An Analytical Solution of the Effect of Peripheral Wall Conduction on Laminar Forced Convection in Rectangular Channels

1965 ◽  
Vol 87 (1) ◽  
pp. 59-66 ◽  
Author(s):  
R. Siegel ◽  
J. M. Savino
Keyword(s):  
Heat Conduction ◽  
Forced Convection ◽  
Wall Temperature ◽  
Energy Equation ◽  
Side Wall ◽  
Transverse Wall ◽  
Short Side ◽  
Rectangular Channels ◽  
Side Walls ◽  
Laminar Forced Convection

This study deals with fully developed laminar forced convection in rectangular channels that are heated on the broad sides. The analysis determines the effect of peripheral heat conduction within the heated walls on the wall temperature distributions. The unheated short side walls are assumed nonconducting. The heat conduction within the broad walls was formulated in terms of an integral equation and coupled with the convective energy equation within the fluid. Analytical solutions were obtained where the heating extends over the entire width of the broad side, is removed from the corner region, or extends beyond the corner into the side wall. Transverse wall conduction produced substantial decreases in the peak wall temperature and in the temperature gradients along the long side.

Entropy Generation in Thermally Developing Laminar Forced Convection Through a Slit Microchannel

2010 ◽  
Author(s):  
Arman Sadeghi ◽  
Mostafa Baghani ◽  
Mohammad Hassan Saidi
Keyword(s):  
Forced Convection ◽  
Entropy Generation ◽  
Energy Equation ◽  
Integral Transform ◽  
Axial Coordinate ◽  
Entropy Generation Number ◽  
Group Parameter ◽  
Laminar Forced Convection ◽  
Thermal Entrance ◽  
Increasing Function

The issue of entropy generation in laminar forced convection of a Newtonian fluid through a slit microchannel is analytically investigated by taking the viscous dissipation effect, the slip velocity and the temperature jump at the wall into account. Flow is considered to be hydrodynamically fully developed but thermally developing. The energy equation is solved by means of integral transform. The results demonstrate that to increase Knudsen number is to decrease entropy generation, while the effect of increasing values of Brinkman number and the group parameter is to increase entropy generation. Also it is disclosed that in the thermal entrance region the average entropy generation number over the cross section of channel is an increasing function of axial coordinate.

Effects of Brownian Diffusion and Thermophoresis on the Laminar Forced Convection of a Nanofluid in a Channel

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Eugenia Rossi di Schio ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Forced Convection ◽  
Wall Temperature ◽  
Homogeneous Model ◽  
Entrance Region ◽  
Brownian Diffusion ◽  
Boundary Temperature ◽  
Coupled Equations ◽  
Thermal Entrance Region ◽  
Laminar Forced Convection ◽  
Thermal Entrance

A steady laminar forced convection in a parallel–plane channel using nanofluids is studied. The flow is assumed to be fully developed, and described through the Hagen–Poiseuille profile. A boundary temperature varying with the longitudinal coordinate in the thermal entrance region is prescribed. Two sample cases are investigated in detail: a linearly changing wall temperature, and a sinusoidally changing wall temperature. A study of the thermal behavior of the nanofluid is performed by solving numerically the fully–elliptic coupled equations. The numerical solution is obtained by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). With reference to both the wall temperature distributions prescribed along the thermal entrance region, the governing equations have been solved separately both for the fully developed region and for the thermal entrance region. The analysis shows that if a linearly varying boundary temperature is assumed, for physically interesting values of the Péclet number the concentration field depends very weakly on the temperature distribution. On the other hand, in case of a longitudinally periodic boundary temperature, nonhomogeneities in the nanoparticle concentration distribution arise, which are wrongly neglected whenever the homogeneous model is employed.

Sign in / Sign up

Export Citation Format

Share Document