Chebyshev finite difference method for the effects of variable viscosity and variable thermal conductivity on heat transfer from moving surfaces with radiation

Elbarbary, Elsayed M. E.; Elgazery, Nasser S.

doi:10.1016/j.ijthermalsci.2004.01.008

Cited by 39 publications

(19 citation statements)

References 18 publications

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“…The set of coupled nonlinear ordinary differential equations (12) and (13) with boundary conditions (14) have been solved numerically by using the Chebyshev pseudospectral method (see, for example, Elbarbary and Elgazery [26][27][28] (12)- (14) are transformed into the following Chebyshev pseudospectral equations: …”

Section: Formulation Of the Problemmentioning

confidence: 99%

The effects of variable fluid properties and magnetic field on the flow of non‐Newtonian fluid film on an unsteady stretching sheet through a porous medium

Elgazery

Hassan

2008

Commun. Numer. Meth. Engng.

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SUMMARYThe effects of variable viscosity, variable thermal diffusivity and magnetic field on the flow and heat transfer in a laminar liquid film of non-Newtonian fluid on a horizontal stretching sheet through a porous medium are analyzed. Using a similarity transformation, the governing time-dependent boundary-layer equations for momentum and thermal energy are reduced to a set of coupled nonlinear ordinary differential equations. The resulting seven-parameter problem is solved numerically by using Chebyshev pseudospectral method for some representative value of the parameters. The numerical results show that variable viscosity, variable thermal diffusivity, the upper limit of apparent viscosity according to biviscosity model, the unsteadiness parameter, the magnetic parameter, and the permeability parameter have significant influences on the velocity and temperature profiles, shear stress, and Nusselt number.It is observed that the presence as well as the increase in the unsteadiness parameter S, variable viscosity parameter 1 , the upper limit of apparent viscosity , and the magnetic parameter M lead to decrease in the fluid film thickness ∞ . Also, as film thickness approaches zero as S comes close to the critical value; then, there is no available solution for the problem. The velocity profiles supported this result, since close to this critical value the velocity of the fluid vanishes.

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Section: Formulation Of the Problemmentioning

confidence: 99%

The effects of variable fluid properties and magnetic field on the flow of non‐Newtonian fluid film on an unsteady stretching sheet through a porous medium

Elgazery

Hassan

2008

Commun. Numer. Meth. Engng.

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“…Hassanien et al (2003) expressed mixed convection along a wedge embedded in a fluid saturated porous medium for the cases of uniform heat flux and uniform mass flux by using the effect of variable viscosity and thermal conductivity. The influence of radiation and variable properties of heat transfer from a moving surface in a micropolar fluid through a porous medium was discussed Elsayed et al (2004). Seddeek and Salama (2007) examined unsteady hydromagnetic heat transfer past a semi-infinite vertical porous moving plate with variable suction taking variable viscosity and thermal conductivity effects into account.…”

Section: Introductionmentioning

confidence: 99%

Scaling Group Transformation for Mixed Convection in a Power-Law Fluid Saturated Porous Medium With Effects of Soret, Radiation and Variable Properties

Pranitha¹,

Suman²,

Srinivasacharya³

2017

Frontiers in Heat and Mass Transfer

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An analysis is performed to investigate the influence of radiation, thermal-diffusion and variable properties on mixed convection flow, heat and mass transfer from a vertical plate in a porous medium saturated with a power-law fluid. The non-linear partial differential equations are reduced to ordinary differential equations by implementing Lie scaling group transformations. These ordinary differential equations are solved numerically by implementing a shooting technique. The numerical results for dimensionless velocity, temperature and concentration profiles for pseudo-plastic, Newtonian and dilatant fluids are presented graphically for different values of variable viscosity, variable thermal conductivity, Soret and radiation parameters. Heat and mass transfer results are presented in tabular form. The present numerical results are compared with previously published work and the results are found to be in excellent agreement.

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“…We chose a Cartesian coordinate system with axis along the upward direction and the axis normal to it as shown in Figure 1. Thermal conductivity ( ) of the fluid is assumed to vary as a linear function of temperature in the form (see [20]…”

Section: Introductionmentioning

confidence: 99%

“…, where is the fluid free stream thermal conductivity and is a constant depending on the nature of the fluid, where > 0 for fluids such as water and air, while < 0 for fluids such as lubrication oils (see [20]). The governing equations under Boussinesq's approximation can be written as…”

Section: Introductionmentioning

confidence: 99%

Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

Hamza

Usman²,

Sule³

2015

Journal of Fluids

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Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

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Chebyshev finite difference method for the effects of variable viscosity and variable thermal conductivity on heat transfer from moving surfaces with radiation

Cited by 39 publications

References 18 publications

The effects of variable fluid properties and magnetic field on the flow of non‐Newtonian fluid film on an unsteady stretching sheet through a porous medium

The effects of variable fluid properties and magnetic field on the flow of non‐Newtonian fluid film on an unsteady stretching sheet through a porous medium

Scaling Group Transformation for Mixed Convection in a Power-Law Fluid Saturated Porous Medium With Effects of Soret, Radiation and Variable Properties

Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

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