A Historical Misperception on Calculating the Average Convection Coefficient in Tubes With Constant Wall Heat Flux

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Ted D. Bennett
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Exact Solutions ◽  
Wall Heat Flux ◽  
First Principle ◽  
Convection Coefficient ◽  
Parallel Plates ◽  
Historical Approach ◽  
First Principle Calculations ◽  
Constant Wall Heat Flux

The historical approach to averaging the convection coefficient in tubes of constant wall heat flux leads to quantitative errors in short tubes as high as 12.5% for convection into fully developed flows and 33.3% for convection into hydrodynamically developing flows. This mistake can be found in teaching texts and monographs on heat transfer, as well as in major handbooks. Using the correctly defined relationship between local and average convection coefficients, eight new correlations are presented for fully developed and developing flows in round tubes and between parallel plates for the constant wall heat flux condition. These new correlations are within 2% of exact solutions for fully developed flows and within 6% of first principle calculations for hydrodynamically developing flows.

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.

scholarly journals HEAT TRANSFER OF LAMINAR FLOW IN VERTICAL TUBES WITH CONSTANT WALL HEAT FLUX

1968 ◽  
Vol 1 (2) ◽  
pp. 120-124 ◽  
Author(s):  
NOBUO MITSUISHI ◽  
OSAMU MIYATAKE ◽  
MITSURU YANAGIDA
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Laminar Flow ◽  
Wall Heat Flux ◽  
Constant Wall Heat Flux ◽  
Vertical Tubes

scholarly journals Axisymmetric stagnation-point flow and heat transfer of nanofluid impinging on a cylinder with constant wall heat flux

2019 ◽  
Vol 23 (5 Part B) ◽  
pp. 3153-3164 ◽  
Author(s):  
Hamid Mohammadiun ◽  
Vahid Amerian ◽  
Mohammad Mohammadiun ◽  
Iman Khazaee ◽  
Mohsen Darabi ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Field ◽  
Stagnation Point ◽  
Base Fluid ◽  
Fluid Velocity ◽  
Wall Heat Flux ◽  
Flow And Heat Transfer ◽  
Constant Wall Heat Flux ◽  
Fluid Velocity Field

The steady-state, viscous flow and heat transfer of nanofluid in the vicinity of an axisymmetric stagnation point of a stationary cylinder with constant wall heat flux is investigated. The impinging free-stream is steady and with a constant strain rate, k ?. Exact solution of the Navier-Stokes equations and energy equation are derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced in this research. The general self-similar solution is obtained when the wall heat flux of the cylinder is constant. All the previous solutions are presented for Reynolds number Re = k ?a2/2n f ranging from 0.1 to 1000, selected values of heat flux and selected values of particle fractions where a is cylinder radius and n f is kinematic viscosity of the base fluid. For all Reynolds numbers, as the particle fraction increases, the depth of diffusion of the fluid velocity field in radial direction, the depth of the diffusion of the fluid velocity field in z-direction, shear-stresses and pressure function decreases. However, the depth of diffusion of the thermal boundary-layer increases. It is clear by adding nanoparticles to the base fluid there is a significant enhancement in Nusselt number and heat transfer.

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.

Friction Losses and Heat Transfer in Laminar Microchannel Single-Phase Liquid Flow

2008 ◽  
Author(s):  
Vaˆnia Silve´rio ◽  
Anto´nio L. N. Moreira
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Liquid Flow ◽  
Single Phase ◽  
Wall Heat Flux ◽  
Oxide Thin Film ◽  
Flow Conditions ◽  
Constant Wall Heat Flux ◽  
Phase Liquid ◽  
Single Phase Liquid Flow

Many studies addressed the validity of macroscale theories to describe momentum and heat transfer in single phase in microtubes, but the results are often inconsistent. It is suggested that the fluid flow and heat transfer in microchannels without phase change is substantially different from that in larger channels. However, these discrepancies may be attributed to experimental uncertainties mainly due to the use of conventional measurement apparatus that are too big to implement in the tested system. Other researchers explain the microfluidic behavior with the ratio of surface forces to body forces which evolve inversely to the hydraulic diameter. The present work considers the use of a dedicated experimental facility built to allow the use of optical diagnostic and flow visualization techniques in heated microtubes and addresses the potential microscale effects which may arise for single phase flow conditions. The experiments encompass measurements of the pressure drop and the longitudinal temperature distribution in the fully developed single phase liquid flow established in circular and square cross section of channels made of borosilicate glass with hydraulic diameters from 50μm up to 500μm. The flow conditions consider a range of Reynolds number from 10 up to around 2500 and the use of diverse fluids to account for the effects of liquid properties. Namely, three distinct fluids were used: distilled water, methoxy-nonafluorobutane and methanol. For heat transfer studies, the channels are heated with constant wall heat flux supplied by Joule effect by means of external wall rf-PERTE deposition of Indium Oxide thin film. The thin transparent film showed good chemical stability in the range of temperatures up to 70°C, therefore indicating that the thermal boundary condition approximates a constant wall heat flux condition. The mass flux is varied from 60 to 3300kg.m−2·s−1 and the heat flux was set between 4 and 6kW.m−2. Experimental uncertainties are estimated to be below 14% for the friction factor and below 24% for Nusselt number; the former is dominated by inaccuracies in the diameter, while the second is dominated by temperature measurements.

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