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The purpose of the current paper is to develop a numerical methodology, based on the immersed boundary-lattice Boltzmann computational framework, for the Neumann and Dirichlet boundary conditions in problems involving natural and forced convection heat transfer.

The direct forcing immersed boundary method is extended to study the heat transfer by incompressible flow within the thermal lattice Boltzmann method (LBM) computational framework. The direct forcing and heating immersed boundary-LBM introduces a heat source term to the thermal LBM to account for the heat transfer occurring at the immersed boundary. New numerical treatments for the Neumann type of boundary condition and for the calculation of the local Nusselt number are developed. The developed methodologies have been applied to flows around immersed bodies with natural and forced convection, including steady as well as unsteady flows.

Numerical experiments involving immersed bodies in natural and forced convection have been performed in order to assess the validity of the direct heating IB-LBM. The flow cases studied also include steady and transient flow phenomena. Flow velocity field and isotherms have been used for qualitative comparisons with existing, published results. The surface averaged Nusselt number, Strouhal number, and lift coefficient (for the unsteady flow cases) have been used for quantitative comparison with published results. The results show that there are satisfactory agreements, qualitatively and quantitatively, between the results obtained by using the present method and those previously published.

Limited application of immersed boundary to thermal flows within the LBM has been studied by researchers; the few past studies were limited to Dirichlet boundary conditions and/or using of feedback forcing and heating approaches. In the current paper, the direct forcing and heating approach was used which helps to eliminate the arbitrary constants used in the feedback approaches. The developed new numerical treatments for the Neumann type of boundary condition and for the calculation of the local Nusselt number eliminate the need to determine surface normal and temperature gradient in the normal direction for heat transfer calculation, which is particularly beneficial in cases with deforming or changing boundaries.

The purpose of this paper is to study the problem of wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal (triangle, square, pentagon and hexagon) cross-section immersed in fluid is using Fourier expansion collocation method, with in the frame work of linearized, three-dimensional theory of thermo-piezoelectricity.

A mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sections immersed in fluid is studied using the three-dimensional theory of elasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for triangular, square, pentagonal and hexagonal cross-sectional bar immersed in fluid. Since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the curved surface of the polygonal bar directly. Hence, the Fourier expansion collocation method is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.

From the literature survey, it is clear that the free vibration of an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid.

Wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes of piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid.

The researchers have discussed the wave propagation in thermo-piezoelectric circular cylinders using three-dimensional theory of thermo-piezoelectricity, but, the researchers did not analyzed the wave propagation in an arbitrary/polygonal cross-sectional bar immersed in fluid. So, the author has studied the free vibration analysis of thermo-piezoelectric polygonal (triangle, square, pentagon and hexagon) cross-sectional bar immersed in fluid using three-dimensional theory elasticity. The problem may be extended to any kinds of cross-sections by using the proper geometrical relations.

The purpose of this paper is to present two efficient immersed boundary methods (IBM) for simulation of thermal flow problems. One method is for given temperature condition (Dirichlet type), while the other is for given heat flux condition (Neumann type). The methods are applied to simulate natural and mixed convection problems to check their performance. The comparison of present results with available data in the literature shows that the present methods can obtain accurate numerical results efficiently.

The paper presents two efficient IBM solvers, in which the effect of thermal boundary to its surrounding fluid is considered through the introduction of a heat source/sink term into the energy equation. One is the temperature correction‐based IBM developed for problems with given temperature on the wall. The other is heat flux correction‐based IBM for problems with given heat flux on the wall. Note that in this solver, the offset of derivative condition is directly used to correct the temperature field.

As compared with existing solvers, the temperature correction‐based IBM determines the heat source/sink implicitly instead of pre‐calculated explicitly, so that the boundary condition for temperature is accurately satisfied. To the best of the authors' knowledge, the work of heat flux correction‐based IBM is the first endeavour for application of IBM to solve thermal flow problems with Neumann (heat flux) boundary condition. It was found that both methods presented in this work can efficiently obtain accurate numerical results for thermal flow problems.

The two methods presented in this paper are novel. They can effectively solve thermal flow problems with Dirichlet and Neumann boundary conditions.

The purpose of this paper is to study the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid using the Fourier expansion collocation method.

A mathematical model is developed for the analytical study on a transversely isotropic thermo-piezoelectric polygonal cross-sectional fiber immersed in fluid using a linear form of three-dimensional piezothermoelasticity theories. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the Fourier expansion collocation method (FECM) at the irregular boundary surfaces of the polygonal cross-sectional fiber. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots.

From the literature survey, it is evident that the analytical formulation of thermo-piezoelectric interactions in a polygonal cross-sectional fiber contact with fluid is not discussed by any researchers. Also, in this study, a polygonal cross-section is used instead of the traditional circular cross-sections. So, the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid are studied using the FECM. The dispersion curves for non-dimensional frequency, phase velocity and attenuation coefficient are presented graphically for lead zirconate titanate (PZT-5A) material. The present analytical method obtained by the FECM is compared with the finite element method which shows a good agreement with present study.

This paper contributes the analytical model to find the solution of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid. The dispersion curves of the non-dimensional frequency, phase velocity and attenuation coefficient are more prominent in flexural modes. Also, the surrounding fluid on the various considered wave characteristics is more significant and dispersive in the hexagonal cross-sections. The aspect ratio (a/b) of polygonal cross-sections is critical to industry or other fields which require more flexibility in design of materials with arbitrary cross-sections.

The purpose of this paper is to numerically investigate two dimensional steady state convective heat transfer in a differentially heated square cavity with constant temperatures and an inner rotating cylinder. The gap between the cylinder and the enclosure walls is filled with power law non-Newtonian fluid.

Finite volume-based CFD software, Fluent (Ansys 15.0) is used to solve the governing equations. Attribution of the various flow parameters of fluid flow and heat transfer are investigated including Rayleigh number, Prandtl number, power law index, the cylinder radius and the angular rotational speed.

Outcomes are reported in terms of isotherms, streamlines and average Nusselt number (Nu) of the heated wall for various considered here.

A detailed investigates is needed in the context of 3D flow. This will be a part of the future work.

The effect of a rotating cylinder on heat transfer and fluid flow in a differentially heated rectangular enclosure filled with power law non-Newtonian fluid has practical importance in the process industry.

The results of this study may be of some interest to the researchers of the field of chemical or process engineers.

The purpose of this study is to investigate the enhancement and suppression of heat transfer for hybrid nanofluids (Cu–Al2O3/water) in a square enclosure containing a thermal-conductive cylinder when the Lorentz force is applied to the hybrid nanofluids.

Since the inner conductive cylinder in present research has a complex geometry, an in-house meshless method, namely, the local radial basis function (LRBF) method, is applied to solve the 2 dimensional (2D) incompressible Navier–Stokes equation in the fluid domain and Fourier heat conduction equation in solid domain. The solid–fluid interface remains the physical continuity of temperature and heat flux. Only the Lorentz force is considered for the presence of the magnetic field. The conjugate natural convection is assumed to be steady, thus only fully developed heat exchange from the nanofluids to solid or vice versa is comprehensively investigated.

It can be concluded that Lorentz force plays a more significant role than hybrid nanofluids in enhancing/suppressing heat transfer when the orientation of magnetic field is the same to the x direction. The thermal conductivity ratio can dramatically change the isotherms and streamlines as well as the mean value of the Nusselt number, resulting in totally different heat transfer phenomena. The included angle of magnetic field also has a significant effect on the heat transfer rate when it changes from horizontal to vertical.

The constant thermo-physical properties of incompressible fluid and the 2D steady flow are considered in this study.

The conjugate MHD natural convection of hybrid nanofluids is numerically investigated by an in-house meshless LRBF method. The enhancement and suppression of heat transfer under the combined influence of the volume fraction of nanoparticles, Hartmann number and the thermal conductivity ratio are comprehensively investigated.

The purpose of this paper is to discuss, with numerical simulations, magnetohydrodynamic (MHD) natural convection laminar flow from an isothermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature.

The governing boundary layer equations are transformed into a non‐dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form, which are solved numerically by two very efficient methods: implicit finite difference method together with Keller box scheme; and direct numerical scheme.

Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin‐friction coefficient and the local Nusselt number for a wide range of MHD parameter, viscosity‐variation parameter and viscous dissipation parameter.

MHD flow in this geometry with temperature dependent viscosity is absent in the literature. IN this paper, the results obtained from the numerical simulations have been verified by two methodologies.

To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal boundary conditions with one cylinder heated isothermally while the other cylinder is kept at the inlet fluid temperature.

A finite‐difference algorithm has been developed to solve the bipolar boundary‐layer equations for the conjugate laminar free convection heat transfer in vertical eccentric annuli.

Numerical results are presented for a fluid of Prandtl number, Pr=0.7 in eccentric annuli. The geometry parameters of NR₂ and E (the fluid‐annulus radius ratio and the eccentricity, respectively) have considerable effects on the results.

Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.

The paper presents results that are not available in the literature for the problem of conjugate laminar free convection in open‐ended vertical eccentric annular channels. Geometry effects having been investigated by considering fluid annuli having radii ratios NR₂=0.1 and 0.3, 0.5 and 0.7 and four values of the eccentricity E=0.1, 0.3, 0.5 and 0.7. Moreover, practical ranges of the solid‐fluid conductivity ratio (KR) and the wall thicknesses that are commonly available in pipe standards have been investigated. Such results are very much needed for design purposes of heat transfer equipment.

The laminar mixed convection boundary‐layer flow of a micropolar fluid past a horizontal circular cylinder in a stream flowing vertically upwards has been studied in both cases of a heated and cooled cylinder. The solutions for the flow and heat transfer characteristics are evaluated numerically for different parameters, such as the mixed convection parameter λ, the material parameter K (vortex viscosity parameter) and the Prandtl number Pr=1 and 6.8, respectively. It is found, as for the case of a Newtonian fluid considered for Pr=1, that heating the cylinder delays separation and can, if the cylinder is warm enough, suppress it completely. Cooling the cylinder, on the other side, brings the separation point nearer to the lower stagnation point and for sufficiently cold cylinder there will not be a boundary‐layer on the cylinder. This model problem may solve industrial problems with processing of polymeric liquids, lubricants and molten plastics.

The purpose of this paper is to provide the current state of the art in the development of a computer code combining an immersed boundary method with a conjugate heat transfer (CHT) approach, including some new findings. In particular, various treatments of the fluid-solid-interface conditions are compared in order to determine the most accurate one. Most importantly, the method is capable of computing a challenging three dimensional compressible turbulent flow past an air cooled turbine vane.

The unsteady Reynolds-averaged Navier–Stokes (URANS) equations are solved within the fluid domain, whereas the heat conduction equation is solved within the solid one, using the same spatial discretization and time-marching scheme. At the interface boundary, the temperatures and heat fluxes within the fluid and the solid are set to be equal using three different approximations.

This work provides an accurate and efficient code for solving three dimensional CHT problems, such as the flow through an air cooled gas turbine cascade, using a coupled immersed boundary (IB) CHT methodology. A one-to-one comparison of three different interface-condition approximations has shown that the two multidimensional ones are slightly superior to the early treatment based on a single direction and that the one based on a least square reconstruction of the solution near the IB minimizes the oscillations caused by the Cartesian grid. This last reconstruction is then used to compute a compressible turbulent flow of industrial interest, namely, that through an air cooled gas turbine cascade. Another interesting finding is that the very promising approach based on wall functions does not combine favourably with the interface conditions for the temperature and the heat flux. Therefore, current and future work aims at developing and testing appropriate temperature wall functions, in order to further improve the accuracy – for a given grid – or the efficiency – for a given accuracy – of the proposed methodology.

An accurate and efficient IB CHT method, using a state of the art URANS parallel solver, has been developed and tested. In particular, a detailed study has elucidated the influence of different interface treatments of the fluid-solid boundary upon the accuracy of the computations. Last but not least, the method has been applied with success to solve the well-known CHT problem of compressible turbulent flow past the C3X turbine guide vane.