The effects on the flow field of retaining the Joule heating and viscous dissipation term in the energy equation for the hydromagnetic free-convective oscillatory flow past a porous limiting surface, I

1984 ◽  
Vol 98 (2) ◽  
pp. 287-298 ◽  
Author(s):  
N. D. Nanousis ◽  
N. G. Kafousias
Keyword(s):  
Flow Field ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Oscillatory Flow ◽  
Energy Equation ◽  
Dissipation Term ◽  
Flow Past ◽  
Limiting Surface

Effect of viscous dissipation in stokes flow between rotating cylinders using BEM

2019 ◽  
Vol 30 (4) ◽  
pp. 2121-2136 ◽  
Author(s):  
Tomasz Janusz Teleszewski
Keyword(s):  
Nusselt Number ◽  
Temperature Distribution ◽  
Viscous Dissipation ◽  
Stokes Flow ◽  
Energy Equation ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Content Type ◽  
Dissipation Term ◽  
Cylinder Diameter

Purpose The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters. Design/methodology/approach The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders. Findings As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases. Originality/value The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

Energy Equation of Gas Flow With Low Velocity in a Micro-Channel

2014 ◽  
Author(s):  
Yutaka Asako
Keyword(s):  
Viscous Dissipation ◽  
Incompressible Flow ◽  
Gas Flow ◽  
Energy Equation ◽  
Outlet Temperature ◽  
Gas Temperature ◽  
Low Velocity ◽  
Dissipation Term ◽  
Pressure Term ◽  
Micro Channels

The energy equation for incompressible flow with the viscous dissipation term is often used for the governing equations of gas flow with low velocity in micro-channels. However, the results which are obtained by solving these equations do not satisfy the first law of the thermodynamics. In the case of ideal gas with low velocity, the inlet and the outlet temperatures of an adiabatic channel are the same based on the first law of the thermodynamics. However, the outlet temperature which is obtained by solving the energy equation for incompressible flow with the viscous dissipation term is higher than the inlet gas temperature, since the viscous dissipation term takes positive value. This inconsistency arose from wrong choice of the relation between the enthalpy and temperature that resulted in neglecting the substantial derivative of pressure term in the energy equation. In this paper the correct energy equation which includes the substantial derivative of pressure term is proposed. Some samples of physically consistent results which are obtained by solving the proposed energy equation are demonstrated.

The velocity field in hydromagnetic oscillatory flow past an impulsively started porous limiting surface with variable suction

1979 ◽  
Vol 63 (2) ◽  
pp. 419-438 ◽  
Author(s):  
G. A. Georgantopoulos ◽  
C. N. Douskos ◽  
G. L. Vassios ◽  
G. A. Katsiaris
Keyword(s):  
Velocity Field ◽  
Oscillatory Flow ◽  
Flow Past ◽  
Limiting Surface ◽  
Variable Suction

Hydromagnetic free convection effects on the oscillatory flow past an impulsively started porous limiting surface: I

1981 ◽  
Vol 76 (1) ◽  
pp. 133-148 ◽  
Author(s):  
N. G. Kafousias ◽  
A. A. Raptis ◽  
G. A. Georgantopoulos ◽  
C. L. Goudas
Keyword(s):  
Free Convection ◽  
Oscillatory Flow ◽  
Flow Past ◽  
Limiting Surface

Energy Equation of Gas Flow With Low Velocity in a Microchannel

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Yutaka Asako
Keyword(s):  
Fluid Flow ◽  
Viscous Dissipation ◽  
Gas Flow ◽  
Energy Equation ◽  
Constant Density ◽  
Outlet Temperature ◽  
Low Velocity ◽  
Average Temperature ◽  
Dissipation Term ◽  
Pressure Term

The energy equation for constant density fluid flow with the viscous dissipation term is often used for the governing equations of gas flow with low velocity in microchannels. If the gas is an ideal gas with low velocity, the average temperatures at the inlet and the outlet of an adiabatic channel are the same based on the first law of the thermodynamics. If the gas is a real gas with low velocity, the average temperature at the outlet is higher or lower than the average temperature at the inlet. However, the outlet temperature which is obtained by solving the energy equation for constant density fluid flow with the viscous dissipation term is higher than the inlet gas temperature, since the viscous dissipation term is always positive. This inconsistency arose from choice of the relationship between the enthalpy and temperature that resulted in neglecting the substantial derivative of pressure term in the energy equation. In this paper, the energy equation which includes the substantial derivative of pressure term is proposed to be used for the governing equation of gas flow with low velocity in microchannels. The proposed energy equation is verified by solving it numerically for flow in a circular microtube. Some physically consistent results are demonstrated.

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