Two-dimensional formulation for inverse heat conduction problems by the calibration integral equation method (CIEM)

• A two-dimensional calibration integral equation is developed and investigated.
• Total surface heat transfer is predicted by this inverse method.
• Numerical results indicate the merit of this approach.

A new calibration integral equation is developed and investigated in the context of two-dimensional linear inverse heat conduction. This paper examines a simplified plate geometry possessing three known boundary conditions and one unknown boundary condition. This plate contains of a series of temperature sensors located on a fixed plane below the surface of interest. A total surface heat transfer (W) calibration integral equation is derived based on a fully two-dimensional analysis. In this form, the total surface heat transfer (i.e., the spatially integrated value along the entire surface of interest), is directly derived and implemented bypassing the need to determine the local surface heat flux (W/m2). This formulation yields a Volterra integral equation of the first kind that is pertinent to many applications where the total surface heat transfer (W) is required. Numerical results indicate the merit of the approach when examining two dissimilar isotropic materials.