Fully Developed Laminar Forced Convection in a Circular Duct for Herschel–Bulkley Fluids With Viscous Dissipation and Axial Heat Conduction

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Rabha Khatyr ◽  
Jaafar Khalid-Naciri ◽  
Ali Il Idrissi
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Circular Duct ◽  
Nusselt Numbers ◽  
Asymptotic Values ◽  
Axial Heat ◽  
Laminar Forced Convection ◽  
Axial Heat Conduction

The asymptotic behavior of laminar forced convection in a circular duct for a Herschel–Bulkley fluid of constant properties is analyzed. The viscous dissipation and the axial heat conduction effects in the fluid are both considered. The asymptotic bulk and mixing temperature field, and the asymptotic values of the bulk and mixing Nusselt numbers are determined for every boundary condition, enabling a fully developed region. In particular, it is proved that whenever the wall heat flux tends to zero, the asymptotic Nusselt number is zero. The obtained results are compared to other existing solutions in the literature for Newtonian and non-Newtonian cases.

scholarly journals Viscous dissipation effect on laminar forced convection in a circular duct with adiabatic walls - preliminary numerical investigation

2018 ◽  
Vol 240 ◽  
pp. 03016
Author(s):  
Tomasz Janusz Teleszewski
Keyword(s):  
Heat Flux ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Heat Flux Density ◽  
Energy Equation ◽  
Brinkman Number ◽  
Circular Duct ◽  
Nusselt Numbers ◽  
Axial Heat ◽  
Laminar Forced Convection

In this work, an analysis of laminar forced convection in a pipe with heated and adiabatic walls for a Newtonian fluid with constant properties is performed by taking the viscous dissipation into account when the axial heat conduction in the fluid is neglected. The Nusselt number versus the Brinkmann, which is based on the total wall heat flux density, have been investigated. In order to determine the temperature field, an analytical solution describing the velocity field in the pipe was used, while the energy equation was determined by the boundary element method (BEM). The results of the calculations of Nusselt numbers as a function of the Brinkman number for different thermal insulation heights to the diameter of the circular duct were presented in the form of diagrams.

Nusselt Numbers in Rectangular Ducts With Laminar Viscous Dissipation

1999 ◽  
Vol 121 (4) ◽  
pp. 1083-1087 ◽  
Author(s):  
G. L. Morini ◽  
M. Spiga
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Viscous Dissipation ◽  
Integral Transforms ◽  
Navier Stokes ◽  
Brinkman Number ◽  
Balance Equations ◽  
Nusselt Numbers ◽  
Finite Integral ◽  
Axial Heat

In this paper, the steady temperature distribution and the Nusselt numbers are analytically determined for a Newtonian incompressible fluid in a rectangular duct, in fully developed laminar flow with viscous dissipation, for any combination of heated and adiabatic sides of the duct, in H1 boundary condition, and neglecting the axial heat conduction in the fluid. The Navier-Stokes and the energy balance equations are solved using the technique of the finite integral transforms. For a duct with four uniformly heated sides (4 version), the temperature distribution and the Nusselt numbers are obtained as a function of the aspect ratio and of the Brinkman number and presented in graphs and tables. Finally it is proved that the temperature field in a fully developed T boundary condition can be obtained as a particular case of the H1 problem and that the corresponding Nusselt numbers do not depend on the Brinkman number.

Axial Heat Conduction Effects in Unsteady Forced Convection Along a Cylinder

1987 ◽  
Vol 109 (3) ◽  
pp. 787-791
Author(s):  
C. D. Surma Devi ◽  
M. Nagaraj ◽  
G. Nath
Keyword(s):  
Heat Conduction ◽  
Forced Convection ◽  
Axial Heat ◽  
Axial Heat Conduction

Performance of Cross Flow Microchannel Heat Exchangers Subjected to Viscous Dissipation

2010 ◽  
Author(s):  
B. Mathew ◽  
T. J. John ◽  
W. Dai ◽  
H. Hegab
Keyword(s):  
Heat Conduction ◽  
Temperature Profile ◽  
Viscous Dissipation ◽  
Heat Exchangers ◽  
Heat Dissipation ◽  
Cross Flow ◽  
Combined Effect ◽  
Cold Fluid ◽  
Axial Heat ◽  
Axial Heat Conduction

This paper analyzes the effect of viscous dissipation on the thermal performance of balanced flow cross flow microchannel heat exchangers. The cross flow microchannel heat exchanger analyzed in this paper is one that is subjected to axial heat conduction. Governing equations are developed for each of the fluids and the wall separating the fluids. The equations are solved simultaneously using the numerical technique of finite difference method to obtain the temperature profile. The effectiveness of each fluid is determined using the temperature profile thus obtained. The effectiveness and the temperature of the fluids are found to depend on NTU, axial heat conduction parameters and the viscous dissipation parameter. In the presence of axial heat conduction the effectiveness of the fluid decreases for a specific NTU. In addition, the effectiveness of the fluids decreases with increase in axial heat conduction parameters at a particular NTU. The effectiveness of the hot fluid in the presence of viscous heat dissipation alone decreased at a particular NTU. On the other hand the effectiveness of the cold fluid for the same amount of viscous heating improved at a specific NTU. The combined effect of axial heat conduction and viscous dissipation on the hot fluid is to decrease its effectiveness. With regard to the cold fluid effectiveness it can either increase or decrease due to the combined effect of axial heat conduction parameter and viscous dissipation.

Viscous Dissipation Effects on Combined Free and Forced Convection Through Vertical Circular Tubes

1970 ◽  
Vol 37 (4) ◽  
pp. 931-935 ◽  
Author(s):  
M. Iqbal ◽  
B. D. Aggarwala ◽  
M. S. Rokerya
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Transfer Rate ◽  
Circular Duct ◽  
Circular Tubes ◽  
Nusselt Numbers ◽  
Fluid Properties ◽  
Flow Phenomena ◽  
Free And Forced Convection

The effect of viscous dissipation on the flow phenomena and heat transfer rate in a vertical circular duct is analyzed for combined free and forced convection. All fluid properties are considered constant, except variation of density in the buoyancy term. It is noted that effect of viscous dissipation is to reduce the temperature differences in the system which in turn counteract the buoyancy effects. Therefore the viscous dissipation reduces the flow velocity near the wall and increases it near the tube center. Viscous dissipation effects reduce the Nusselt numbers. The reduction in Nusselt numbers is about six percent at the high values of the buoyancy rate (Rayleigh number = 1000) and the dissipation effect Eckert number/Reynolds number = 0.0005 was used in the present study.

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