Research Projects

Nanofluids, comprising nanoparticles dispersed in a base fluid, have transformed heat transfer technologies across various industries. Nanofluids exhibit superior thermal performance relative to base fluids or traditional suspensions of particles and fluids. Because of this advantage, nanofluids have found widespread use in scientific and biomedical fields—for example, in drug and gene delivery, blood clotting processes, cell transport within veins and arteries, and the production of nanocomposite materials. A substantial body of literature regards the base fluid in nanofluids as Newtonian, but in many applications, such as polymer processing, blood pumps, and food processing, the base fluid is inherently non-Newtonian, mainly shear-thinning. Here, the fluid behaviour is more complex due to its change of viscosity with the local shear rate. This variation introduces nonlinearity into the flow analysis, which makes solving the problem more challenging. In the past few years, a few computational techniques have been employed to simulate the flow characteristics of non-Newtonian nanofluids. The most commonly used methods are the finite volume method, lattice Boltzmann method, and the finite element method. Majority of these methods are second-order accurate and often relied on two-dimensional assumptions. So, there is a growing need of more accurate and computationally efficient methods, especially to deal with complex three-dimensional (3D) non-Newtonian nanofluids. From the literature, it is observed that efficient finite difference methods are not used adequately to study non-Newtonian flow problems, especially to study 3D problems, despite their efficiency and simplicity. This may be the reason that the variable viscosity as well as the pressure terms in the 3D model make it more challenging to investigate the behaviour of 3D non-Newtonian fluids. Recently, we have developed a new class of Higher-Order Super-Compact (HOSC) finite difference schemes to study 3D Newtonian, non-Newtonian, and nanofluid fluid flow and heat transfer problems. These HOSC schemes have shown their ability and efficiency to study 3D complex flow dynamics and heat transfer phenomena. These newly developed schemes are second order accurate in time and fourth order accurate in space variables. Also, to discretize the governing equation, this scheme utilizes 19 grid points at the n^th time level and only 7 grid points at the 〖(n+1)〗^th time level from the compact stencil. Furthermore, the system of algebraic equations resulting from HOSC discretization, is handled by advanced iterative solvers such as the hybrid biconjugate gradient stabilized method, resulting in a highly accurate numerical solution at a low computational cost. To the best of our knowledge, this is the first finite difference scheme developed to solve 3D non-Newtonian Power law model, which is higher order accurate and utilize minimum grid points. Through this project, we want to developed a new class of HOSC schemes to study 3D non-Newtonian nanofluid flow problems and its various extensions, like effects of Natural convection, Magnetohydrodynamics, and porous media on the non-Newtonian nanofluids. We first develop the proposed HOSC schemes, validate them by solving various benchmark problems, and confirm the performance (i.e., efficiency, robustness, stability, etc.) of these schemes through different tests. Finally, proposed HOSC schemes will be applied to study different industrial and real-life problems. Outcomes of this project will directly or indirectly help different industries, like food processing industries, bio-medical industries, chemical industries, etc., and enhance the knowledge base and applicability of the HOSC schemes. We strongly believe that our proposed research work will open up a new direction to investigate the complex 3D non-Newtonian nanofluids problems.