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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.

This study aims to present an analysis on heat transfer attributes of fluid-particle interaction over a permeable elastic sheet. The fluid streaming on the sheet is Casson fluid (CF) with uniform distribution of dust particles.

The basic steady equations of the CF and dust phases are in the form of partial differential equations (PDEs) which are remodeled into ordinary ones with the aid of similarity transformations. In addition to analytical solution, numerical solution is obtained for the reduced coupled non-linear ordinary differential equations (ODEs) to validate the results.

The solution seems to be influenced by significant physical parameters such as CF parameter, magnetic parameter, suction parameter, fluid particle interaction parameter, Prandtl number, Eckert number and number density. The impact of these parameters on flow field and temperature for both fluid and dust phases is presented in the form of graphs and discussed in detail. The effect on skin friction coefficient and heat transfer rate is also presented in tabular form. It has been observed that an increase in the CF parameter curtails the fluid velocity as well as the particle velocity however enhances the heat transfer rate at the wall. Furthermore, comparison of the numerical and analytical solution is also made and found to be in excellent agreement.

Although the analysis of dusty fluid flow has been widely examined, however, the present study obtained both analytical and numerical results of power law temperature distribution in dusty Casson fluid under the influence of magnetic field which are new and original for such type of flow.

In this paper, temperature distribution and fin efficiency in a moving porous fin have been discussed. The heat transfer equation is formulated by using Darcy's model. Heat transfer coefficient and thermal conductivity vary with temperature. The surface emissivity of the fin varies with temperature as well as with wavelength. Thermal conductivity is taken as a linear and quadratic form of temperature. The entire analysis of the paper is presented in non-dimensional form.

In this study, a new mathematical model is investigated. The novelty of this model is surface emissivity which is considered temperature and wavelength dependent. Another interesting point is the addition of porous material. The Legendre wavelet collocation method has been used to solve the nonlinear heat transfer equation. Numerical simulations are carried out in MATLAB software.

An attempt has been made to discuss temperature distribution in the presence of porosity and wavelength-temperature-dependent surface emissivity. The effect of various parameters on temperature has been discussed, including thermal conductivity, emissivity, convection-radiation, Peclet number, sink temperature, exponent “n” and porosity. Fin efficiency is also calculated for some parameters. According to the study, heat transfer rate increases with higher radiation-convection, emissivity, wavelength and porosity parameters.

The numerical results are carried out by using the Legendre wavelet collocation method, which has been compared with exact results in a particular case and found to be in good agreement. The percent error is calculated to find the error between the current method and the exact result. A comparison of the obtained results with the previous data is presented to validate the numerical results.

This paper aims to discuss the stagnation-point flow and heat transfer for power-law fluid pass through a stretching surface with heat generation effect. Unlike the previous considerations about the research on stagnation-point flow, the process of heat transfer and the convective heat transfer boundary condition use the modified Fourier’s law in which the heat flux is power-law-dependent on velocity gradient.

The similarly transformation is used to convert the governing partial differential equations into a series of ordinary differential equations which are solved analytically by using the differential transform method and the base function method.

The variations of the velocity and temperature fields for different specific related parameters are graphically discussed and analyzed. There is a special phenomenon that all the velocity profiles converge from the initial value of velocity to stagnation parameter values. And the larger power-law index enhancesthe momentum diffusion. A significant phenomenon can be observed that the larger power-law index causes a decline in the heat flux. This influence indicates that the higher viscosity restricts the heat transfer. Furthermore, both velocity gradient and temperature gradient play an indispensable role in the processes of heat transfer.

This paper researches the process of heat transfer of stagnation-point flow ofpower-law magneto-hydro-dynamical fluid over a stretching surface with modified convective heat transfer boundary condition.

The purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.

The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.

As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.

Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

To investigate the forced convection heat transfer to hydrodynamically and thermally fully developed laminar steady flow of power‐law non‐Newtonian fluid in a partially porous square duct.

The modified Brinkmann‐Forchheimer extended Darcy model for power‐law fluids is used in the porous layer. The solutions for the velocity and temperature fields are obtained numerically using the finite volume method. Computations are performed over a range of Darcy number, power‐law indices, porous insert thickness and thermal conductivity ratio.

The average Nusselt number and the Fanning factor, so obtained are found to be in good agreement with the literature. It is highlighted that a heat transfer improvement is obtained when the channel is entirely porous and this enhancement is maximized at low permeability. While depending on the working conditions, heat transfer enhancement can also be obtained by filling partially the duct with the porous insert, even if the conductivity ratio is equal to 1. The results indicate also that the conductivity ratio has a strong impact on the heat transfer enhancement at high permeability, while this impact is significant beyond a critical thickness of the porous layer at low permeability. It is found that both shear‐thinning (n<1) and shear‐thickening (n>1) fluids allow obtaining the highest Nusselt number according to the properties of the porous insert. The presence of the porous insert causes a significant increase in pressure drop. This added pressure drop is found to be more important with shear thickening fluids (n>1).

The results of this paper are valid for square ducts and H1 thermal boundary condition, corresponding to an axially uniform heat flux and peripherally uniform temperature. The inertial effects are neglected in the porous region.

The obtained results can be used in the design of heat exchangers and in the cooling of electronic equipments.

This work investigates some interesting ways to enhance heat transfer in three‐dimensional square ducts by using porous substrates and non‐Newtonian fluids. It is believed that the case studied in this paper has not previously been investigated.

The thermal-diffusion (Soret) and the diffusion-thermo (Dufour) effects play a crucial role in double diffusive mixed convection in a lid-driven cavity; but they have not been studied properly by researchers. The purpose of this paper is to investigate effects of Soret and Dufour parameters on double diffusive laminar mixed convection of shear-thinning and Newtonian fluids in a two-sided lid-driven cavity.

Finite Difference Lattice Boltzmann method (FDLBM) has been applied to solve the complex problem. This study has been conducted for the certain pertinent parameters of Richardson number (Ri=0.00062-1), power-law index (n=0.2-1), Soret parameter (Sr=−5-5) as Dufour number effects have been investigated from Dr=−5 to 5 at Buoyancy ratio of N=1 and Lewis number of Le=5.

Results indicate that the augmentation of Richardson number causes heat and mass transfer to decrease. The fall of the power-law index declines heat and mass transfer at Ri=0.00062 and 0.01 in various Dufour and Soret parameters. At Ri=1, the heat and mass transfer rise with the increment of power-law index for Dr=0 and Sr=0. The least effect of power-law index on heat and mass transfer among the studied Richardson numbers was observed at Ri=1. The positive Dufour numbers augment the heat transfer gradually as the positive Soret numbers enhance the mass transfer. The Dr=−5 and Sr=−5 provokes the negative average Nusselt and Sherwood numbers, respectively, to be generated. The least magnitude of the average Nusselt and Sherwood numbers were obtained at Dr=−1 and Sr=−1, respectively.

Soret and Dufour effects in double diffusive mixed convection has not been studied in a lid-driven cavity. In addition. this study has been conducted also for shear-thinning fluids.

The flow development and heat transfer in a differentially heated cavity containing a non‐Newtonian fluid is studied using CFD techniques. Investigations are made for a fluid obeying a power‐law type behaviour, for a nominal Rayleigh number of 10⁵. Both dilatant and pseudoplastic regimes are considered and the Nusselt number is obtained for a range of power‐law index values. The results, given in a graphical and tabular form, suggest that deviations from Newtonian stress‐strain behaviour can lead to large changes in overall heat transfer. These changes are due to the behaviour of the wall boundary layers. In the dilatant, or shear‐thickening regime, the isothermal wall layers are thick and slow‐moving; as a consequence, buoyancy induced flow affects the whole of the cavity volume. In contrast, the pseudoplastic (or shear‐thinning) regime leads to thin, fast‐moving wall layers whose effect does not propagate to the core of the cavity which remains stagnant. This behaviour, which is directly attributable to the local value of the fluid viscosity, causes the average Nusselt number to decrease with the power‐law index, n. Pseudoplastic fluids are therefore better at conducting heat than Newtonian fluids, and conversely dilatant fluids are worse. The information contained in this paper is of general interest to workers in heat transfer, but is more specifically relevant to researchers in non‐Newtonian fluids. Example applications include biotechnology, where close temperature control of bio‐cultures in enclosed vessels is required, the food processing industry, the metals casting industry and areas where heat transfer in fine suspensions is required.

Heat transfer characteristics of a non‐Newtonian fluid on a power‐law stretched surface with suction or injection were investigated. Similarity solutions of the laminar boundary layer equations describing heat transfer flow in a quiescent fluid were obtained and solved numerically. Temperature profiles as well as the Nusselt number Nu, were obtained for two thermal boundary conditions; namely, uniform surface temperature (b=0) and cooled surface temperature (b=–1), for different governing parameters such as Prandtl number Pr, injection parameter d and power‐law index n. It was found that decreasing injection parameter d and power‐law index n and increasing Prandtl number Pr enhanced the heat transfer coefficient.

The purpose of this paper is to present a boundary layer analysis for the mixed convection past a vertical wedge in a porous medium saturated with a power law type non-Newtonian nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le and the power law exponent n. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

This general non-linear problem cannot be solved in closed form and, therefore, a numerical solution is necessary to describe the physics of the problem. An implicit, tri-diagonal finite-difference method has proven to be adequate and sufficiently accurate for the solution of this kind of problems. Therefore, it is adopted in the present study. Variable step sizes were used. The convergence criterion employed in this study is based on the difference between the current and the previous iterations. When this difference reached 10−5 for all the points in the η directions, the solution was assumed to be converged, and the iteration process was terminated.

The results indicate that as the buoyancy ratio parameter (Nr) and thermophoresis parameter (Nt) increase, the friction factor increases whereas the heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) decrease. As the Brownian motion parameter (Nb) increases, the friction factor and surface mass transfer rates increase whereas the surface heat transfer rate decreases. As Le increases, mass transfer rates increase. As the power law exponent n increases, the heat and mass transfer rates increase.

The analysis is valid for natural convection dominated regime. The combined forced and natural convection dominated regimes will be reported in a future work.

The approach used is useful in optimizing the porous media heat transfer problems in geothermal energy recovery, crude oil extraction, ground water pollution, thermal energy storage and flow through filtering media.

The results of the study may be of some interest to the researchers of the field of porous media heat transfer. Porous foam and microchannel heat sinks used for electronic cooling are optimized utilizing the porous medium. The utilization of nanofluids for cooling of microchannel heat sinks requires understanding of fundamentals of nanofluid convection in porous media.