Three-Dimensional Transient Heat Conduction Equation Solution for Accurate Determination of Heat Transfer Coefficient

Accurate quantification of local heat transfer coefficient (HTC) is imperative for design and development of heat exchangers for high heat flux dissipation applications. Liquid crystal and infrared thermography (IRT) are typically employed to measure detailed surface temperatures, where local HTC values are calculated by employing suitable conduction models, e.g., one-dimensional (1D) semi-infinite conduction model on a material with the low thermal conductivity and low thermal diffusivity. Often times, this assumption of 1D heat diffusion and ignoring its associated lateral conduction effects leads to significant errors in HTC determination. Prior studies have identified this problem and quantified the associated errors in HTC determination for some representative cooling concepts, by accounting for lateral heat diffusion. In this paper, we have presented a procedure for solution of three-dimensional (3D) transient conduction equation using alternating direction implicit (ADI) method and an error minimization routine to find accurate HTCs at relatively lower computational cost. Representative cases of a single jet and an array jet impingement under maximum crossflow condition have been considered here, for IRT and liquid crystal thermography, respectively. Results indicate that the globally averaged HTC obtained using the 3D model was consistently higher than the conventional 1D model by 7-14%, with deviation levels reaching as high as 20% near the stagnation region. Proposed methodology was computationally efficient and is recommended for studies aimed toward local HTC determination.