Estimation of Boundary Heat Flux
with Conjugate Gradient Method
by Experimental Transient Temperature
Data
Parth Sathavara, Ajit Kumar Parwani, Maulik Panchal,
and Paritosh Chaudhuri
Abstract In this work, the estimation of heat flux for one-dimensional transient
heat conduction problem has been done with the help of the search-based conjugate
gradient method with an adjoint problem. The finite volume approach is applied to
discretize the differential equations which are solved by using developed in-house
MATLAB code. The novelty of this paper is justified as the required temperature data
to solve the CGM algorithm are obtained by using real-time experimentation instead
of performing the numerical simulation. The RMS error of the estimation of heat
flow is obtained from that we can conclude that the accuracy is increased by using
multiple sensors. The value of estimated heat flux is affected by the measurement
errors which is inherently present in the measurement data.
Keywords One-dimensional transient heat conduction · Finite volume method ·
Conjugate gradient method (CGM)
1 Introduction
The conventional heat conduction problem generally deals with obtaining the temperature distribution within a heated body when heat flow, the initial and boundary
conditions, thermal and physical properties, and geometric specifications are known.
However, in some heat transfer situations, few parameters are not available where the
inverse method is useful to determine these unknowns. In literature, various works
are done in inverse heat transfer areas like the measurement of heat flux [1] during
P. Sathavara (B) · A. K. Parwani
Institute of Infrastructure Technology Research and Management, Ahmedabad 380026, India
e-mail: parth.sathvara@iitram.ac.in
M. Panchal · P. Chaudhuri
Institute for Plasma Research Bhat, Gandhinagar 382008, India
P. Chaudhuri
Homi Bhabha National Institute (HBNI), Anushaktinagar, Mumbai 400094, India
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. K. Parwani et al. (eds.), Recent Advances in Mechanical Infrastructure,
Lecture Notes in Intelligent Transportation and Infrastructure,
https://doi.org/10.1007/978-981-33-4176-0_30
343
with Conjugate Gradient Method
by Experimental Transient Temperature
Data
Parth Sathavara, Ajit Kumar Parwani, Maulik Panchal,
and Paritosh Chaudhuri
Abstract In this work, the estimation of heat flux for one-dimensional transient
heat conduction problem has been done with the help of the search-based conjugate
gradient method with an adjoint problem. The finite volume approach is applied to
discretize the differential equations which are solved by using developed in-house
MATLAB code. The novelty of this paper is justified as the required temperature data
to solve the CGM algorithm are obtained by using real-time experimentation instead
of performing the numerical simulation. The RMS error of the estimation of heat
flow is obtained from that we can conclude that the accuracy is increased by using
multiple sensors. The value of estimated heat flux is affected by the measurement
errors which is inherently present in the measurement data.
Keywords One-dimensional transient heat conduction · Finite volume method ·
Conjugate gradient method (CGM)
1 Introduction
The conventional heat conduction problem generally deals with obtaining the temperature distribution within a heated body when heat flow, the initial and boundary
conditions, thermal and physical properties, and geometric specifications are known.
However, in some heat transfer situations, few parameters are not available where the
inverse method is useful to determine these unknowns. In literature, various works
are done in inverse heat transfer areas like the measurement of heat flux [1] during
P. Sathavara (B) · A. K. Parwani
Institute of Infrastructure Technology Research and Management, Ahmedabad 380026, India
e-mail: parth.sathvara@iitram.ac.in
M. Panchal · P. Chaudhuri
Institute for Plasma Research Bhat, Gandhinagar 382008, India
P. Chaudhuri
Homi Bhabha National Institute (HBNI), Anushaktinagar, Mumbai 400094, India
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. K. Parwani et al. (eds.), Recent Advances in Mechanical Infrastructure,
Lecture Notes in Intelligent Transportation and Infrastructure,
https://doi.org/10.1007/978-981-33-4176-0_30
343