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This paper mainly analyzes the heat transfer of Carreau fluid over an infinite rotating disk, and two models with variable thermal conductivity are considered. Firstly, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by similarity transformation. Then, the boundary value problem is solved by improved bvp4c method, which reduced sensitivity to the initial values. For shear-thinning and shear-thickening fluids, the effects of Carreau fluid index n and Prandtl number Pr on velocity and temperature fields are shown and analyzed when 0.5 ≤ n ≤ 1.5 , 1 ≤ P r ≤ 10. Furthermore, the thermal conductivity is computed under two cases. [ABSTRACT FROM AUTHOR]

The paper shows application of the method of fundamental solutions in combination with the radial basis functions for analysis of fluid flow and heat transfer in an internally corrugated tube. Cross-section of such a tube is mathematically described by a cosine function and it can potentially represent a natural duct with internal corrugations, e.g. inside arteries. The boundary value problem is described by two partial differential equations (one for fluid flow problem and one for heat transfer problem) and appropriate boundary conditions. During solving this boundary value problem the average fluid velocity and average fluid temperature are calculated numerically. In the paper the Nusselt number and the product of friction factor and Reynolds number are presented for some selected geometrical parameters (the number and amplitude of corrugations). It is shown that for a given number of corrugations a minimal value of the product of friction factor and Reynolds number can be found. As it was expected the Nusselt number increases with increasing amplitude and number of corrugations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate magnetohydrodynamic free convective flow of micropolar fluid over a moving flat plate using the Lie group transformations and numerical methods. Instead of using conventional no-slip boundary conditions, we used both the velocity and thermal slip boundary conditions to achieve physically realistic and practically useful results. The governing boundary layer equations are non-dimensionalized and transformed into a set of coupled ordinary differential equations (ODEs) using similarity transformations generated by the Lie group, before being solved numerically using Matlab stiff ODE solver ode15s and Matlab trust-region-reflective algorithm lsqnonlin . The effects of governing parameters on the dimensionless velocity, angular velocity, temperature, skin friction and heat transfer rate are investigated. Our analysis revealed that the dimensionless velocity and angular velocity decrease whilst the dimensionless temperature increases with the velocity slip parameter. Thermal slip reduces the dimensionless velocity and temperature but raises the dimensionless angular velocity. Magnetic field suppresses the velocity but elevates the temperature and angular velocity. Results reported in this paper are in good agreement with the ones reported by the previous authors. [ABSTRACT FROM AUTHOR]

In this paper, we extend the lattice Boltzmann method (LBM) in combination with the immersed boundary method (IBM) to simulate the steady-state fluid–solid conjugate heat transfer problems in complex geometries. The no-slip boundary condition is handled by the immersed boundary method. The “pseudo-solid-specific-heat” technique is used to ensure the continuity of heat flux at the fluid–solid interface. The present LB thermal field solver retains the simple structure of standards thermal LB model. The performance of the present method is validated by several heat conduction/convection problems. The numerical results agree well with exact solutions or published results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the unsteady flow and heat transfer of a dusty fluid between two parallel plates with variable viscosity and electric conductivity. The fluid is driven by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates with a Navier slip boundary condition. The governing non-linear partial differential equations are solved numerically using a semi-implicit finite difference scheme. The effect of the wall slip parameter, viscosity and electric conductivity variation and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed. [Copyright &y& Elsevier]

Abstract: This paper describes the reconstruction of the heat transfer coefficient (space, Problem I, or time dependent, Problem II) in one-dimensional transient inverse heat conduction problems from surface temperature or average temperature measurements. Since the inverse problem posed does not involve internal temperature measurements, this means that non-destructive testing of materials can be performed. In the formulation, convective boundary conditions relate the boundary temperature to the heat flux. Numerical results obtained using the boundary element method are presented and discussed. [Copyright &y& Elsevier]

Abstract: In this paper we will conduct an analytic comparative study between the powerful Adomian method and the traditional separation of variables method. This is achieved by handling homogeneous and non-homogeneous boundary value problem for one-dimensional heat equation. The study shows the reliability and efficiency of Adomian method. Adomian method provides the solution in a rapidly convergent series through evaluating elegantly computable components. [Copyright &y& Elsevier]