In this work, the field (continuity, momentum and thermal energy) equations togetherwith a cell model have been solved numerically to elucidate the influence of non-Newtonian (Power law rheology) liquid characteristics on liquid-solid heat transfer in packed and fluidised beds of spherical particles. The results presented herein relate to wide ranges of conditions of bed voidage, power-law index and Peclet number but are limited to low Reynolds number (less than or equal to 1) flow conditions. Within the range of conditions, the effect of power-law index is found to be small and this is also consistent with the available experimental results on liquid-solid mass transfer in these systems.