Dulal Pal

Mixed convection heat transfer in the boundary layers on an exponentially stretching surface with magnetic field

An analysis has been carried out to describe mixed convection heat transfer in the boundary layers on an exponentially stretching continuous surface with an exponential temperature distribution in the presence of magnetic field, viscous dissipation and internal heat generation/absorption. Approximate analytical similarity solutions of the highly non-linear momentum and energy equations are obtained. The present results are found to be in excellent agreement with previously published work on various special cases of the problem. Numerical results for temperature distribution and the local Nusselt number have been obtained for different values of the governing parameters. The numerical solutions are obtained by considering an exponential dependent stretching velocity and prescribed boundary temperature on the flow directional coordinate. The effects of various physical parameters like Prandtl number, Hartman number, Grashof number on dimensionless heat transfer characteristics are discussed in detail. In particular, it has been found that increase in Prandtl number decreases the skin-friction coefficient at the stretching surface, while increase in the strength of the magnetic field leads to increase in the local Nusselt number.

Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge

An analysis has been carried out to study heat transfer characteristics of an incompressible Newtonian electrically conducting and heat generating/absorbing fluid having temperature-dependent viscosity over a non-isothermal wedge in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The wedge surface is assumed to be permeable so as to allow for possible wall suction or injection. The effects of viscous dissipation, Joule heating, stress work and thermal radiation are included in the model. The governing differential equations are derived and transformed using a non-similarity transformation. The transformed equations are solved numerically by applying a fifth-order Runge-Kutta-Fehlberg scheme with shooting technique. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity and temperature profiles for a prescribed magnetic field parameter as well as the development of the local skin-friction coefficient and local Nusselt number with the magnetic field and radiation parameters are presented graphically and in tabulated form to elucidate the influence of the various physical parameters.

Flow and heat transfer of nanofluids at a stagnation point flow over a stretching/shrinking surface in a porous medium with thermal radiation

Abstract In this paper, the effects of thermal radiation and viscous dissipation on a stagnation point flow and heat transfer over a flat stretching/shrinking surface in nanofluids are analyzed. The effects of suction/injection are also considered. Using a similarity transformation, the governing equations are transformed into a system of nonlinear ordinary differential equations. The resulting system is then solved numerically by Runge–Kutta–Fehlberg method with shooting technique. It is observed that the local Nusselt number increases with increment in the suction/injection parameter for stretching sheet whereas reverse effect is observed for shrinking sheet. It is found that skin-friction coefficient increases for both stretching/shrinking sheet with increase in volume fraction of the nanoparticles.

Hall current and MHD effects on heat transfer over an unsteady stretching permeable surface with thermal radiation

The influence of Hall current and thermal radiation on flow and heat transfer characteristics in a viscous fluid over an unsteady stretching permeable surface is studied in this paper. The unsteadiness in the flow and temperature fields is because of the time-dependent stretching velocity and surface temperature. Similarity transformations are used to convert the governing time dependent nonlinear boundary layer equations for momentum and thermal energy to a system of nonlinear ordinary differential equations. These equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method and analytically by differential transform method with Pade approximants (DTM-Pade). Comparison of the numerical results and analytical solutions (based on DTM-Pade approximant) is made with the earlier published results. The effects of the unsteadiness parameter, thermal radiation, Hall effects, suction/injection parameter and non-uniform heat source/sink parameter on flow and heat transfer characteristics as well as on the local Nusselt number are shown graphically.

Soret and Dufour effects on MHD convective-radiative heat and mass transfer of nanofluids over a vertical non-linear stretching/shrinking sheet

A numerical investigation is applied to study the influence of the Soret and Dufour effect on mixed convection heat and mass transfer of nanofluids in the boundary layer region over a non-linear stretching and shrinking sheets in the presence of thermal radiation. The governing differential equations are solved numerically using a fifth-order Runge-Kutta-Fehlberg integration scheme with a shooting technique. The influence of mixed convection parameter, Soret and Dufour number, magnetic field and thermal radiation parameters on velocity, temperature and concentration fields as well as on the skin-friction coefficient, local Nusselt number and local Sherwood number are illustrated graphically for three types of metallic or nonmetallic nanoparticles, namely copper (Cu), alumina (Al2O3) and titanium dioxide (TiO2) in the base fluid water in order to show some interesting phenomena. The obtained results show appreciable effects of Soret and Dufour numbers i.e. the effects of increase in Soret number (or decrease in Dufour number) decrease the skin-friction coefficient and Nusselt number for shrinking sheet, whereas the reverse effects are found for stretching sheet.

Heat Transfer due to Magnetohydrodynamic Stagnation-Point Flow of a Power-Law Fluid towards a Stretching Surface in the Presence of Thermal Radiation and Suction/Injection

An analysis is made on the study of two-dimensional MHD (magnetohydrodynamic) boundary-layer stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point in the presence of thermal radiation and suction/injection. The paper examines heat transfer in the stagnation-point flow of a power-law fluid except when the ratio of the free stream velocity and stretching velocity is equal to unity. The governing partial differential equations along with the boundary conditions are first brought into a dimensionless form and then the equations are solved by Runge-Kutta fourth-order scheme with shooting techniques. It is found that the temperature at a point decreases/increases with increase in the magnetic field when free stream velocity is greater/less than the stretching velocity. It is further observed that for a given value of the magnetic parameter , the dimensionless rate of heat transfer at the surface and decreases/increases with increase in the power-law index . Further, the temperature at a point in the fluid decreases with increase in the radiation parameter when free stream velocity is greater/less than the stretching velocity.

Effectiveness of convection-radiation interaction on stagnation-point flow of nanofluids past a stretching/shrinking sheet with viscous dissipation

In this paper, a numerical model is developed to study mixed convection heat transfer on a stagnation-point flow over a stretching/shrinking sheet in nanofluids in the presence of thermal radiation and viscous dissipation. Three types of nanofluids, namely copper-water, alumina-water, and titanium dioxide-water are considered. It is observed that the local buoyancy parameter, effective Prandtl number, and internal heat generation/absorption give some interesting and significant results on the skin-friction coefficient and local Nusselt number for all three types of nanofluids. It is found that the variation in the suction/injection parameter plays an important role in having dual solutions.

Effects of hall current and chemical reaction on oscillatory mixed convection-radiation of a micropolar fluid in a rotating system

This article is concerned with the analysis of the effects of thermal radiation on oscillatory mixed convection flow of a micropolar fluid in a rotating frame of reference in the presence of transverse magnetic field and Hall current. The influence of a first-order homogeneous chemical reaction and heat source effects is also analyzed. The governing partial differential equations with the appropriate boundary conditions are reduced to a set of ordinary differential equations using similarity transformations. The dimensionless governing equations for this investigation are solved analytically after using small perturbation approximation. The effects of various parameters on the velocity, temperature, and concentration fields as well as on skin-friction coefficient, Nusselt number, and Sherwood number with their amplitude and phase are discussed in detail. Numerical results are discussed with the help of graphs and tables. Present results are also compared with previously published work.

Perturbation technique for unsteady MHD mixed convection periodic flow, heat and mass transfer in micropolar fluid with chemical reaction in the presence of thermal radiation

An analytical study is presented for the problem of unsteady hydromagnetic heat and mass transfer for a micropolar fluid bounded by semi-infinite vertical permeable plate in the presence of first-order chemical reaction, thermal radiation and heat absorption. A uniform magnetic field acts perpendicularly to the porous surface which absorbs the micropolar fluid with a time-dependent suction velocity. The basic partial differential equations are reduced to a system of nonlinear ordinary differential equations which are solved analytically using perturbation technique. Numerical calculations for the analytical expressions are carried out and the results are shown graphically. The effects of the various dimensionless parameters related to the problem on the velocity, angular velocity, temperature and concentration fields are discussed in detail.

MHD Mixed Convection Stagnation-Point Flow of a Micropolar Fluid in a Porous Medium Towards a Heated Stretching Sheet with Thermal Radiation

Abstract The present investigation is concerned with the study of heat and mass transfer characteristics on MHD boundary layer flow of an electrically conducting micropolar fluid over a non-isothermal stretching sheet embedded in a porous medium of variable thermal conductivity by applying prescribed heat flux for the heating processes. The thermal boundary layer equation takes into account of Ohmic dissipation due to transverse magnetic and electric fields. The governing system of partial differential equations is transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed non-linear coupled differential equations are linearized by quasi-linearization method and then solved very efficiently by finite-difference method. Attention has been focused to study the effects of various physical parameters on velocity, temperature and concentration in the boundary layer. Numerical data for the local skin friction coefficient, surface temperature and surf...