Steady Laminar Heat Transfer in a Circular Tube with Conduction in Tube Wall

Mori, Susumu; Sakakibara, Mikio; Tanimoto, Akira

doi:10.1252/kakoronbunshu1953.38.144

Cited by 25 publications

(32 citation statements)

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“…A detailed review on early developments on axial wall conduction in conventional-size heat exchangers was presented by Peterson [49], according to which, one of the first studies in this field dates back to as early as 1926. Subsequently, a range of related issues have been addressed in the literature [2,3,8,11,12,46,50] for conventional-size heat exchangers.…”

Section: What Is Axial Back Conduction?mentioning

confidence: 99%

“…Mori et al [46] studied the effect of conduction in the tube wall on steady-state heat transfer to laminar flow in circular tube. For the case of a circular tube, Faghri and Sparrow [12] indicated that the wall conduction parameter measures the strength of axial conduction in its wall and defined it as…”

Section: Axial Back Conduction In Conventional-size Channelsmentioning

confidence: 99%

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Axial Back Conduction through Channel Walls During Internal Convective Microchannel Flows

Khandekar

Moharana

2015

Springer Tracts in Mechanical Engineering

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Recent developments during the last decade in the field of manufacturing and development of many high-power mini-/micro-devices led to increased interest in microfluidic devices involving heat transfer. Since the pioneering work by Tuckerman and Pease (IEEE Electron Device Lett 2:126-129, 1981) on the use of microchannels for high heat flux removal, certainly a lot of developments has been witnessed through ever-increasing analytical, experimental, and highly sophisticated numerical studies by many researchers across the globe. In spite of this progress, many fundamental understandings of flow and heat transfer phenomena in mini-/microchannel systems are still obscure. One such phenomenon is the flow of heat in the solid wall of microchannel systems by means of conduction normally in a direction opposite to that of internal convective mini-/microchannel flow of fluid, called "axial wall conduction" or "axial back conduction." Axial back conduction is not a new phenomenon, rather mostly neglected unintentionally because of its convincingly smaller influence on heat transfer in conventional-size channels. As the hydraulic diameter of a channel decreases, the coupling between the substrate and bulk fluid temperatures becomes significant because of the relative size of the fluid to the solid wall. Unlike in conventional-size channels, negligence of axial back conduction along the solid walls of micro heat exchangers frequently leads to erroneous conclusions and inconsistencies in the interpretation of transport data. Thus, it is important to explicitly identify the thermofluidic parameters of interest which lead to a distortion in the boundary conditions and thus the true estimation of species transfer coefficients. In this chapter, we focus our attention on the axial back conduction in the solid substrate/channel wall as against the axial back conduction in the liquid flow domain; thus, a detailed review of the state-of-the-art on axial back conduction in both conventional as well as mini-/microchannel systems is presented.

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Section: What Is Axial Back Conduction?mentioning

confidence: 99%

Section: Axial Back Conduction In Conventional-size Channelsmentioning

confidence: 99%

Axial Back Conduction through Channel Walls During Internal Convective Microchannel Flows

Khandekar

Moharana

2015

Springer Tracts in Mechanical Engineering

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“…However, limited studies have been done on the problems of convective boundaries, that is, problems involving boundary conditions of the third kind [4][5][6]. Among the earlier studies on conjugate heat transfer are Mori et al [7][8], who considered the effect of wall conduction between parallel plates and in circular pipes for uniform heat flux and constant surface temperature boundary conditions. The effect of axial wall conduction between parallel plates was analyzed for Couette flow by Davis and Gill [9].…”

Section: Introductionmentioning

confidence: 99%

Effects of the thick walled pipes with convective boundaries on laminar flow heat transfer

2014

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Highlights Analytical approach is employed to solve the energy equations with convective boundary condition of the third kind.  The wall thickness, Bi and k pf significantly influence the interfacial heat flux, the wall and fluid bulk temperatures.  The fluid bulk and wall temperatures decrease with decreasing pipe wall thickness and increasing Bi number and k pf .  Increase in the convective heat loss corresponds to a decrease in wall thickness but increase in both Bi and k pf .  The thermal entrance length increases with pipe wall thickness while it decreases with increase in both Bi and k pf . ABSTRACTConjugate heat transfer in laminar tube flow with convective boundary conditions is considered analytically. The steady state problem involving two-dimensional wall and axial fluid conduction is solved using separation of variables for a thick walled cylindrical pipe. The effects of the wall thickness, external Biot number and wall-tofluid thermal conductivity ratio are investigated on the heat flux, fluid bulk and wall temperatures. Results are presented for the cases when the wall thickness is between 0.1 and 2, Biot number ranging between 0.1 and 10, and the ratio of wall-to-fluid thermal conductivity between 3 and 100. These parameters are found to significantly affect the heat transfer characteristics at the thermal entrance region, for instance, increase in wall thickness results in reduced heat flux while increase in Biot number and the ratio of the wall-to-fluid thermal conductivity result in increased heat flux. Decrease in wall thickness, increase in both Biot number and the ratio of the wall-to-fluid thermal conductivity correspond to decreased fluid bulk and wall temperature profiles.Keywords: thick-walled pipe; Biot number; Peclet number; wall-to-fluid thermal conductivity ratio; convective heat transfer characteristic eigen values or roots of pipe eq.

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“…Mori et al (1974) used the solution of Graetz problem applying the superposition technique to obtain the temperature "eld along the pipe length. Conjugate heat transfer analysis in the entrance region of a circular pipe was carried out by Yen and Lee (1991).…”

Section: Introductionmentioning

confidence: 99%

Entropy analysis of conjugate heating in a pipe flow

Hyder

Yilbaş

2002

Int. J. Energy Res.

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SUMMARYIn the present study, an analytical approach governing the temperature rise in the solid pipe and #uid is presented. The entropy analysis in the #uid system due to heat transfer is introduced to obtain the integrated entropy generation in the system. Coolanol, water and mercury are selected as #uids while copper and steel are considered as pipe materials. In order to simplify the analysis, the heat transfer coe$cient at solid}liquid interface is kept constant during the calculations. It is found that the #uid temperature rise in the early heating period and the integrated entropy generation in the #uid system is lower in the case of a copper pipe.

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Steady Laminar Heat Transfer in a Circular Tube with Conduction in Tube Wall

Cited by 25 publications

References 0 publications

Axial Back Conduction through Channel Walls During Internal Convective Microchannel Flows

Axial Back Conduction through Channel Walls During Internal Convective Microchannel Flows

Effects of the thick walled pipes with convective boundaries on laminar flow heat transfer

Entropy analysis of conjugate heating in a pipe flow

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