Temperature distribution for MHD flow between coaxial cylinders with discontinuity in wall temperatures

1979 ◽  
Vol 35 (1) ◽  
pp. 67-83 ◽  
Author(s):  
Bani Singh ◽  
Jia Lal
Keyword(s):  
Temperature Distribution ◽  
Mhd Flow ◽  
Coaxial Cylinders

A note on the temperature distribution in a channel bounded by two co-axial cylinders

1966 ◽  
Vol 62 (2) ◽  
pp. 301-302
Author(s):  
P. L. Bhatnagar ◽  
V. G. Tikekar
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Unit Volume ◽  
Initial Conditions ◽  
Coaxial Cylinders ◽  
Image Position

If we neglect the viscous dissipation, the temperature distribution in an incompressible fluid flowing in the annulus between two coaxial cylinders with radii r1 and r2 (> r1) is determined by the equationInitial conditionsBoundary conditionswhere ∂Q/∂t is a function of time alone representing the rate of heat generation per unit volume per unit time in the fluid.

scholarly journals Entropy Optimized Flow of Hybrid Nanomaterial over a Porous Stretchable Surface

2021 ◽  
Author(s):  
T. Hayat ◽  
Zobia Kainat ◽  
Sohail A. Khan ◽  
A. Alsaedi
Keyword(s):  
Temperature Distribution ◽  
Entropy Generation ◽  
Opposite Effect ◽  
Mhd Flow ◽  
Second Law Of Thermodynamics ◽  
Nonlinear Flow ◽  
Solution Technique ◽  
Hybrid Nanomaterial ◽  
Numerical Result ◽  
Aqueous Nanostructures

The aim of this articles is to investigate the entropy optimization in unsteady MHD flow Darcy-Forchheimer nanofluids towards a stretchable sheet. The surface we tend to think about is porous and stretchy under acceleration. Flow occurs due to the stretching of the surface. Four distinct types of aqueous nanostructures are taken in this examination where copper oxide ( ), copper ( ), titanium dioxide ( ) and aluminum oxide ( ) are the nanoparticles. Irreversibility analysis are discussed through second law of thermodynamics. The expression of energy is mathematically designed and discussed according to heat generation / absorption, dissipation, thermal radiation, and joule heating. The nonlinear PDE (partial differential conditions) is first changed to ODE (normal differential conditions) through appropriate similarity variables. Here we used the numerically embedded solution technique to develop a numerical result for the obtained nonlinear flow expression. Influence of various flow parameter velocity temperature distribution and entropy generation are discussed. Reduction occurs in velocity profile for larger porosity and magnetic parameters. An enhancement in entropy generation and temperature distribution is seen for Brinkman number. An opposite effect is noticed in velocity and temperature through solid volume friction.

scholarly journals Dissipative Heating in a Rotational Viscometer with Coaxial Cylinders

10.14311/1053 ◽  
2008 ◽  
Vol 48 (5) ◽  
Author(s):  
F. Rieger
Keyword(s):  
Temperature Distribution ◽  
Heat Resistance ◽  
Power Law ◽  
Outer Cylinder ◽  
Rheological Behaviour ◽  
Dissipative Heating ◽  
Diameter Ratio ◽  
Rotational Viscometer ◽  
Coaxial Cylinders ◽  
Temperature Time

Rotational viscometers with coaxial cylinders are often used for measuring rheological behaviour. If the inner to outer cylinder diameter ratio does not differ significantly from 1, the curvature can be neglected and the flow reduces to the flow between moving and stationary plates. The power-law and Bingham models are often used for describing rheological behaviour. This paper deals with the temperature distribution obtained by solving the Fourier-Kirchhoff equation and in the case of  negligible inner  heat resistance it also covers temperature time dependence. The solution is illustrated by a numerical example. 

scholarly journals Analytical Solutions of Fractional Walter’s B Fluid with Applications

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Qasem Al-Mdallal ◽  
Kashif Ali Abro ◽  
Ilyas Khan
Keyword(s):  
Mass Transfer ◽  
Temperature Distribution ◽  
Heat And Mass Transfer ◽  
Mass Concentration ◽  
Mathematical Formulation ◽  
Mhd Flow ◽  
Rheological Parameters ◽  
Physical Parameters ◽  
General Solutions ◽  
Walter’S B Fluid

Fractional Walter’s Liquid Model-B has been used in this work to study the combined analysis of heat and mass transfer together with magnetohydrodynamic (MHD) flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD) has been used in the mathematical formulation of the problem. By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. The problem is solved analytically and solutions of mass concentration, temperature distribution, and velocity field are obtained in the presence and absence of porous and magnetic field impacts. The general solutions are expressed in the format of generalized Mittag-Leffler function MΩ2,Ω3Ω1χ and Fox-H function Hp,q+11,p satisfying imposed conditions on the problem. These solutions have combined effects of heat and mass transfer; this is due to free convections differences between mass concentration and temperature distribution. Graphical illustration is depicted in order to bring out the effects of various physical parameters on flow. From investigated general solutions, the well-known previously published results in the literature have been recovered. Graphs are plotted and discussed for rheological parameters.

Analysis of MHD flow of Burgers’ fluid with heat transfer in helical screw rheometer

2015 ◽  
Vol 93 (8) ◽  
pp. 871-879 ◽  
Author(s):  
T. Haroon ◽  
A.M. Siddiqui ◽  
M. Zeb
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Volume Flow Rate ◽  
Mhd Flow ◽  
Flow Profile ◽  
Electrically Conducting ◽  
Stress Components ◽  
Hall Parameter ◽  
Burgers Fluid ◽  
Fluid Parameters

This paper aims to study the influence of Hall current and heat transfer on the magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers’ fluid in a helical screw rheometer. The screw and barrel are electrically insulated and kept at two different constant temperatures. A uniform magnetic field is applied perpendicular to the flow. Exact solutions are obtained for the velocity profile, volume flow rate, temperature distribution and rate of heat transfer. Expressions for the shear and normal stress components are also calculated. It is observed that the Burgers’ fluid parameters contribute in normal and tangential stresses, only. The effects of Hall parameter, Hartmann number, pressure distribution, and Brinkman number are investigated on flow profile, temperature distribution, and heat flux.

Numerical simulation of MHD flow of micropolar fluid inside a porous inclined cavity with uniform and non-uniform heated bottom wall

2018 ◽  
Vol 96 (6) ◽  
pp. 576-593 ◽  
Author(s):  
Mubbashar Nazeer ◽  
N. Ali ◽  
Tariq Javed
Keyword(s):  
Magnetic Field ◽  
Temperature Distribution ◽  
Micropolar Fluid ◽  
Nonlinear Partial Differential Equations ◽  
Numerical Data ◽  
Mhd Flow ◽  
Bottom Wall ◽  
Nusselt Numbers ◽  
Two Dimensional Flow ◽  
Inclined Cavity

Buoyancy-driven, incompressible, two-dimensional flow of a micropolar fluid inside an inclined porous cavity in the presence of magnetic field is investigated. The nonlinear partial differential equations are solved by employing a robust Galerkin finite element scheme. The pressure term in this scheme is eliminated by using the penalty method. The results are exhibited in the form of streamlines, isotherms, and local and average Nusselt numbers for two cases, namely, the constant and the sinusoidal heated lower wall of the conduit. In both cases, the side walls of the cavity are cold and the upper side is insulated. The main difference between the two cases is observed from temperature contours. For constant heated bottom wall a finite discontinuity appears in the temperature distribution at the corners of the bottom wall. In contrast, no such discontinuity appears in the temperature distribution for non-uniform heated bottom wall. The quantitative changes in temperature contours in different portions of the cavity are identified by comparing the results for both cases. The code is also validated and benchmarked with the previous numerical data available in the literature. It is found that the magnetic field inclined at a certain angle either suppresses or enhances the intensity of primary circulations depending on the inclination of the cavity. Further, the average Nusselt number at the bottom wall is higher when magnetic field is applied vertically irrespective of the inclination of cavity. The analysis presented here has potential application in solar collectors and porous heat exchangers.

scholarly journals Irreversibility Analysis in Darcy-Forchheimer Flow of Nanofluid by a Stretched Surface

2021 ◽  
Author(s):  
T Hayat ◽  
Zobia Kainat ◽  
A Alsaedi ◽  
Sohail A. Khan
Keyword(s):  
Temperature Distribution ◽  
Entropy Generation ◽  
Opposite Effect ◽  
Flow Parameter ◽  
Mhd Flow ◽  
Second Law Of Thermodynamics ◽  
Nonlinear Flow ◽  
Solution Technique ◽  
Numerical Result ◽  
Aqueous Nanostructures

Abstract The aim of this articles is to investigate the entropy optimization in unsteady MHD flow Darcy-Forchheimer nanofluids towards a stretchable sheet. The surface we tend to think about is porous and stretchy under acceleration. Flow occurs due to the stretching of the surface. Four distinct types of aqueous nanostructures are taken in this examination where copper oxide (CuO), copper (Cu), titanium dioxide (TiO2) and aluminum oxide (Al2O3) are the nanoparticles. Irreversibility analysis are discussed through second law of thermodynamics. The expression of energy is mathematically designed and discussed according to heat generation / absorption, dissipation, thermal radiation, and joule heating. The nonlinear PDE (partial differential conditions) is first changed to ODE (normal differential conditions) through the use of appropriate similarity variables. Here we used the numerically embedded solution technique to develop a numerical result for the obtained nonlinear flow expression. Influence of various flow parameter velocity temperature distribution and entropy generation are discussed. Reduction occurs in velocity profile for larger porosity and magnetic parameters. An enhancement in entropy generation and temperature distribution is seen for Brinkman number. An opposite effect is noticed in velocity and temperature through solid volume friction.

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