Abstarct: In this study, a hybrid immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to simulate the flow and heat transfer in presence of stationary and moving boundaries. IB-NLBM is capable of modelling the heat transfer of bodies having complex geometries and posing variable surface temperature. This method can be considered as a non-body conformal approach which the fluid domain and immersed boundary are presented by fixed Eulerian nodes and Lagrangian points, respectively. The proposed hybrid method can effectively take the advantages of both immersed boundary and lattice Boltzmann methods. Two important properties of the presented method, direct numerical simulation and local calculation of viscosity with second order accuracy, make this method an appropriate choice for simulation of non-Newtonian fluid flow including the moving boundaries. In the presented work, different types of sharp and diffuse interface are studied in order to lixnk both Eulerian and Lagrangian nodes. Compared to the common IB-LBMs, the presented study also considers the external force causing from the accelerated mass which is a necessary factor for realistic modelling of movement in non-Newtonian fluids. The split-forcing algorithm used in this method reduces the negative effect of discretization of the solution domain and leads to a second order recovery of Navier-Stokes equations. Furthermore, a simple technique baxsed on sharp and diffuse IB-LBM is introduced for calculation of Nusselt number in non-isothermal particulate flows. The accuracy of the proposed method is proved comparing it with several examples of analytical, numerical and experimental benchmarks in the literature including non-Newtonian fluid flow in the channel, the fluid flow and heat transfer over the fixed boundaries of different geometries, and fall of the particles in the isothermal and non-isothermal fluids. Novelties of this thesis can be generally fallen into two main categories: Firstly, development and optimization of Immersed Boundary – non-Newtonian lattice Boltzmann method in particulate flows with constant and variable surface temperature. Secondly, the results obtained for the first time concerning the behaviour of non-Newtonian fluids in presence of non-isothermal moving boundaries. baxsed on the comparisons conducted in this study, the sharp interface algorithm is appropriate to simulate the flow in the vicinity of the fixed boundaries. Moreover, four-point diffuse interface algorithm is suitable for modelling the geometries including the moving boundaries. In the present work, phenomenon involving the interaction between particles such as, Drafting, Kissing, and Tumbling (DKT) in problems related to the sedimentation of two particles or more in shear-thinning and shear-thickening non-Newtonian fluids is investigated for the first time. The results indicate that the shear-thinning properties of the fluid increases Kissing time. Additionally, the transverse component of the particle velocity for the shear-thinning fluids during the Tumbling period is different from Newtonian and shear-thickening fluids. The results of the thermal simulation problem of particle sedimentation with variable surface temperature reveal that the assumption of constant surface temperature creates unacceptable errors for simulation of real thermal systems. The proposed IB-NLBM can be appropriately utilized for simulation of different applied problems such as direct contact heat exchanger and the isothermal or non-isothermal non-Newtonian particulate flow in biological environments or chemical industries.