Two-dimensional finite element inverse heat transfer approach with conjugate gradient method to evaluate the energy requirement of bread under various conditions

Direct heat transfer problems can be solved analytically or numerically to predict the temperature profile when the thermal properties, boundary conditions, and other relevant parameters are known. Though it is common practice to measure temperature experimentally, heat transfer parameters and boundary conditions are more challenging to measure and can instead be inferred through the use of inverse heat transfer (IHT) techniques, which can be solved through optimization. In this study, the IHT method with the conjugate gradient method is used to determine the energy consumption of bread during the cooking process in a developed baking oven with and without a reflector. A complex variable differentiation method is integrated to calculate the accurate sensitivity coefficient matrix. The results demonstrated that the estimated heat flux is very close to the exact heat flux and relative error is less than measurement errors.