and bulk fluid temperatures and wall heat flux, in addition to local and thermally developed Nusselt numbers for both periodic and steady state situations. Through consideration of practical values for, respectively, the modified Biot number, Bi, fluid-to-wall heat capacitance ratio, $a*$, and Reynolds Number, Re, the thermal response of the system and convergence characteristics of the hybrid analytical-numerical models, here advanced, were critically examined, while the limitations associated with the decoupled system discussed within the realms of the variable system parameters and convergence criteria.In the final phase, an experimental apparatus was designed and built (by the author) and used to provide validation data for the theoretical studies, representing the "first set" of systematically evaluated benchmark experimental results for the circular duct geometry, particularly applicable to unsteady forced convection with the fifth-kind boundary condition and periodic inlet fluid temperature variations. Based on the cases considered, simplified analytic formulas are proposed for accurately predicting the variation in phase lags and amplitudes of wall heat flux, fluid centerline and bulk temperatures along the thermal entrance region. Further, the analysis here advanced can easily be applied to other flow passage geometries through transformation.


Engineering, Mechanical

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