Similarity solutions for flow and heat transfer of non-Newtonian fluid over a stretching surface

Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

Magnetic convection heat transfer in an open ended enclosure filled with paramagnetic fluids

Numerical simulations of thermomagnetic convection of paramagnetic fluids placed in a micro-gravity condition (g nearly 0) and under a uniform vertical gradient magnetic field in an open ended square enclosure with ramp heating temperature condition applied on a vertical wall is investigated in this study. In presence of the strong magnetic gradient field thermal convection of the paramagnetic fluid might take place even in a zero-gravity environment as a direct consequence of temperature differences occurring within the fluid. The thermal boundary layer develops adjacent to the hot wall as soon as the ramp temperature condition is applied on it. There are two scenario that can be observed based on the ramp heating time. The steady state of the thermal boundary layer can be reached before the ramp time is finished or vice versa. If the ramp time is larger than the quasi-steady time then the thermal boundary layer is in a quasi-steady mode with convection balancing conduction after the quasi-steady time. Further increase of the heat input simply accelerates the flow to maintain the proper thermal balance. Finally, the boundary layer becomes completely steady state when the ramp time is finished. Effects of magnetic Rayleigh number, Prandtl number and paramagnetic fluid parameter on the flow pattern and heat transfer are presented.

Heat transfer analysis of viscous incompressible fluid by combined natural convection and radiation in an open cavity

The effect of radiation on natural convection of Newtonian fluid contained in an open cavity is investigated in this study. The governing partial differential equations are solved numerically using the Alternate Direct Implicit method together with the Successive Over Relaxation method. The study is focused on studying the flow pattern and the convective and radiative heat transfer rates are studied for different values of radiation parameters namely, the optical thickness of the fluid, scattering albedo, and the Planck number. It was found that in the optically thin limit, an increase in the optical thickness of the fluid raises the temperature and radiation heat transfer of the fluid. However, a further increase in the optical thickness decreases the radiative heat transfer rate due to increase in the energy level of the fluid, which ultimately reduces the total heat transfer rate within the fluid.

CFD simulations of flow and heat transfer through the porous interface of a metal foam heat exchanger

This paper offers numerical modelling of a waste heat recovery system. A thin layer of metal foam is attached to a cold plate to absorb heat from hot gases leaving the system. The heat transferred from the exhaust gas is then transferred to a cold liquid flowing in a secondary loop. Two different foam PPI (Pores Per Inch) values are examined over a range of fluid velocities. Numerical results are then compared to both experimental data and theoretical results available in the literature. Challenges in getting the simulation results to match those of the experiments are addressed and discussed in detail. In particular, interface boundary conditions specified between a porous layer and a fluid layer are investigated. While physically one expects much lower fluid velocity in the pores compared to that of free flow, capturing this sharp gradient at the interface can add to the difficulties of numerical simulation. The existing models in the literature are modified by considering the pressure gradient inside and outside the foam. Comparisons against the numerical modelling are presented. Finally, based on experimentally-validated numerical results, thermo-hydraulic performance of foam heat exchangers as waste heat recovery units is discussed with the main goal of reducing the excess pressure drop and maximising the amount of heat that can be recovered from the hot gas stream.

Natural convection heat transfer in a baffled triangular enclosure

To reduce the natural convection heat loss from enclosures many researchers used convection suppression devices in the past. In this study a single baffle is used under the top tip to investigate numerically the natural convection heat loss in an attic shaped enclosure which is a cost effective approach. The case considered here is one inclined wall of the enclosure is uniformly heated while the other inclined wall is uniformly cooled with adiabatic bottom wall. The finite volume method has been used to discretize the governing equations, with the QUICK scheme approximating the advection term. The diffusion terms are discretized using central-differencing with second order accuracy. A wide range of governing parameters are studied (Rayleigh number, aspect ratio, baffle length etc.). It is observed that the heat transfer due to natural convection in the enclosure reduces when the baffle length is increased. Effects of other parameters on heat transfer and flow field are described in this study.

Numerical study of turbulent fluid flow and heat transfer in lateral perforated extended surfaces

Numerical study has been performed in this study to investigate the turbulent convection heat transfer on a rectangular plate mounted over a flat surface. Thermal and fluid dynamic performances of extended surfaces having various types of lateral perforations with square, circular, triangular and hexagonal cross sections are investigated. RANS (Reynolds averaged Navier–Stokes) based modified k–ω turbulence model is used to calculate the fluid flow and heat transfer parameters. Numerical results are compared with the results of previously published experimental data and obtained results are in reasonable agreement. Flow and heat transfer parameters are presented for Reynolds numbers from 2000 to 5000 based on the fin thickness.

Transition to an unsteady flow induced by a fin on the sidewall of a differentially heated air-filled square cavity and heat transfer

The transition from a steady to an unsteady flow induced by an adiabatic fin on the sidewall of a differentially heated air-filled cavity is numerically investigated. Numerical simulations have been performed over the range of Rayleigh numbers from Ra = 105–109. The temporal development and spatial structures of natural convection flows in the cavity with a fin are described. It has been demonstrated that the fin may induce the transition to an unsteady flow and the critical Rayleigh number for the occurrence of the transition is between 3.72 × 106 and 3.73 × 106. Furthermore, the peak frequencies of the oscillations triggered by different mechanisms are obtained through spectral analysis. It has been found that the flow rate through the cavity with a fin is larger than that without a fin under the unsteady flow, indicating that the fin may improve the unsteady flow in the cavity.

Radiation effects on natural convection laminar flow from a horizontal circular cylinder

The effect of radiation on natural convection flow from an isothermal circular cylinder has been investigated numerically in this study. The governing boundary layer equations of motion are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are reduced to convenient boundary layer equations, which are then solved numerically by two distinct efficient methods namely: (i) implicit finite differencemethod or the Keller-Box Method (KBM) and (ii) Straight Forward Finite Difference Method (SFFD). Numerical results are presented by velocity and temperature distribution 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 surface heating parameter and radiation-conduction parameter. Due to the effects of the radiation the skin-friction coefficients as well as the rate of heat transfer increased and consequently the momentum and thermal boundary layer thickness enhanced.

The effect of temperature dependent viscosity on MHD natural convection flow from an isothermal sphere

Laminar magnetohydrodynamic (MHD) natural convection flow from an isothermal sphere immersed in a fluid with viscosity proportional to linear function of temperature has been studied. 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, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distribution, streamlines and isotherms of the fluid as well as heat transfer characteristics, namely the local skin-friction coefficients and the local heat transfer rate for a wide range of magnetohydrodynamic paramagnet and viscosity-variation parameter.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) 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 magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat and mass flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. For smooth integrations the boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation as well as the free variable formulation. The nonsimilar parabolic partial differential equations are integrated numerically for Pr ≪1 that is appropriate for liquid metals against the local Hartmann parameter ξ . Further, asymptotic solutions are obtained near the leading edge using regular perturbation method for smaller values of ξ . Solutions for values of ξ ≫ 1 are also obtained by employing the matched asymptotic technique. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10:0.

Natural convection due to differential heating of inclined walls and heat source placed on bottom wall of an attic shaped space

Numerical investigation of free convection heat transfer in an attic shaped enclosure with differentially heated two inclined walls and filled with air is performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is uniformly cooled. There is a heat source placed on the right side of the bottom surface. Rest of the bottom surface is kept as adiabatic. Finite volume based commercial software ANSYS 15 (Fluent) is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 103 to 106, heater size from 0.2 to 0.6, heater position from 0.3 to 0.7 and aspect ratio from 0.2 to 1.0 with a fixed Prandtl number of 0.72. Outcomes have been reported in terms of temperature and stream function contours and local Nusselt number for various Ra, heater size, heater position, and aspect ratio. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement.

Non-Newtonian mixed convection flow from a horizontal circular cylinder with uniform surface heat flux

Mixed convection laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is investigated from a horizontal circular cylinder with uniform surface heat flux using a modified power-law viscosity model, that contains no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid temperature distributions, rate of heat transfer in terms of the local Nusselt number.