Some boundary value problems of temperature fields in oil strata

Nakhi, Y. Ben; Kalla, S. L.

doi:10.1016/s0096-3003(02)00529-5

Cited by 12 publications

(9 citation statements)

References 2 publications

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“…In Eqs. (21,22), α, ω and β are the weights that can be adjusted in order to minimize E 1 and E 2 such that E approaches to 0. Hence, the approximate solutionφ of the problem will be near to the exact solution ϕ.…”

Section: B Objective Functionmentioning

confidence: 99%

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Analysis of a Mathematical Model for Drilling System With Reverse Air Circulation by Using the ANN-BHCS Technique

et al. 2021

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Section: B Objective Functionmentioning

confidence: 99%

“…In the method of reverse air circulation, the drilling bit has some particular structure. Some researchers, like Bulroc and Numa have primarily focussed on external jetting nozzles [20], [21]. Meanwhile, some studies have concentrated on bottom jetting nozzle bits [22].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Mathematical Model for Drilling System With Reverse Air Circulation by Using the ANN-BHCS Technique

et al. 2021

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“…As for fractional partial differential equations (FPDEs), maybe the most famous model is the fractional diffusion equation used to describe the anomalous diffusion in porous medium. Further applications and numerical methods for fractional diffusion equation were discussed (e.g., [25][26][27][28][29] and references therein).…”

Section: Introductionmentioning

confidence: 99%

A Spectral Deferred Correction Method for Fractional Differential Equations

Jia¹,

Huang

Zhao³

et al. 2013

Abstract and Applied Analysis

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A spectral deferred correction method is presented for the initial value problems of fractional differential equations (FDEs) with Caputo derivative. This method is constructed based on the residual function and the error equation deduced from Volterra integral equations equivalent to the FDEs. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDEs without the penalty of a huge computational cost due to the nonlocality of Caputo derivative. Finally, preliminary numerical experiments are given to verify the efficiency and accuracy of this method.

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“…The problems connected with various approaches heat conduction in a stratum were considered in many papers, see for instance Rudraiah and Nagaraj [9], Jha [10], Lu and Ge [11], Nahhi and Kalla [12], Kou and Lu [13], Povstenko [14].…”

Section: Introductionmentioning

confidence: 99%

Temperature distributions in a periodically stratified layer with a vertical dug well

Matysiak

Perkowski

2012

Heat Mass Transfer

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The stationary problems of heat conduction in a periodically stratified layer with a vertical cylindrical hole is considered. The lateral surface of the hole is kept at a given piece-wise constant temperature. The boundary planes at zero temperature are taken into account, and the ideal thermal contact between the composite constituents is assumed. The problem within the homogenized model with microlocal parameters is solved.

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Some boundary value problems of temperature fields in oil strata

Cited by 12 publications

References 2 publications

Analysis of a Mathematical Model for Drilling System With Reverse Air Circulation by Using the ANN-BHCS Technique

Analysis of a Mathematical Model for Drilling System With Reverse Air Circulation by Using the ANN-BHCS Technique

A Spectral Deferred Correction Method for Fractional Differential Equations

Temperature distributions in a periodically stratified layer with a vertical dug well

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