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

Abstract

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.

Citation

Kumar Parwani, A., Talukdar, P. and Subbarao, P.M.V. (2014), "Estimation of transient boundary flux for a developing flow in a parallel plate channel", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 3, pp. 522-544. https://doi.org/10.1108/HFF-01-2012-0020