Estimation of transient boundary flux for a developing flow in a parallel plate channel

2014 ◽  
Vol 24 (3) ◽  
pp. 522-544 ◽  
Author(s):  
Ajit Kumar Parwani ◽  
Prabal Talukdar ◽  
P.M.V. Subbarao
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Parallel Plate ◽  
Practical Importance ◽  
Unknown Boundary ◽  
Parallel Plates ◽  
Content Type ◽  
Developing Flow ◽  
Boundary Flux ◽  
Plate Channel

Purpose – The purpose of this paper is to develop a numerical model for estimating the unknown boundary heat flux in a parallel plate channel for the case of a hydrodynamically and thermally developing laminar flow. Design/methodology/approach – The conjugate gradient method (CGM) is used to solve the inverse problem. The momentum equations are solved using an in-house computational fluid dynamics (CFD) source code. The energy equations along with the adjoint and sensitivity equations are solved using the finite volume method. Findings – The effects of number of measurements, distribution of measurements and functional form of unknown flux on the accuracy of estimations are investigated in this work. The prediction of boundary flux by the present algorithm is found to be quite reasonable. Originality/value – It is noticed from the literature review that study of inverse problem with hydrodynamically developing flow has not received sufficient attention despite its practical importance. In the present work, a hydrodynamically and thermally developing flow between two parallel plates is considered and unknown transient boundary heat flux at the upper plate of a parallel plate channel is estimated using CGM.

scholarly journals Leveque-Type Similarity Transformation for a Thermally Developing Viscous Dissipative Flow in a Parallel Plate Channel

2021 ◽  
Vol 39 (4) ◽  
pp. 1389-1394
Author(s):  
Gooi Mee Chen ◽  
Yew Hau Yip
Keyword(s):  
Heat Flux ◽  
Forced Convection ◽  
Parallel Plate ◽  
Similarity Transformation ◽  
Axial Direction ◽  
Transformation Method ◽  
Uniform Heat Flux ◽  
Practical Applications ◽  
Developing Flow ◽  
Plate Channel

Compared to the existing more elaborate eigenvalues-eigenfunction analytical solution where the solution of a thermally developing forced convection problem converges very slowly at the beginning of thermal entrant region, Leveque-type similarity transformation method provides a more convenient way to look into the insights of the problem. Assuming that the wall heat flux and viscous dissipation only has an effect within the thin thermal boundary layer at the beginning of the thermal entrance region, this study intends to solve the governing thermal energy equation for a thermally developing flow in a parallel plate channel, subjected to uniform heat flux, by means of Leveque-type similarity transformation. The resulting ordinary differential equation, is subsequently solved by a fourth order Runge Kutta method. A comparison of the Nusselt number along the axial direction, at the beginning of the thermally developing region with the literature, reveals less than 10% discrepancy for Brinkman number less than one, which is a commonly acceptable range for practical applications. Although its accuracy depletes downstream the channel, similarity transformation provides sufficiently accurate temperature distribution, and captures the heat transfer insights for a thermally developing viscous dissipative forced convection.

Linear Spatial Stability of Developing Flow in a Parallel Plate Channel

1981 ◽  
Vol 48 (1) ◽  
pp. 192-194 ◽  
Author(s):  
S. C. Gupta ◽  
V. K. Garg
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Parallel Plate ◽  
Critical Reynolds Number ◽  
Two Dimensional ◽  
Spatial Stability ◽  
Percent Change ◽  
Developing Flow ◽  
The Stability ◽  
Plate Channel

It is found that even a 5 percent change in the velocity profile produces a 100 percent change in the critical Reynolds number for the stability of developing flow very close to the entrance of a two-dimensional channel.

Entrance and Exit Losses for Developing Flow in Plain Fin Heat Sinks

2003 ◽  
Author(s):  
Ralph L. Webb ◽  
Jin Wook Paek
Keyword(s):  
Pressure Drop ◽  
Parallel Plate ◽  
Flow Region ◽  
Heat Sinks ◽  
Graphical Form ◽  
Parallel Plates ◽  
Fully Developed Flow ◽  
Developing Flow ◽  
Contraction Ratio ◽  
Electronic Heat

Prediction of pressure drop for duct flow through heat sinks involves calculation of inlet and exit losses. These predictions are typically done using Kc and Ke for “parallel plate channels” from the Kays and London book, Compact Heat Exchangers. However, these equations assume fully developed flow at the exit and thus include the effect of full velocity profile development. Electronic heat sinks operate in the “developing flow” region. So, use of the published Kc and Ke from the Kays and London book will result in over-estimate of the actual Kc and Ke values. The authors have performed analysis that allows accurate calculation of Kc and Ke values with parallel plate channels for operation in the “developing flow” region. The results are presented in graphical form as a function of contraction ratio and x+ (= x/DhRe). These results will allow accurate estimate of Kc and Ke values for developing flow. Entrance and exit losses can account for as much as 30% of the total pressure drop in electronic heat sinks having short flow lengths. However, the error associated with evaluation of Kc and Ke based on fully developed flow for parallel plates is small.

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