Generalized Lévêque Solution for Ducts of Arbitrary Cross-Section

The asymptotic limit for perimeter averaged convection is generalized for short ducts of arbitrary cross-section. A correction factor to Lévêque's original analysis is derived in terms of the state of wall shear stress under conditions of fully developed flows for walls of constant temperature (T) and constant heat flux (H1 and H2). This analysis is performed for four duct geometries: elliptic, rhombic, rectangular, and regular polygons. The importance of this correction is greatest for the H2 wall condition and for ducts having walls with acute corners. The results of this analysis can be incorporated into a generalized correlation for the full Graetz problem in ducts of arbitrary cross-section.

The level of N-terminal pro-brain natriuretic peptide depending on vascular wall condition and bone mass in postmenopausal women

Aim. To assess the relationship of serum N-terminal pro-brain natriuretic peptide (NT-proBNP) levels with vascular wall condition and bone mineral density (BMD) in postmenopausal women.Material and methods. The cross-sectional study included 107 outpatients aged 45-82 years who signed informed consent. The inclusion criterion was a menopause during ≥1 year. The level of serum NT-proBNP was determined by electrochemiluminescence. BMD was assessed by dual energy x-ray absorptiometry. Intima-media thickness (IMT), the presence and number of atherosclerotic plaques were evaluated using carotid duplex scanning. Pulse wave velocity (PWV) and augmentation index were estimated by applanation tonometry. To assess 10-year cardiovascular risk, the SCORE high-risk charts were used. Using the Russian model of FRAX® score, 10-year fracture risk was assessed.Results. NT-proBNP level in women with postmenopause >10 years was significantly higher than in those with postmenopause <5 years — 98,7 vs 56,3 pg/ml (p<0,001), but there was no independent relationship according to the regression analysis. According to multivariate regression analysis adjusted for age, menopause duration, systolic blood pressure, hypercholesterolemia, smoking, elevated C-reactive protein and interleukin-6 levels, there were independent relationship between the following parameters: NT-proBNP and IMT (β=2,38, p<0,03), NT-proBNP and PWV (β=1,76, p<0,001). NT-proBNP level in patients with osteoporosis was significantly higher than in women with normal bone mass (p<0,01). A negative correlation was observed between NT-proBNP and BMD of the proximal femur (r=-0,26, p<0,05), while the relationship between BMD of the lumbar vertebrae (L1-L4) and NT-proBNP did not reach significance. In multivariate regression analysis, this relationship has not been confirmed. A positive correlation was obtained between cardiovascular risk (SCORE) and NT-proBNP levels (r=0,28, p<0,001). NT-proBNP levels did not differ in women with a high and low 10-year risk of both major osteoporotic fractures and femoral fractures.Conclusion. An independent relationship of NT-proBNP with vascular stiffness and preclinical atherosclerosis was demonstrated: IMT and PWV. This indicates the participation of NT-proBNP in the atherosclerosis development. The association of elevated NT-proBNP levels with osteoporosis is significant, but not independent, and is apparently related to other factors.

Heat Transfer Enhancement in Unsteady MHD Natural Convective Flow of CNTs Oldroyd-B Nanofluid under Ramped Wall Velocity and Ramped Wall Temperature

This article analyzes heat transfer enhancement in incompressible time dependent magnetohydrodynamic (MHD) convective flow of Oldroyd-B nanofluid with carbon nanotubes (CNTs). Single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are immersed in a base fluid named Sodium alginate. The flow is restricted to an infinite vertical plate saturated in a porous material incorporating the generalized Darcy’s law and heat suction/injection. The governing equations for momentum, shear stress and energy are modelled in the form of partial differential equations along with ramped wall temperature and ramped wall velocity boundary conditions. Laplace transformation is applied to convert principal partial differential equations to ordinary differential equations first and, later, complex multivalued functions of Laplace parameter are handled with numerical inversion to obtain the solutions in real time domain. Expression for Nusselt number is also obtained to clearly examine the difference in rate of heat transfer. A comparison for isothermal wall condition and ramped wall condition is also made to analyze the difference in both profiles. A graphical study is conducted to analyze how the fluid profiles are significantly affected by several pertinent parameters. Rate of heat transfer increases with increasing volume fraction of nanoparticle while shear stress reduces with elevation in retardation time. Moreover, flow gets accelerated with increase in Grashof number and Porosity parameter. For every parameter, a comparison between solutions of SWCNTs and MWCNTs is also presented.

Refinement of the Generalized Graetz Problem Correlation With New Benchmark Calculations

A recently proposed generalized correlation for the Graetz problem in heat transfer has two fitted constants that can be related back to two fundamental constants of fully developed transport. A new set of benchmark solutions for convection in annular tubes is used to assess the best linear relationship between fitted and fundamental constants used in this correlation for conditions spanning from circular tubes to parallel plate ducts. This work also improves the Lévêque limit of the general correlation by considering peripheral variation in flow friction. The refined Graetz problem correlation for fully developed flow is able to predict exact thermal entry region solutions to within ±1.2% for all annular tube geometries having either constant temperature (T) or constant heat flux (H1) wall condition.