Numerical Simulation of Forced Convection in a Porous Circular Tube with Constant Wall Heat Flux: An Extended Graetz Problem with Viscous Dissipation

2007 ◽  
Vol 30 (10) ◽  
pp. 1362-1368 ◽  
Author(s):  
S. Tada ◽  
K. Ichimiya
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Circular Tube ◽  
Wall Heat Flux ◽  
Graetz Problem ◽  
Constant Wall Heat Flux ◽  
Extended Graetz Problem

Effect of Wall Electrical Conductance on Magnetohydrodynamic Heat Transfer in a Channel

1963 ◽  
Vol 85 (4) ◽  
pp. 371-377 ◽  
Author(s):  
J. T. Yen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Electrical Conductance ◽  
Wall Heat Flux ◽  
Constant Wall Heat Flux

Effect of wall electrical conductance on laminar fully developed magnetohydrodynamic heat transfer in a channel with constant wall heat flux and exact magnetohydrodynamic boundary conditions are investigated. For channels with insulated walls, viscous dissipation is more important than joule heating for all Ec and M. For sufficiently large wall conductance, viscous dissipation is dominated by joule heating for all Ec, if M is large enough; both are in turn dominated by wall heat flux if Ec is large enough for all M. These and other conclusions are discussed in this paper.

Laminar Forced Convection in Transversely Corrugated Microtubes

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Forced Convection ◽  
Wall Temperature ◽  
Wall Heat Flux ◽  
Bulk Temperature ◽  
Straight Tube ◽  
Computational Domain ◽  
Constant Wall Temperature ◽  
Constant Wall Heat Flux

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for nonuniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

A Numerical Study of the Extended Graetz Problem in a Microchannel with Constant Wall Heat Flux: Shear Work Effects on Heat Transfer

2015 ◽  
Vol 31 (6) ◽  
pp. 733-743 ◽  
Author(s):  
K. Ramadan ◽  
I. Tlili
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Flow Region ◽  
Wall Heat Flux ◽  
Flux Boundary Condition ◽  
Developing Flow ◽  
Constant Wall Heat Flux ◽  
Work Effect

ABSTRACTHeat convection of a microchannel gas flow with constant wall heat flux boundary condition is investigated numerically, considering viscous dissipation and axial conduction. The shear work due to the slipping fluid at the wall is incorporated in the analysis. An analytical solution for fully developed conditions is also derived. The effect of the shear work on heat transfer is quantified through a comparative analysis in both the entrance- and the fully developed- regions. The analysis shows that the shear work effect on heat transfer is considerable, and neglecting this term leads to an overestimation of the Nusselt number in gas heating and an underestimation in gas cooling. The over/under estimation of the Nusselt number is dependent on both the Knudsen number and the Brinkman number. The results presented also demonstrate the significance of the shear work in the developing flow region. It is shown that in the developing flow region the Nusselt number is less sensitive to viscous dissipation when the shear work is neglected. It can be concluded from this study that the shear work effect is significant and neglecting it can lead to considerable errors in microchannel flow heat transfer.

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