External heating of a flat plate in a convective flow

Abstract

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(<t ->• 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.

Conjugate Forced Convection Heat Transfer From a Heated Flat Plate of Finite Thickness and Temperature- Dependent Thermal Conductivity

“…The preceding criterion, as in Eq. (5), for supposing uniform temperature in transversal coordinate is already stated in reference [5]; however, it has been left unproved. Applying the energy balance in a control volume of width, dx, and height, b (with uniform temperature along the transversal coordinate), the energy equation is obtained as…”

“…In order to verify the results obtained by DTM, the results are compared with those attained with the numerical finite-volume analysis. Ultimately, the results are compared with the approximate correlation existing in reference [5] using the perturbation method. To the best of our knowledge among the recent researchers the problem stated in reference [5] is the closest one to the conditions of our problem defined in the present study.…”

“…Ultimately, the results are compared with the approximate correlation existing in reference [5] using the perturbation method. To the best of our knowledge among the recent researchers the problem stated in reference [5] is the closest one to the conditions of our problem defined in the present study. The effects of several physical parameters on the plate temperature, Nusselt number of the flow and the heat flux distribution at the upper plate surface, which have not been addressed in reference [5], are aimed in the present study.…”

“…The solution for conjugate heat transfer in a circular tube was obtained by Nagasue [4] on the basis of the superposition principle and Green's function. The process of the external heating of a flat plate under a convective flow with inclusion of the axial heat conduction through the plate was studied by Trevino and Liñan [5]. Olek [6] used the eigenfunction expansion method to derive an exact solution for heat transfer in laminar flow of a non-Newtonian fluid inside a circular or parallel-plate duct, including axial heat conduction.…”

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

“…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).…”