Darcy–Forchheimer up/downflow of entropy optimized radiative nanofluids with second‐order slip, nonuniform source/sink, and shape effects

Heat Transfer ◽  
2021 ◽  
Author(s):  
Sudhanshu Shekhar Samantaray ◽  
Sachin Shaw ◽  
Ashok Misra ◽  
Manoj Kumar Nayak ◽  
Jagdish Prakash
Keyword(s):  
Second Order ◽  
Shape Effects ◽  
Source Sink

scholarly journals Simultaneous solutions for first order and second order slips on micropolar fluid flow across a convective surface in the presence of Lorentz force and variable heat source/sink

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
K. Anantha Kumar ◽  
V. Sugunamma ◽  
N. Sandeep ◽  
M. T. Mustafa
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Micropolar Fluid ◽  
Velocity Slip ◽  
Second Order ◽  
Nonlinear Odes ◽  
Similarity Transformations ◽  
Runge Kutta Method ◽  
Micropolar Fluid Flow ◽  
Source Sink

Abstract This report presents the flow and heat transfer characteristics of MHD micropolar fluid due to the stretching of a surface with second order velocity slip. The influence of nonlinear radiation and irregular heat source/sink are anticipated. Simultaneous solutions are presented for first and second-order velocity slips. The PDEs which govern the flow have been transformed as ODEs by the choice of suitable similarity transformations. The transformed nonlinear ODEs are converted into linear by shooting method then solved numerically by fourth-order Runge-Kutta method. Graphs are drowned to discern the effect of varied nondimensional parameters on the flow fields (velocity, microrotation, and temperature). Along with them the coefficients of Skin friction, couple stress, and local Nussel number are also anticipated and portrayed with the support of the table. The results unveil that the non-uniform heat source/sink and non-linear radiation parameters plays a key role in the heat transfer performance. Also, second-order slip velocity causes strengthen in the distribution of velocity but a reduction in the distribution of temperature is perceived.

A simplest steady-state Munch-like model of phloem translocation, with source and pathway and sink

2009 ◽  
Vol 36 (7) ◽  
pp. 629 ◽  
Author(s):  
William F. Pickard ◽  
Barbara Abraham-Shrauner
Keyword(s):  
Steady State ◽  
Flow Model ◽  
Sieve Tube ◽  
Steady State Solution ◽  
Second Order ◽  
Axial Position ◽  
Pressure Drops ◽  
Low Viscosity ◽  
Phloem Translocation ◽  
Source Sink

In the 80 years since its introduction by Münch, the pressure-driven mass-flow model of phloem translocation has become hegemonic, and has been mathematically modelled in many different fashions but not, to our knowledge, by one that incorporated the equations of hydrodynamics with those of osmosis and slice-source and slice-sink boundary conditions to yield a system that admits of an analytical steady-state solution for the sap velocity in a single sieve tube. To overcome this situation, we drastically simplified the problem by: (i) justifying a low Peclet number idealisation in which transverse variations could be neglected; (ii) justifying a low viscosity idealisation in which axial pressure drops could be neglected; and (iii) assuming a sink of strength sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it became unimportant. The resulting ordinary nonlinear second-order differential equation in sap velocity and axial position was of a generalised Liénard form with a single forcing parameter; and this is reason enough for the lack of a known analytic solution. However, since the forcing parameter was very large, it was possible to deduce approximate second-order solutions for behavior in the source, sink and transport regions: the sap velocity is zero at the slice-source, climbs with exponential rapidity to a plateau, maintains this plateau over most of the sieve tube, and then drops with exponential rapidity to zero at the slice-sink.

ESR LINE-SHAPE EFFECTS IN THE PRESENCE OF SECOND-ORDER SPLITTINGS OBSERVED FOR 4,4′-DIFLUOROBIPHENYL CATION

1975 ◽  
Vol 4 (6) ◽  
pp. 567-568
Author(s):  
Fujito Nemoto ◽  
Fumio Shimoda ◽  
Kazuhiko Ishizu
Keyword(s):  
Line Shape ◽  
Second Order ◽  
Shape Effects

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Multislice calculations for quasi-periodic and non-periodic objects

1990 ◽  
Vol 48 (4) ◽  
pp. 138-139
Author(s):  
R. Herrera ◽  
A. Gómez
Keyword(s):  
Electron Diffraction ◽  
Computer Simulations ◽  
Periodic Table ◽  
Amorphous Materials ◽  
Space Group ◽  
Essential Step ◽  
Shape Effects ◽  
Atomic Scattering ◽  
Diffraction Patterns ◽  
Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

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