SESSION 12
FORCED CONVECTION 2
TRANSIENT CONJUGATED HEAT TRANSFER IN FULLY DEVELOPED LAMINAR FLOW IN THICKNESS DUCT: NUMERICAL APPROACH
S. ABBOUDI & A. OMARA
Laboratoire LERMPS, EA 1701, Institut Polytechnique de Sévenans,
B.P. 449  90010 Belfort Cedex, France.
We propose in this work a numerical approach by finite difference method of transient conjugated forced convection heat transfer with fully developed laminar flow in cylindrical thickness wall. The unsteady regime is provoked by a perturbation of the wall flux or the fluid inlet temperature. The originality of this work can be explain by the plug in account of by the axial conductions in fluid and wall. A study of the energy behavior of the system is presented in detail as well as a comparison between the cases with and without axial conduction in the wall and in the fluid. We present finally, for the general case, the transient distribution of wall and fluid mean temperatures, the Nusselt number, the interfacial heat flux and the effects of the physical and geometrical properties on the heat transfer.
INSTABILITIES IN THE THERMAL ENTRANCE REGION OF A COUNTERCURRENT HORIZONTAL HEAT EXCHANGER  EXPERIMENTAL APPROACH 
L. ESTEL, F. BAGUI, M.A. ABDELGHANIIDRISSI, and N. MOUHAB
P.S.O.P.I.C.
INSA de Rouen
BP 08  Place Emile BLONDEL
76131 Mont Saint Aignan Cedex
FRANCE
Experimental studies are presented to put in obviousness the effect of combined natural and forced convection in horizontal pipe cooled by uniform flux. The experimental is undertaking in a coaxial countercurrent heat exchanger. Temperature profiles show the influence of buoyancy forces and radial conduction. In steady state we deal with temperature fluctuations along the internal tube of the heat exchanger du to the combined of mixed convection and radial conduction. In order to characterize the amplitude and frequency of temperature fluctuations, frequency analysis was presented.
EXPERIMENTAL STUDY OF AN UNSTEADY CONVECTIVE HEAT TRANSFER OF GASES AND LIQUIDS FLOWING IN THE CHANNELS
G.A. Dreitser
Department of AviationSpace Thermal Technics
Moscow Aviation Institute, Moscow, 125871, Russia
The paper presents an analysis and generalization of experimental data on the unsteady heat transfer of gases and liquids flowing in the tubes under the conditions of heating, cooling and variation in the flow rate, heat release in the tube walls, and entrance flow temperature. The experimental investigations were provided in round tubes in wide range of regime parameters. Comparison of the analytical and experimental data has made it possible to find a tube radius distribution of turbulent flow parameters, and to specify the effect of an unsteady impact on turbulent flow characteristics with the experimental ones. As a result, the generalizations have been derived to calculate unsteady heat transfer coefficient. Engineering methods are proposed to predict real unsteady thermal processes.
UNSTEADY CONVECTIVE HEAT TRANSFER TO A LOW FREQUENCY OSCILLATING FLOW IN A CHANNEL
Ýrfan Karagöz
University of Uludađ, Dept. of Mechanical Engineering
16059 GörükleBursa, TURKEY
Laminar fluid flow and convective heat transfer in a channel subjected to sinusoidally varying inlet velocity have been analysed numerically. Except a heated wall section placed in the middle of the bottom wall, all the channel walls were assumed adiabatic. The governing equations for the laminar, incompressible and two dimensional flow were solved iteratively by a control volume based finite difference method. The parameters involved are the Wormersley number varied between 3 and 24, averaged heat transfer coefficient, Reynolds and Nusselt numbers. Computed velocity and temperature profiles are compared with experimental values. The results show that the averaged heat transfer coefficient and the averaged Nusselt number increase with the increase of the Wormersley and the averaged Reynolds numbers.
AN APPROXIMATE APPROACH FOR TRANSIENT BEHAVIOUR OF FINNEDTUBE CROSSFLOW HEAT EXCHANGERS
Ö. ERCAN ATAER, A. YALÇIN GÖĐÜŢ^{*}
Mechanical Engineering Department, Gazi University, Maltepe, 06570 Ankara, Turkey
Aeronautical Engineering Department, METU, 06531 Ankara, Turkey
A closed approximate, analytical solution is obtained for transient behaviour of finnedtube crossflow heat exchangers for the step change in the inlet temperature of the hot fluid. In the analysis the heat capacity of the wall is added to the capacity of the hot fluid and capacity of the fins, cold and hot fluids are considered. The temperature variation of both fluids between inlet and exit is assumed to be linear. It is also assumed that flow rates and inlet conditions remain fixed for both fluids, except for the step change imposed on the inlet temperature of the hot fluid. Energy equations for the hot and cold fluids and fins are derived and solved analytically. The dynamic behavior of the heat exchanger is summarized by the gain, time constant and delay time. To show the validity of this theoretical approach an experimental study is performed and results are compared with the results obtained from the experimental study.
MIXED COMPUTATION IN TRANSIENT HEAT CONVECTION
M. D. Mikhailov^{*}
Mechanical Engineering Department
Laboratério de Transmissão et Tecnologia do Calor  LTTC
EE / COPPE / UFRJ, Universidade Federal do Rio de Janeiro
Cidade Universitária, Rio de Janeiro, RJ, 21945970, BRASIL
This presentation demonstrates that mixed computation can be a quite useful tool in studying transient heat convection. One version of the integral transform method, when the inversion formula is expanded at the very beginning, is employed. As an illustrative example, two dimensional transient convection of a Boussinesq fluid in a square cavity, with side walls at different temperatures and insulated top and bottom walls, is solved by using only 5 degrees of freedom. The transient temperature field is animated. The results can be reproduced for any other values of the parameters since this paper is a Mathematica notebook.
*Technical University, Sofia, Bulgaria
TRANSIENT RESPONSE OF A STEADY VERTICAL FLOW WHICH IS SUBJECTED TO A CHANGE IN SURFACE HEAT FLUX IN POROUS MEDIA
S. D. Harris^{*}, D. B. Ingham^{*} and I. Pop^{**}
^{*}Department of Applied Mathematical Studies,
University of Leeds, Leeds, LS2 9JT, England;
^{**}Faculty of Mathematics, University of Cluj,
R3400 Cluj, CP 253, Romania
This paper analyses the transient free convection from a vertical flat plate which is embedded in a fluidsaturated porous medium arising from a sudden change of the level of the constant uniform flux dissipation rate. From an analytical investigation of the governing boundarylayer equations, both a series solution which is valid at small values of the nondimensional time and a solution which is valid at large times, when the transport of energy is steady, are derived. A numerical solution of the full boundarylayer equations is then obtained for the whole transient regime. Results are presented to illustrate the occurrence of transients from both small and large increases and decreases in the levels of the existing energy inputs.
TRANSITION ELEMENTS BETWEEN FINE AND COARSE MESHES IN FINITE ELEMENT TREATMENT OF CONVECTIVE HEAT TRANSFER^{*}
J. M. GERDAY, M. HOGGE, P. STIENON
LTASMilleux Continus & Tbermomécanique
Université de Liège
Rue E. Solvay, 21, B4000 LIEGE, BELGIUM
Té1. +324366.91.26 Fax +324253.25.81
Email :hogge@asterix.ltas.ulg.ac.be
A transition element for incompressible NavierStokes flows easing the merge of computational domains with different finite element (FE) mesh refinements is deviced : only normal balance of heat flow and fluid momentum (through the viscous shear forces) is enforced, with variable linking parameters that can be fixed by the user and differ from one problem to the other.
Particular cases are the impervious boundary between non mixing flows or the completely permeable boundary where temperature and velocities continuity is assumed in the weak sense.
Independent meshes with their own refinements can then be merged easily with very little topological interaction, while retaining (nearly) complete physical interaction. The effectiveness of the transition element has been validated on academic computational examples dealing with 2D situations and applied to thermal control problems encountered in electronic devices where local power dissipations, thin channels and their boundary flows require local refinements which would otherwise diffuse through the whole computational domain and yield untractable models.
^{*}This Research has been made possible through a grant under the MULTIMATERIAL SETUP PROGRAMME of the Walloon Region of Belgium 9195 (Convections n^{o} 1671 and 2339).
ESTIMATION OF THE TIMEWISE AND SPACEWISE VARIATION OF THE WALL HEAT FLUX TO A NONNEWTONIAN FLUID IN A PARALLEL PLATE CHANNEL
H.A. Machado and H.R.B. Orlande
Department of Mechanical  COPPE
Federal University of Rio de Janeiro/UFRJ
Cx. Postal: 68503  21945970
Rio de Janeiro  RJ  Brasil
In this paper we apply the conjugate gradient method with adjoint equation to solve the inverse problem of estimating the unknown transient boundary heat flux, which is also supposed to vary along the flow direction, in a parallel plate channel The physical problem involves the flow of a powerlaw fluid inside the chamel. Simulated temperature measurements are used in the inverse analysis. The effects on the inverse problem solution of number and location of sensors, powerlaw index and random measurement errors are examined.
