Purpose The purpose of this paper is to apply the Steady State Kalman Filter for temperature measurements of tissues via magnetic resonance thermometry. Instead of using classical direct inversion, a methodology is proposed that couples the magnetic resonance thermometry with the bioheat transfer problem and the local temperatures can be identified through the solution of a state estimation problem. Design/methodology/approach Heat transfer in the tissues is given by Pennes’ bioheat transfer model, while the Proton Resonance Frequency (PRF)-Shift technique is used for the magnetic resonance thermometry. The problem of measuring the transient temperature field of tissues is recast as a state estimation problem and is solved through the Steady-State Kalman filter. Noisy synthetic measurements are used for testing the proposed methodology. Findings The proposed approach is more accurate for recovering the local transient temperatures from the noisy PRF-Shift measurements than the direct data inversion. The methodology used here can be applied in real time due to the reduced computational cost. Idealized test cases are examined that include the actual geometry of a forearm. Research limitations/implications The solution of the state estimation problem recovers the temperature variations in the region more accurately than the direct inversion. Besides that, the estimation of the temperature field in the region was possible with the solution of the state estimation problem via the Steady-State Kalman filter, but not with the direct inversion. Practical implications The recursive equations of the Steady-State Kalman filter can be calculated in computational times smaller than the supposed physical times, thus demonstrating that the present approach can be used for real-time applications, such as in control of the heating source in the hyperthermia treatment of cancer. Originality/value The original and novel contributions of the manuscript include: formulation of the PRF-Shift thermometry as a state estimation problem, which results in reduced uncertainties of the temperature variation as compared to the classical direct inversion; estimation of the actual temperature in the region with the solution of the state estimation problem, which is not possible with the direct inversion that is limited to the identification of the temperature variation; solution of the state estimation problem with the Steady-State Kalman filter, which allows for fast computations and real-time calculations.

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The ability of various arrays of micro pin-fins to reduce maximum temperature of an integrated circuit with a 4 × 3 mm footprint and a 0.5 × 0.5 mm hot spot was investigated numerically. Micro pin-fins having circular, symmetric airfoil and symmetric convex lens cross sections were optimized to handle a background uniform heat flux of 500 W cm−2 and a hot spot uniform heat flux of 2000 W cm−2. A fully three-dimensional conjugate heat transfer analysis was performed and a multi-objective, constrained optimization was carried out to find a design for each pin-fin shape capable of cooling such high heat fluxes. The two simultaneous objectives were to minimize maximum temperature and minimize pumping power, while keeping the maximum temperature below 85 °C. The design variables were the inlet average velocity and shape, size and height of the pin-fins. A response surface was generated for each of the objectives and coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Stress–deformation analysis incorporating hydrodynamic and thermal loads was performed on the three Pareto optimized configurations. Von-Mises stress for each configuration was found to be significantly below the yield strength of silicon.

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