Thermal and rheological effects in a classical Graetz problem using a nonlinear Robertson‐Stiff fluid model

Heat Transfer ◽  
2020 ◽  
Author(s):  
Muhammad Waris Saeed Khan ◽  
Nasir Ali ◽  
Zeeshan Asghar
Keyword(s):  
Fluid Model ◽  
Stiff Fluid ◽  
Graetz Problem

The Graetz Problem for the Ellis Fluid Model

2018 ◽  
Vol 74 (1) ◽  
pp. 15-24 ◽  
Author(s):  
N. Ali ◽  
M.W.S. Khan
Keyword(s):  
Energy Equation ◽  
Fluid Model ◽  
Separation Of Variables ◽  
Surface Heat ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Graetz Problem ◽  
Developing Flow ◽  
Sturm Liouville

AbstractThe determination of temperature and auxiliary quantities such as local and average Nusselt numbers for thermally developing flow is referred as the Graetz problem. In the classical Graetz problem, the fluid entering the tube or channel is Newtonian in nature. Here, an extension of the classical Graetz problem is presented by assuming that the fluid entering the tube or channel obeys the Ellis constitutive equation. The energy equation for the considered problem is solved using the separation of variables technique supplemented with the MATLAB routine bvp4c for computation of the eigenvalues and numerical solution of the associated Sturm-Liouville boundary value problem. The problem is solved for two types of thermal boundary conditions, namely, uniform surface temperature and uniform surface heat flux for both flat and circular geometries. Expressions for bulk mean temperature and local and average Nusselt numbers are presented and discussed through tables and graphs.

MAXWELL FIELDS IN ANISOTROPIC SPACETIMES

1998 ◽  
Vol 07 (05) ◽  
pp. 749-771 ◽  
Author(s):  
MATTHIAS WOLLENSAK
Keyword(s):  
Bianchi Type ◽  
Fluid Model ◽  
Analytic Solutions ◽  
Type I ◽  
Time Behavior ◽  
Stiff Fluid ◽  
Transversality Conditions ◽  
Maxwell Fields ◽  
Bianchi Type I Universe ◽  
Short Time

Maxwell's equations are rewritten with respect to anholonomic orthonormal frames and applied to the case when the background is described by a diagonal Bianchi Type I universe with line element [Formula: see text]. It is generally shown that solutions analogous to plane wave solutions in flat spacetime must obey two transversality conditions when the spacetime is anisotropic i.e., when at least one of the coefficients αj(t) differs from the others. Analytic solutions are presented for propagation along the respective coordinate axes and a special stiff fluid model. Furthermore, by use of a generally applicable ansatz the long- and short-time behavior of waves traveling in the axisymmetric Kasner universe have been investigated.

scholarly journals The Chaplygin gas as a model for modified teleparallel gravity?

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Shambel Sahlu ◽  
Joseph Ntahompagaze ◽  
Maye Elmardi ◽  
Amare Abebe
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Fluid Model ◽  
State Parameter ◽  
Teleparallel Gravity ◽  
Chaplygin Gas ◽  
Stiff Fluid ◽  
Fluid Systems ◽  
Equation Of State Parameter ◽  
Lagrangian Densities

Abstract This paper explores the possibility of treating the exotic Chaplygin-gas (CG) fluid model as some manifestation of an f(T) gravitation. To this end, we use the different cosmological CG equations of state, compare them with the equation of state for the modified teleparallel gravity and reconstruct the corresponding Lagrangian densities. We then explicitly derive the equation of state parameter of the torsion fluid $$w_T$$wT and study its evolution for vacuum-torsion, radiation-torsion, dust-torsion, stiff fluid-torsion and radiation-dust-torsion multi-fluid systems. The obtained Lagrangians have, in general, matter dependence due to the matter-torsion coupling appearing in the energy density and pressure terms of the modified teleparallel gravity theory. For the simplest CG models, however, it is possibly to reconstruct f(T) Lagrangians that depend explicitly on the torsion scalar T only. The preliminary results show that, in addition to providing Chaplygin-gas-like solutions to the modified teleparallel gravitation, which naturally behave like dark matter and dark energy at early and late times respectively, the technique can be used to overcome some of the challenges attributed to the CG cosmological alternative.

Magnetostatic stiff-fluid model of cylindrical symmetry in general relativity

1991 ◽  
Vol 185 (2) ◽  
pp. 299-304 ◽  
Author(s):  
Raj Bali ◽  
Atul Tyagi
Keyword(s):  
General Relativity ◽  
Fluid Model ◽  
Cylindrical Symmetry ◽  
Stiff Fluid

Bianchi type-I cosmological effective stiff fluid model in Saez and Ballester theory

2004 ◽  
Vol 291 (1) ◽  
pp. 75-83 ◽  
Author(s):  
G. Mohanty ◽  
S.K. Sahu
Keyword(s):  
Bianchi Type ◽  
Fluid Model ◽  
Type I ◽  
Stiff Fluid ◽  
Bianchi Type I

INFLUENCE OF HEAT AND CHEMICAL REACTIONS ON HYPERBOLIC TANGENT FLUID MODEL FOR BLOOD FLOW THROUGH A TAPERED ARTERY WITH A STENOSIS

2012 ◽  
Vol 43 (1) ◽  
pp. 69-94 ◽  
Author(s):  
Noreen Sher Akbar ◽  
Sohail Nadeem ◽  
Mohamed Ali
Keyword(s):  
Blood Flow ◽  
Chemical Reactions ◽  
Fluid Model ◽  
Hyperbolic Tangent ◽  
Tapered Artery ◽  
Flow Through

ENTROPY GENERATION IN BLOOD FLOW WITH HEAT AND MASS TRANSFER FOR THE ELLIS FLUID MODEL

2018 ◽  
Vol 49 (8) ◽  
pp. 747-760 ◽  
Author(s):  
Muhammad Mubashir Bhatti ◽  
M. Ali Abbas ◽  
M. M. Rashidi
Keyword(s):  
Mass Transfer ◽  
Blood Flow ◽  
Heat And Mass Transfer ◽  
Entropy Generation ◽  
Fluid Model
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