scholarly journals Isoperimetric inequalities for the heat potential operator

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 903-910
Author(s):  
Tynysbek Kal’menov ◽  
Aidyn Kassymov ◽  
Durvudkhan Suragan
Keyword(s):  
Circular Cylinder ◽  
Isoperimetric Inequalities ◽  
Potential Operator ◽  
Heat Potential

In this paper we prove that the circular cylinder is a maximizer of the Schatten p-norm of heat potential operator among all Euclidean cylindric domains of a given measure. We also give analogues of a Rayleigh-Faber-Krahn and a Hong-Krahn-Szeg? type inequalities.

scholarly journals Isoperimetric inequalities for the Cauchy-Dirichlet heat operator

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 885-892
Author(s):  
Tynysbek Kal’menov ◽  
Aidyn Kassymov ◽  
Durvudkhan Suragan
Keyword(s):  
Circular Cylinder ◽  
Isoperimetric Inequalities ◽  
Heat Operator ◽  
Krahn Inequality

In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in a circular cylinder among all Euclidean cylindric domains of a given measure. It is an analogue of the Rayleigh-Faber-Krahn inequality for the heat operator. We also prove a Hong-Krahn-Szeg? and a Payne-P?lya-Weinberger type inequalities for the Cauchy-Dirichlet heat operator.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

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