We investigate analytically the First and the Second Law (of Thermodynamics) characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy-Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions are presented for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in terms of the system parameters. The conclusion of this analytical study will make it possible to compare and evaluate alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation.
A theoretical analysis is presented to investigate thermally and hydrodynamically fully developed forced convection in a duct of rectangular cross section filled with a hyper-porous medium. The Darcy-Brinkman model was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e., the H boundary condition in the terminology of Kays and Crawford (1993, Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, NY), is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.
The effects of blood velocity on gas transport within the alveolar region of lungs, and on the lung diffusing capacity DL have for many years been regarded as negligible. The present work reports on a preliminary, two-dimensional investigation of CO convection-diffusion phenomenon within a pulmonary capillary. Numerical simulations were performed using realistic clinical and morphological parameter values, with discrete circular red blood cells (RBCs) moving with plasma in a single capillary. Steady-state simulations with stationary blood (RBCs and plasma) were performed to validate the model by comparison with published data. Results for RBCs moving at speeds varying from 1.0 mm/s to 10 mm/s, and for capillary hematocrit (Ht) from 5% to 55%, revealed an increase of up to 60% in DL, as compared to the stationary blood case. The increase in DL is more pronounced at low Ht (less than 25%) and high RBC speed and it seems to be caused primarily by the presence of plasma. The results also indicate that capillary blood convection affects DL not only by improving the plasma mixing in the capillary bed but also by replenishing the capillary with fresh (zero concentration) plasma, providing an additional reservoir for the consumption of CO. Our findings cast doubt on the current belief that an increase in the lung diffusing capacity of humans (for instance, during exercising), with fixed hematocrit, can only be accomplished by an increase in the lung volume effectively active in the respiration process.
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