Well‐posedness of thermal boundary layer equation in two‐dimensional incompressible heat conducting flow with analytic datum

2020 ◽  
Author(s):  
Ya‐Guang Wang ◽  
Shi‐Yong Zhu
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Boundary Layer Equation ◽  
Heat Conducting ◽  
Well Posedness ◽  
Two Dimensional

Two-Phase Microscopic Heat Transfer Model for Three-Dimensional Stagnation Boundary-Layer Flow in a Porous Medium

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shashi Prabha Gogate S.
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Thermal Boundary Layer ◽  
Solid Phase ◽  
Boundary Layer Equation ◽  
Three Dimensional ◽  
Fluid Phase ◽  
Transfer Model ◽  
Layer Flow

Abstract This work examines the steady three-dimensional forced convective thermal boundary-layer flow of laminar and incompressible fluid in a porous medium. In this analysis, it is assumed that the solid phase and the fluid phase, which is immersed in a porous medium are subjected to local thermal nonequilibrium (LTNE) conditions, which essentially leads to one thermal boundary-layer equation for each phase. Suitable similarity transformations are introduced to reduce the boundary-layer equations into system of nonlinear ordinary differential equations, which are analyzed numerically using an implicit finite difference-based Keller-box method. The numerical results are further confirmed by the asymptotic solution of the same system for large three-dimensionality parameter, and the corresponding results agree well. Our results show that the thickness of boundary layer is always thinner for all permeability parameters tested when compared to the nonporous case. Also, it is noticed that the temperature of solid phase is found to be higher than the corresponding fluid phase for any set of parameters. There is a visible temperature difference in the two phases when the microscopic interphase rate is quite large. The physical hydrodynamics to these parameters is studied in some detail.

Thermal instability of two-dimensional stagnation-point boundary layers

1983 ◽  
Vol 132 ◽  
pp. 49-63 ◽  
Author(s):  
K. Chen ◽  
M. M. Chen ◽  
C. W. Sohn
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Thermal Instability ◽  
Critical Rayleigh Number ◽  
Two Dimensional ◽  
Point Boundary ◽  
Stagnation Flow ◽  
Boundary Layer Approximation ◽  
Prandtl Numbers ◽  
Critical Wavenumber

A study of thermal instability for the two-dimensional stagnation flow for Prandtl numbers ranging from 0.7 to infinity is presented. The analysis represents an exact solution since neither the boundary-layer approximation nor the parallel-flow assumption was invoked. Of particular interest is that the critical Rayleigh number and the critical wavenumber, when defined on the basis of the thermal boundary-layer lengthscale, are found to be relatively insensitive to the Prandtl number for the range of Prandtl numbers studied.

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