Approximate Analytical And High-order Numerical Studies On Conjugate Heat Transfer Problems In Axisymmetric Flows

In the fluid flow and heat transfer processes, the fluid properties especially viscosity changes with temperature, the apparent viscosity of non-Newtonian fluid is also related to shear rate, which affects the distribution of flow field in various degree, and then the interaction between the velocity and temperature distributions becomes more complex. These influences will cause the difficultly in solving the corresponding mathematical models. Therefore, it is worthwhile to make a further research on the rules of momentum and energy transfer in convective heat transfer of fluid with variable transport properties, which is an interdisciplinary research combining heat transfer, fluid mechanics and applied mathematics.This research mainly analyses a series of axsymmetric flow and heat transfer coupled problems systematically, including the conjugate heat transfer problems along the accelerating/decelerating vertical stretched cylinders, vertical rotating cone and in the concentric annulus. In these models, temperature-dependent physical parameters (viscosity, thermal conductivity, the power law index) are taken into account by applying different empirical formulas, to give a more accurate description of the flow field and temperature field. The nonlinear partial differential governing equations and the corresponding boundary/initial conditions are obtained, by constructing the mathematical models of these axisymmetric flow and heat transfer problems.In above nonlinear governing partial differential equations and solution conditions, some difficulties are encountered in high-dimensional, high-order and high-degree terms, variable coefficients terms and irregular domain, etc, which are attributed to the variable transport properties, buoyancy effect caused by temperature difference, power-law constitutive relation of power-law fluid. It is difficult to give the exact analytical solutions of those problems, so the present research aims to the fast and widely used approximate analytical methods and numerical algorithms with high accuracy in the following two aspects:(1) Based on the new features when applying the traditional homotopy analysis method (HAM) in different physical problems, we propose the concept of3D convergence curve, which can help to visually judge the convergence region of series solution and evaluate the auxiliary parameters. The calculation results show that we can reduce the number of iterations, and speed up the convergence effectively by using two-parameter HAM combined with the square residual function.(2) As spectral methods is difficult to solve regional problems and irregular domain problems, we select the appropriate mapping techniques, and then use fast Fourier transform (FFT) to reduce the computation in a large degree. Moreover, the accuracy test and error estimation are done by using manufactured solutions, and the results show that the convergence of the spectral method is exponentially fast.New approximate analytical and numerical solutions are obtained by doing above calculation, and the effects of pertinent physical parameters, such as variable transport properties, buoyancy force, and magnetic field on the flow and heat transfer are discussed. The results show that, compared to the fluid with constant viscosity coefficient, the rheological properties of fluids with variable viscosity change obviously near the solid surface, and the heat transfer would be enhanced or weakened under different circumstances. The viscosity-temperature characteristic of fluid, namely the sensitivity of viscosity to temperature plays an important role in the heat transfer.