Mixed convection of electrically conducting and viscous fluid in a vertical channel using Robin boundary conditions

2015 ◽  
Vol 93 (6) ◽  
pp. 698-710 ◽  
Author(s):  
J. Prathap Kumar ◽  
J.C. Umavathi ◽  
Ali J. Chamkha ◽  
Y. Ramarao
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Vertical Channel ◽  
Robin Boundary Conditions ◽  
Electrically Conducting ◽  
Robin Boundary

scholarly journals Effect of viscous dissipation on mixed convection flow in a vertical double passage channel using Robin boundary conditions

1970 ◽  
Vol 8 (3) ◽  
pp. 27-47
Author(s):  
J. Prathap Kumar ◽  
J.C. Umavathi ◽  
M. Karuna Prasad
Keyword(s):  
Boundary Conditions ◽  
Mixed Convection ◽  
Perturbation Method ◽  
Viscous Dissipation ◽  
Perturbation Parameter ◽  
Differential Transform Method ◽  
Robin Boundary Conditions ◽  
Transform Method ◽  
Differential Transform ◽  
Robin Boundary

The laminar fully developed flow in a vertical double passage channel filled with clear fluid has been discussed using Robin boundary conditions. The thin perfectly conductive baffle is inserted in the channel. The governing equations of the fluid which are coupled and nonlinear are solved analytically by the perturbation method and semi analytically using differential transform method (DTM). The reference temperature of the external fluid is considered to be equal and different. The perturbation method which is valid for small values of perturbation parameter is used to find the combined effects of buoyancy forces and viscous dissipation. The limitation imposed on the perturbation parameter is relaxed by solving the basic equations using differential transform method. The influence of mixed convection parameter, Biot number for symmetric and asymmetric wall temperatures on the velocity, temperature and the Nusselt number is explored at different positions of the baffle. The solutions obtained by differential transform method are justified by comparing with the solutions obtained by perturbation method and the solutions agree very well for small values of the perturbation parameter.Keywords: Baffle, Differential Transform Method, Perturbation Method, Viscous dissipation, Robin Boundary Conditions, Double passage channel.

Soret effects on the mixed convection flow using Robin boundary conditions

2019 ◽  
Vol 49 (1) ◽  
pp. 154-179 ◽  
Author(s):  
Jawali C. Umavathi ◽  
Mikhail A. Sheremet ◽  
Sapnali Limbraj Patil
Keyword(s):  
Boundary Conditions ◽  
Mixed Convection ◽  
Convection Flow ◽  
Robin Boundary Conditions ◽  
Mixed Convection Flow ◽  
Robin Boundary

scholarly journals An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Bin Liu ◽  
Ying Liang ◽  
Xiaobing Bao ◽  
Honglin Fang
Keyword(s):  
Boundary Conditions ◽  
Grid Method ◽  
Posteriori Error ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Euler Formula ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Robin Boundary

AbstractA system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

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