On the inverse heat convection problem of the flow over a cascade of rectangular blades

Chen, Wen-Lih; Yu, Yang

doi:10.1016/j.ijheatmasstransfer.2008.02.002

Cited by 20 publications

(13 citation statements)

References 18 publications

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“…To study the difficulties associated with the inverse convection problem, Chen and Yang [13] carried out inverse heat convection problem of flow over a cascade of rectangular blades. They found that at high Reynolds number the accuracy of the inverse method strongly depends on the relative position between the estimated and measured quantities.…”

Section: Introductionmentioning

confidence: 99%

Inverse conjugate mixed convection in a vertical substrate with protruding heat sources: a combined experimental and numerical study

Ahamad

Balaji

2015

Heat Mass Transfer

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heat inputs, CFD simulations were again run to compare the temperature distribution at the back of the PCB board with measurements. List of symbolsa Absorption coefficient (m −1 ) A Area of heat source (m 2 ) B Distance from the edge of the plate to the nearest chip edge (m) C p Specific heat (J/kg k) D Spacing between the heat sources (m) d Height of the heat source (m) Gr Grashof number, Gr = gβ∆TL 3 υ 2 g Acceleration due to gravity (9.81 m/s 2 ) H Height of the duct/channel (m) h Convective heat transfer coefficient (W/m 2 K) I Total radiation intensity (W/m 3 ) k s Thermal conductivity of solid (W/m K) L Characteristic length (height of the heat source in this case) (m) N Length of substrate in Z direction (m) n Refractive index p Pressure (N/m 2 ) S Sum of the residues, as the case may be (Eq. 12) s Direction vector Q Power input (W) Q ANN Heat input value measured by ANN (W) Q Expt Heat input value measured by experiments (W) Re Reynolds number, U α L υ Ri Richardson number, Ri = Gr Re 2 S Spacing between the two walls of the channel (m) t Heat source thickness (m) T Temperature (K) U ∝ Inlet air velocity (m/s) V Velocity vector (m/s) Abstract This paper reports the results of a combined numerical and experimental study to estimate the heat inputs of three protruding heat sources of the same size placed on a vertically placed PCB board of height 150 mm, depth 250 mm, and thickness 5 mm. First, limited measurements of temperatures were recorded at eight locations along the height of the back of the PCB board for different (and known) values of heat inputs of the protruding heat sources and different velocities. These were followed by three-dimensional calculations of fluid flow and conjugate heat transfer for various heat transfer coefficients on the backside of the PCB board. The difference between the CFD predicted and experimentally measured temperature distributions on the back of the PCB board was minimized using least squares and the best value of heat transfer coefficient was obtained. Using this 'data assimilated' CFD model, detailed CFD simulations were done for various values of heat input values and Reynolds numbers (each of these can be different from one another) of the flow. The temperatures at the same eight locations at the back of the PCB board were noted. An artificial neural network was then developed with ten inputs (eight temperatures together with the input velocity and the ambient temperature) to estimate the three outputs (three heat inputs) after carrying out extensive studies on the architecture of the network. This inverse solution was then tested with experiments for validating the ANN approach to solve the inverse conjugate heat transfer problem. Finally, with the ANN estimated

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Section: Introductionmentioning

confidence: 99%

Inverse conjugate mixed convection in a vertical substrate with protruding heat sources: a combined experimental and numerical study

Ahamad

Balaji

2015

Heat Mass Transfer

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“…An error or cost function is defined first for the optimized procedure, and desired unknown functions or parameters are determined by minimizing the error or cost function. A variety of numerical and analytical techniques for solving the inverse problem have been proposed in the literature (12)(13)(14)(15)(16)(17) . Most of them can be classified into two major methods; one is the gradient-based method and the other is the stochastic method.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed method is tested against several cases and numerical results are encouraging. Based on an advantage of short computational time, the conjugate gradient method has been adopted by many researchers to estimate the inlet flow temperatures (14) , surface heat flux (15,16) and thermal properties of fluid (17) for the inverse convection problems. The advantage of the stochastic methods is their capability searching for the global optimum instead of local optimum.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Method for Determination of Thermal Diffusivity of Liquid Flowing in a Pipe

Saengswarng

Khunthong

2013

JTST

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The paper deals with determination of thermal diffusivity of liquid flowing in a pipe based on inverse problem. The hybrid method was developed to improve the inverse solution. The proposed method is a combination of the artificial neural network and inverse solution algorithm. The artificial neural network is adopted for making a good initial-guessed value for the inverse solution. Numerical examples are included to demonstrate the performance of the proposed method. In comparison with the simple inverse solution, the proposed hybrid method is efficiently converged to yield good estimates.

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“…Over the past decades, the studies of inverse heat conduction problem (IHCP) have offered convenient alternatives, which largely scale down experimental work, to obtain accurate thermophysical quantities in many heat conduction problems. To date, a variety of analytical and numerical techniques have been developed for the solution of IHCP, for example, the conjugate gradient method (CGM) [9][10][11][12][13][14], the function-specification method [15], the space-marching method [16], the Tikhonov regularization method [17], and the genetic algorithm [18].…”

Section: Introductionmentioning

confidence: 99%

“…Such weak relationship exists in many engineering problems, for example, convective heat transfer and transient heat conduction. Chen and Yang [13] reported that the relative position between the measured and estimated quantities is one of the most crucial factors to whether an inverse analysis being successful or not in a heat convection problem. Detailed discussion on the mechanism behind the phenomenon was also documented.…”

Section: Introductionmentioning

confidence: 99%

Inverse prediction of frictional heat flux and temperature in sliding contact with a protective strip by iterative regularization method

Chen¹,

Yu²

2011

Applied Mathematical Modelling

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a b s t r a c tIn this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent frictional heat flux at the interface of two semi-spaces, one of them is covered by a strip of coating, during a sliding-contact process from the knowledge of temperature measurements taken within one of the semi-space. It is assumed that no prior information is available on the functional form of the unknown heat generation; hence the procedure is classified as the function estimation in inverse calculation. Results show that the relative position between the measured and the estimated quantities is of crucial importance to the accuracy of the inverse algorithm. The current methodology can be applied to the prediction of heat generation in engineering problems involving sliding-contact elements.

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On the inverse heat convection problem of the flow over a cascade of rectangular blades

Cited by 20 publications

References 18 publications

Inverse conjugate mixed convection in a vertical substrate with protruding heat sources: a combined experimental and numerical study

Inverse conjugate mixed convection in a vertical substrate with protruding heat sources: a combined experimental and numerical study

Hybrid Method for Determination of Thermal Diffusivity of Liquid Flowing in a Pipe

Inverse prediction of frictional heat flux and temperature in sliding contact with a protective strip by iterative regularization method

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