Heat transfer in laminar flow through circular tubes accounting for two-dimensional wall conduction

Campo, Antônio; Schuler, Carlos

doi:10.1016/0017-9310(88)90157-3

Cited by 37 publications

(8 citation statements)

References 6 publications

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“…A fundamental characteristic of a heat exchanger is the phenomenon of conjugate heat transfer which involves an interaction between the conduction of the solid wall material and the convection of the fluid flowing over that wall. The problems of conjugate heat transfer are very important and have already been examined by a number of researchers [4][5][6]. Many other important engineering devices also involve conjugate heat transfer problems such as flows over fins.…”

Section: Introductionmentioning

confidence: 99%

Inverse estimation for unknown fouling-layer profiles with arbitrary geometries on the inner wall of a forced-convection duct

Chen

2010

International Journal of Thermal Sciences

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Section: Introductionmentioning

confidence: 99%

Inverse estimation for unknown fouling-layer profiles with arbitrary geometries on the inner wall of a forced-convection duct

Chen

2010

International Journal of Thermal Sciences

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“…The first M. E. ARICI 1035 part of these studies deals with forced convection heat transfer including the wall axial conduction effects for various boundary conditions at the outer surface of the wall. A fully numerical study by Campo and Schuler [2] provides a finite-difference procedure and examines the influence of a finite heated length on the heat transfer characteristics of laminar flow through a thick-walled circular pipe. A one-dimensional domain approximation of the conduction equation for the wall is also included in their work.…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer Analysis for a Concentric Tube Heat Exchanger Including the Wall Axial Conduction

Arici

2010

Heat Transfer Engineering

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The effect of wall axial conduction on the heat transfer in a concentric tube heat exchanger is examined for the inner flow laminar flow regime. The procedure used for the current analysis combines the analytical solution for the inner fluid with a numerical approximation for the wall conduction and has the capability of handling the temperature variation for the outer fluid. Both parallel and counterflow cases are evaluated for the analysis, and results are presented in terms of the axial variations of fluids and wall temperatures. Effects of the heat capacity rate ratio of the fluids on the temperature variations and on the mean heat flux are also pointed out. The effect of the exchanger length is included for the analysis. It is concluded that the total heat transfer between the fluids is greatly influenced by the wall axial conduction for the counterflow arrangement and is not ignorable when the heat capacity rate ratio of fluids are smaller than unity.

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“…The conjugated problem has been addressed for the first time for heat transfer applications by Mori et al [8] and latter by Faghri and Sparrow [9] in the situation of high conduction in the solid meaning that only the steady state regime has been studied. A special attention to axial conduction has been investigated in [10,11,12] but once again in steady state regime both in the liquid and in the solid. More recently, Zhang et al [13] achieved a numerical work of the conjugated problem by solving the Navier-Stokes equations and the two energy equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of generalized Graetz problem in circular tube with a mass transfer coupling between the solid and the liquid

Pigeonneau

Jaffrennou

Letailleur

et al. 2016

International Journal of Heat and Mass Transfer

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International audienceThe unsteady diffusion equation in a tube and the advection/diffusion equation in laminar flow in a liquid of a solute are theoretically established. The most important parameters are the migration strength α and the so-called Graetz number Gr. The former dimen-sionless number is the product of the partition coefficient of the solute at the solid/liquid interface, the ratio of the tube thickness to the interior radius and the ratio of diffusion coefficients of the solute in the liquid and in the solid. The Graetz number Gr is the ratio of the diffusion time scale in the liquid based on the interior radius of the pipe to the advection time over the tube length. The problem is applied to the plasticizer migration from a polyvinyl chloride material to a liquid with the safety food applications in mind. The migration of the plasticizer is solved numerically for various tube sizes, flow conditions and partition coefficients of the plasticizer in the liquid. For comparison, the numerical results obtained in static condition are also provided. The average plasticizer concentration in the liquid behaves following two main regimes as a function of the migration strength. When α is much smaller than one, the average plasticizer concentration in the liquid is an algebraic function of the axial coordinate, z, at the power two third and increases linearly with time. Conversely, when α is much larger than one, the average plasticizer concentration is linear as a function of axial distance and increases as a function of the square root of time. Moreover, the concentration is much smaller of few orders of magnitude in dynamic condition than in static working showing that in the context of food contamination the dynamic approach is more appropriate and relevant for demonstration of compliance with the safety authorities requirements

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Heat transfer in laminar flow through circular tubes accounting for two-dimensional wall conduction

Cited by 37 publications

References 6 publications

Inverse estimation for unknown fouling-layer profiles with arbitrary geometries on the inner wall of a forced-convection duct

Inverse estimation for unknown fouling-layer profiles with arbitrary geometries on the inner wall of a forced-convection duct

Heat Transfer Analysis for a Concentric Tube Heat Exchanger Including the Wall Axial Conduction

Numerical investigation of generalized Graetz problem in circular tube with a mass transfer coupling between the solid and the liquid

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