Journal ArticleDOI
Boundary value problems in transport with oblique and mixed derivative boundary conditions: More on steady state solutions
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In this article, the energy equation is decomposed into a pair of first order systems, and the originally non-selfadjoint boundary value problems can be reduced to selfadjoint problems.About:
This article is published in Chemical Engineering Science.The article was published on 1981-01-01. It has received 9 citations till now. The article focuses on the topics: Boundary value problem & Mixed boundary condition.read more
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Conjugated Graetz Problems. I : General Formalism and a Class of Solid-Fluid Problems
TL;DR: In this article, a general formalism is presented for the analysis of conjugated Graetz problems, employing a matrix differential operator with respect to the radial variable and following the decomposition technique.
Journal ArticleDOI
Conjugated Graetz problems—II: Fluid-fluid problems
TL;DR: In this paper, the authors show that analytical and computationally efficient solutions may be obtained only for these problems where the temperature profile at the entrance of the heating section is known for at least one of the fluids.
Journal ArticleDOI
Solutions to the Extended Graetz Problem for a Power-Model Fluid with Viscous Dissipation and Different Entrance Boundary Conditions
Ching-Tien Liou,Feng-Sheng Wang +1 more
TL;DR: In this paper, the authors studied the transport phenomena of the extended Graetz problem with three different entrance boundary conditions and showed that the expansion coefficients of the solution corresponding to the different conditions play an important role in effecting the solution form.
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The unsteady-state solution by an operator theory for a dispersion-type tubular reactor with an immobile zone
TL;DR: In this paper, the analytical solution for an unsteady-state, dispersion-type, tubular reactor model with an immobile zone is obtained by an operator theory in a Hilbert space.
Journal ArticleDOI
Solution of low Pe´clet number heat transfer with viscous dissipation in the semi-infinite axial region of a tube via functional analytic methods
Ching-Tien Liou,Feng-Sheng Wang +1 more
TL;DR: In this article, a solution of the extended Graetz problem with prescribed wall heat flux and viscous dissipation in a semi-infinite axial region of a tube is obtained by functional analytic methods.
References
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Boundary value problems in transport with mixed and oblique derivative boundary conditions-II: Reduction to first order systems
TL;DR: In this article, the second order partial differential equations have been decomposed into first order systems, which under suitable circumstances can be conveniently adapted to satisfy the mixed or oblique derivative boundary conditions.
Journal ArticleDOI
Boundary value problems in transport with mixed or oblique derivative boundary conditions—I: Formulation of equivalent integral equations
TL;DR: In this paper, it was shown that the mixed derivative boundary value problem can be reduced to equivalent singular integral equations, which is the more realistic condition in the present context of axial conduction in the coolant fluid.
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