Convective heat transfer to laminar flow over a plate of finite thickness

Payvar, Parviz

doi:10.1016/0017-9310(77)90165-x

Cited by 50 publications

(20 citation statements)

References 2 publications

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“…The temperature distribution in a horizontal flat plate of finite thickness was analyzed by Luikov [1] and Payvar [2]. In this conjugate problem the lower surface was maintained at a uniform temperature, while the upper surface was transferring heat to a laminar boundary layer by convection.…”

Section: Introductionmentioning

confidence: 99%

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Two Dimensional Temperature Distributions in Plate Heat Exchangers: An Analytical Approach

2015

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Analytical solutions are developed to work out the two-dimensional (2D) temperature changes of flow in the passages of a plate heat exchanger in parallel flow and counter flow arrangements. Two different flow regimes, namely, the plug flow and the turbulent flow are considered. The mathematical formulation of problems coupled at boundary conditions are presented, the solution procedure is then obtained as a special case of the two region Sturm-Liouville problem. The results obtained for two different flow regimes are then compared with experimental results and with each other. The agreement between the analytical and experimental results is an indication of the accuracy of solution method.

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Section: Introductionmentioning

confidence: 99%

“…The first solution was performed considering low Prandtl number assumption, while the second solution was conducted using polynomial forms for the velocity and temperature profiles. In the case of large Prandtl numbers the Lighthill approximation [3] was used by Payvar [2] and an integral equation was obtained and then solved numerically.…”

Section: Introductionmentioning

confidence: 99%

Two Dimensional Temperature Distributions in Plate Heat Exchangers: An Analytical Approach

2015

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“…For a flat plate boundary layer flow there are several works involving these coupled forms of heat transfer [1][2][3][4][5][6]. Luikov [3] and Payvar [4] analysed the problem where the lower surface of the plate is maintained at a constant and uniform temperature. At the other surface of the plate there is a boundary layer flow.…”

Section: Introductionmentioning

confidence: 99%

“…The Brun number is defined as the ratio of the thermal resistance of the plate to that of the fluid. Payvar [4] used the Lighthill approximation [7] to obtain an integral equation which was solved numerically. For large and small Brun numbers, he obtained asymptotic solutions for the problem.…”

Section: Introductionmentioning

confidence: 99%

External heating of a flat plate in a convective flow

Treviño

Liñán

1984

International Journal of Heat and Mass Transfer

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Abstract-The steady-stale and transient processes of the external heating of a flat plate under a convective flow is studied in this paper, with inclusion of the axial heat conduction through the plate. The balance equations reduce to a single integro-differential equation with only one parameter, a, denoting the ratio of the ability of the plate to carry heat in the streamwise direction to the ability of the gas to carry heat out of the plate. The two limits ofagood conducting plate(« -+ oo)andabad conducting plate(• 0) are analysed through the appUcationof a regular perturbation procedure for the first case and a singular perturbation technique for the latter. The existence oftwo boundary layers at both edges of the plate is shown and theirstructure are analysed.The evolution of the temperature of the plate is then obtained for a constant external energy flux input.

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“…A very important problem in the field was formulated by Luikov, who presented the solution when one of the plate surfaces has a fixed constant temperature and the other one was cooled by forced laminar flow (Luikov, 1974). Subsequently, flat plate problems have been treated in many papers (Payvar, 1977;Karvinen, 1978a;Pozzi and Lupo, 1989;Pop and Ingham, 1993;Treviño et al, 1997;Treviño and Liñán, 1984;Mosaad, 1999). Two-dimensional analyses, in which the effect of longitudinal and transversal conduction are included are also found in the literature (Vynnycki et al, 1998;Chida, 2000).…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for a Class of Flat Plate Conjugate Convective Heat Transfer Problems

Lehtinen¹,

Karvinen²

2012

Frontiers in Heat and Mass Transfer

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Analytical solutions for three different flat plate conjugate heat transfer cases are presented. The cases are as follows:transient heat transfer of a thin plate with uniform heat generation; the Luikov problem in which one plate surface is kept in a constant temperature and the other one is cooled by forced convection ; and a modified Luikov problem with heat generation on one surface and convection on both surfaces of the plate. All the cases are solved for both laminar and turbulent flows with P r 1. The solutions in the paper are based on the superposition principle and analytical expressions are used to couple the temperature and the heat flux distributions on the surface of the plate. The results of the Luikov problem and transient plate are also compared to other solutions presented earlier in the literature.

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Convective heat transfer to laminar flow over a plate of finite thickness

Cited by 50 publications

References 2 publications

Two Dimensional Temperature Distributions in Plate Heat Exchangers: An Analytical Approach

Two Dimensional Temperature Distributions in Plate Heat Exchangers: An Analytical Approach

External heating of a flat plate in a convective flow

Analytical Solution for a Class of Flat Plate Conjugate Convective Heat Transfer Problems

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