F. S. Ibrahim

Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet

In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter NR, and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.

Forced Convection Heat Transfer on a Flat Plate Embedded in Porous Media for Power-Law Fluids

The effect of the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate to power-law non- Newtonian fluid-saturated porous medium, has been investigated. Numerical results are presented for the distribution of velocity and temperature profiles within the boundary layer. The effects of the flow index, first-order and second-order resistance on the velocity, and temperature profiles are discussed. The missing wall values of the velocity and thermal functions are tabulated.

Influence of variable permeability on combined convection along a nonisothermal wedge in a saturated porous medium

Mixed convection along a vertical nonisothermal wedge embedded in a fluid-saturated porous media incorporating the variation of permeability and thermal conductivity is studied. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter ζ and a pseudo-similarity variable η are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter ζ=[1+(Rax/Pex)1/2]−1 from pure forced convection (ζ=1) to pure free convection (ζ=0). The problem is solved using nonsimilarity solution for the case of variable wall temperature. Velocity and temperature profiles as well as local Nusselt number are presented. The wedge angle geometry parameter is ranged from 0 to 1.

Mixed convection-radiation interaction in boundary-layer flow over horizontal surfaces

The effect of buoyancy forces and thermal radiation on the steady laminar plane flow over an isothermal horizontal flat plate is investigated within the framework of first-order boundary-layer theory, taking into account the hydrostatic pressure variation normal to the plate. The fluid considered is a gray, absorbing-emitting but nonscattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Both a hot surface facing upward and a cold surface facing downward are considered in the analysis. Numerical results for the local Nusselt number, the local wall shear stress, the local surface heat flux, as well as the velocity and temperature distributions are presented for gases with a Prandtl number of 0.7 for various values of the radiation-conduction parameter, the buoyancy parameter, and the temperature ratio parameter.

Local nonsimilarity solutions for mixed convection boundary layer flow of a micropolar fluid on horizontal flat plates with variable surface temperature

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid over a semi-infinite horizontal flat plate with nonuniform surface temperatures. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter @x and a pseudo-similarity variable @h are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The mixed convection parameter is chosen to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameter, the exponent for the power-law variation in wall temperature and the nonsimilar mixed convection parameter are considered. The micropolar fluids are observed to display drag reduction and reduce surface heat transfer rate when compared to Newtonian fluid. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress. The local heat transfer rate is found to increase with increase in the exponent value of the power-low variation in wall temperature.

Non‐Darcy mixed convection flow along a vertical plate embedded in a non‐Newtonian fluid saturated porous medium with surface mass transfer

The present analysis investigates the non‐Darcy mixed convection of a non‐Newtonian fluid from a vertical isothermal plate embedded in a homogeneous porous medium, in the presence of surface injection or suction. After a suitable coordinate transformation to reduce the complexity of the governing boundary‐layer equations, the resulting nonlinear, coupled differential equations were solved with an implicit finite difference scheme. The value of mixed convection parameter χ lies between 0 and 1. In addition, the power‐law model is used for non‐Newtonian fluids with exponent n 1 for dilatant fluids. The effects of the mixed‐convection parameter χ, the power‐law viscosity index n, the suction/injection parameter ξ, and the non‐Darcy parameter Re* on the velocity and temperature profiles, and the local Nusselt number are discussed.

Mixed convection over a horizontal plate with vectored mass transfer in a transverse magnetic field

An exact similarity solution is presented for developing mixed convection flows of electrically conducting fluids over a semi-infinite horizontal plate with vectored mass transfer at the wall which are subjected to an applied transverse magnetic field. This solution is given for the case of a wall temperature that is inversely proportional to the square root of the distance from the leading edge. By application of appropriate coordinate transformations, the governing momentum and energy boundary-layer equations are expressed as a set of coupled ordinary differential equations that depend on a magnetic parameter, the buoyancy parameter, and the Prandtl number. The shear stress, the total heat transfer, and the displacement thickness are calculated for different values of both buoyancy and magnetic parameters.

Boundary-Layer Flow in a Porous Medium of a Nanofluid Past a Vertical Cone

The natural convection flow over a surface embedded in saturated porous media is encountered in many engineering problems such as the design of pebble-bed nuclear reactors, ceramic processing, crude oil drilling, geothermal energy conversion, use of fibrous material in the thermal insulation of buildings, catalytic reactors and compact heat exchangers, heat transfer from storage of agricultural products which generate heat as a result of metabolism, petroleum reservoirs, storage of nuclear wastes, etc.

Unsteady mixed convection boundary layer flow along a symmetric wedge with variable surface temperature embedded in a saturated porous medium

Purpose – The purpose of this paper is to study laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past a symmetric wedge embedded in a porous medium in the presence of the first and second orders resistances. Design/methodology/approach – The governing boundary-layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations were solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. The obtained results will be compared with earlier papers on special cases of the problem to examine validity of the method of solution. Findings – The effects of various parameters on the fluid velocity and fluid temperature as well as the wa...

Effect of Variable Viscosity on Vortex Instability of Non-Darcy Mixed Convection Boundary Layer Flow Adjacent to a Nonisothermal Horizontal Surface in a Porous Medium

We study the effect of variable viscosity on the flow and vortex instability for non-Darcy mixed convection boundary layer flow on a nonisothermal horizontal plat surface in a saturated porous medium. The variation of viscosity is expressed as an exponential function of temperature. The analysis of the disturbance flow is based on linear stability theory. The base flow equations and the resulting eigenvalue problem are solved using finite difference schemes. It is found that the variable viscosity effect enhances the heat transfer rate and destabilizes the flow for liquid heating, while the opposite trend is true for gas heating.