This paper reports the efficacy of the Least Square Residual (LSR) method in parameter estimation when more than one mode of heat transfer is encountered. A vertical flat plate, made of aluminium, to ensure that lumped formulation is valid, is allowed to cool in quiescent air. The novelty arises in coating the plate with a paint of known emissivity, in this case black board paint with ε = 0.85 and using the experimentally obtained transient temperature history to develop an expression for convective Nusselt number. The same plate is then given a different coating of unknown emissivity, and using the just established relationship for convective Nusselt number, by a regular parameter estimation using LSR, the emissivity is calculated. The synergy arises by using known information on emissivity to estimate convection in the first case and the reverse to back calculate an unknown emissivity. The ubiquitous vertical flat plate, thus serves as a simple, inexpensive, yet a potent emissivity comparator. © 2003 Elsevier Science Ltd.

C. Balaji

Department of Mechanical Engineering

Aluminum

Comparator circuits

Least squares approximations

Nusselt number

Parameter estimation

Thermal effects

SYNERGISTIC APPROACH

Heat transfer

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IIT Madras

A synergistic approach to parameter estimation in multimode heat transfer

International Communications in Heat and Mass Transfer

Steady state numerical computations and experiments were performed to study three-dimensional, conjugate laminar natural convection heat transfer from multiple identical heat generating modules (heat sources) in a vertical duct. The heat sources were mounted on a wall at different positions in a defined grid of 5 × 5 positions. Air is used as the cooling medium. The governing flow and energy equations were solved using FLUENT 6.3. The optimum geometric configuration of the five heat sources that maximizes the heat transfer was determined by the introduction of a dimensionless distance parameter and an exhaustive search. The heuristic procedure based on the geometric parameter was tested for varying number of heat sources and for different heat source strengths. Experiments were performed to study the effect of modified Grashof number and the duct spacing on maximum temperatures of different configurations in order to support the numerical findings. Additionally, the temperatures of the heat sources arranged in the optimum configuration obtained by the heuristic approach have been experimentally validated. © 2009 Elsevier Ltd. All rights reserved.

International Journal of Heat and Mass Transfer

A heuristic approach to optimal arrangement of multiple heat sources under conjugate natural convection

This article reports the results of an experimental study, where a vertical aluminum plate embedded with a heater standing in quiescent air is considered. The temperature time history of the plate for the three stages of the experiment, namely (i) heating, (ii) steady state, and (iii) cooling, has been obtained. Using the temperature time history from heating and cooling, a crucial thermal property of the surface of the plate, namely emissivity together with the heat transfer coefficient from the plate under natural convection, is estimated. The parameter estimation is done through the stochastic-based Bayesian inference method, by posing the inverse problem as a minimization problem, wherein the sum of the squares of the difference between the measured temperature time history and numerically generated temperature time history with guess values of the parameters is minimized. Experiments have been done for (i) a plate with black coating, (ii) a plate with aluminum coating, and (iii) a polished plate. The novelty in the work is the simultaneous estimation of the two properties without the need for vacuum, and the results compare favorably with benchmarks in the literature. Finally, the results from the steady state are also obtained for validating the estimates obtained from transient experiments. The Bayesian method allows the simultaneous estimation of the standard deviation of the estimates. Copyright © Taylor & Francis Group, LLC.

Experimental Heat Transfer

An inexpensive technique to simultaneously determine total emissivity and natural convection heat transfer coefficient from transient experiments

Transient cooling experiments of a heated vertical aluminum plate with an embedded heater, in quiescent air were conducted for the simultaneous estimation of total hemispherical emissivity and specific heat of the plate material. During cooling, the heat loss from the hot plate by natural convection and radiation was taken into account. During the experiments, plate temperatures were recorded at several locations using a data acquisition system. A numerically computed transient response of the plate is then compared with the experimentally known transient response to estimate the residual, the minimization of which using Levenberg-Marquardt's iterative procedure retrieves the parameters pertinent to the problem. The experiments were conducted for three different surface emissivities of the plate obtained by using suitable surface treatment. A consistency test for the present approach was also done by conducting transient heating experiments using the retrieved values of parameters and a comparison of simulated and calculated natural convection heat transfer coefficients as a function of temperature. The experiments have been performed over a temperature range of 320-430 K and a Rayleigh number range of 2 × 106-2 × 107. The emissivity values are in good agreement with previous reported results. Copyright © 2008 by ASME.

Journal of Heat Transfer

Simultaneous retrieval of total hemispherical emissivity and specific heat from transient multimode heat transfer experiments

In this paper, the results of an experimental and semi-experimental investigation of steady laminar natural convection and surface radiation between three parallel vertical plates, viz., a central hot plate coated with blackboard paint and two unheated side plates that are polished, symmetrically spaced on each side, with air as the intervening medium, are presented. In the semi-experimental method, the measured wall temperatures are fed as (a) segmental values and (b) average value, into a numerical program for generating the values of convective Nusselt number, and these are compared with the experimental results obtained by calorimetry. The radiative heat transfer rate at the hot surface was computed by the radiosity-irradiation method and this was deducted from the power input to the heater, to obtain experimentally the convective heat transfer rates and hence the convective Nusselt numbers. The experiments were done for six plate spacings ranging from 12.66 to 52.2 mm and for an order of magnitude range of wall-to-ambient temperature difference. The analysis brings out the significance of radiation heat transfer rate even at low temperatures of 310 K. The concordance between the average convective Nusselt numbers obtained from the experimental, and semi-experimental investigation taking into account the variation of temperature along the plate and under the isothermal assumptions, shows that the isothermal approximation itself is adequate. A correlation for the average convective Nusselt number in terms of Grashof number and the aspect ratio is developed based on 133 data for a Grashof number range 2370 < Gr < 872700 and an aspect ratio range 2.88 ≤ A ≤ 11.85. © 2004 Elsevier Inc. All rights reserved.

Experimental Thermal and Fluid Science

Combined experimental and numerical approaches to multi-mode heat transfer between vertical parallel plates

Results of an experimental study of natural convection and surface radiation between three parallel vertical plates, symmetrically spaced, with air as the intervening medium are presented. The analysis consists of heating the central plate at different levels and recording the temperatures of both the central and the side plates at steady state conditions. Based on the measurements, a correlation for the maximum temperature excess of the "hot" plate in terms of the emissivity of the central and the side plates, the aspect ratio, and the dimensionless total heatflux is given, valid for a range of emissivity 0.05≤εc, εs≤0.85, aspect ratio 2.38 ≤A ≤17, and total heat flux 32≤q≤1590 W/m2. Through this, the heat transfer enhancement due to radiation has been succinctly brought out. Copyright © 2004 by ASME.

Journal	International Communications in Heat and Mass Transfer
ISSN	07351933
Open Access	No