Variable Surface Heat Flux Research Articles

Effects of viscous dissipation on a power-law fluid over plate embedded in a porous medium

The present study is devoted to investigate the influences of viscous dissipation on buoyancy induced flow over a horizontal or a vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface temperature (PT) or with prescribed variable surface heat flux (PHF) for the horizontal plate case. While, the similarity solutions are obtained with prescribed variable surface heat flux for the vertical plate case. Different similar transformations, for each case, are used. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Nusselt number associated with temperature distributions and excess surface temperature associated with heat flux distributions which are entered in tables have been presented for different values of the power-law index n and the exponent λ as well as Eckert number.

Combined effect of magnetic field and viscous dissipation on a power-law fluid over plate with variable surface heat flux embedded in a porous medium

An analysis is presented to investigate the influences of viscous dissipation on buoyancy-induced flow over (a horizontal or a vertical flat plate) embedded in a non-Newtonian fluid saturated porous medium under the action of a transverse magnetic field. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface heat flux, for each position of the plate. Numerical results for the details of the velocity and temperature profiles are shown on graphs, for the two cases horizontal and vertical plate, for different values of the magnetic field parameter, power-law index n and the exponent λ as well as the Eckert number. Values of the excess surface temperature which are entered in tables or plotted in figures have been presented for different values of the different parameters, for the two cases, horizontal and vertical plate.

Variable permeability effects on mixed convection along a vertical wedge embedded in a porous medium with variable surface heat flux

The problem of mixed convection from impermeable vertical wedge in a fluid saturated porous medium incorporating the variation of permeability and thermal conductivity is analyzed. A nonsimilarity solution is obtained for the case of variable surface heat flux in the form q w ( x)= bx m . The entire mixed convection regime is covered by the single nonsimilarity parameter ξ=[1+( Ra x / Pe x 3/2) 1/3] −1 from pure forced convection ( ξ=1) to pure free convection ( ξ=0). A finite-difference scheme was used to solve the system of transformed governing equations. Velocity and temperature profiles, and local Nusselt number are presented. The wedge angle geometry parameter is ranged from 0 to 1.

The mixed convection along a vertical plate embedded in non-Darcian porous medium with suction and injection

The effect of surface mass flux on mixed convection along a vertical plate embedded in porous medium is studied. The solutions are obtained for the case of variable surface heat flux in the form q ω ( x)= Ax n . A finite difference scheme was used to solve the system of transformed governing equations. Velocity and temperature profiles increase as the mixed convection parameter increases. As n increases, the velocity decreases and temperature increases. The dimensionless wall shear stress increases and the temperature decreases as the mixed convection parameter increases.

The mixed convection along a vertical plate with variable surface heat flux embedded in porous medium

An analysis is performed for mixed convection along a vertical plate with variable surface heat flux embedded in a non-Darcian porous medium. The non-Darcian convective, boundary viscous and inertia effects are all considered. A finite difference scheme was used to solve the system of transformed governing equations. The results indicate that the non-Darcian effects decrease the velocity and increase the temperature. As the mixed convection parameter increases, the dimensionless wall shear stress increases and the wall temperature decreases.

Laminar flow and heat transfer of non-newtonian falling liquid film on a horizontal tube with variable surface heat flux

An analysis is performed to study the laminar flow and heat transfer of non-Newtonian falling liquid film on a horizontal tube for the case of variable surface heat flux. The inertia and convection terms are taken into account. The governing boundary layer equations are solved numerically using an implicit finite difference method. Of particular interest are the effects of the mass flow rate Γ, the concentration C of carboxymethylcellulose (CMC) solutions, the exponent m for the power-law surface heat flux, and the tube diameter D on the film thickness profiles, as well as on the local and average Nusselt numbers. It was found that an increase in the mass flow rate Γ and exponent value m increases the local and average heat transfer rates. Finally, the present simulation is found to be in good agreement with previous experimental and numerical results for Newtonian films.

Combined convection in non-Newtonian fluids along a nonisothermal vertical plate in a porous medium with lateral mass flux

A boundary layer analysis has been presented for interaction of combined convection from vertical surface in a porous medium saturated with a power-low type non-Newtonian fluid with presence suction and injection. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The effect of fluid suction/injection on the heat transfer rate is discussed.

Mass transfer effects on the non-Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux

The present study is devoted to investigate the influences of mass transfer on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solution for the transformed governing equations is obtained with prescribed variable surface heat flux. Numerical results for the details of the velocity, temperature and concentration profiles are shown on graphs. Excess surface temperature as well as concentration gradient at the wall associated with heat flux distributions, which are entered in tables, have been presented for different values of the power-law index n, buoyancy ration B and the exponent λ as well as Lewis number Le.

Thermal Dispersion Effects on Combined Convection in Non-Newtonian Fluids Along a Nonisothermal Vertical Plate in a Porous Medium

The method of non-similarity solution is used to study the influence of thermal dispersion on combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented.

Mixed convection cooling of a heated, continuously stretching surface

An numerical study of the flow and heat transfer characteristics associated with a heated, continuously stretching surface being cooled by a mixed convection flow has been carried out. The relevant heat transfer mechanisms are of interest in a wide variety of practical applications, such as hot rolling, continuous casting, extrusion, and drawing. The surface velocity of the continuously stretching sheet was assumed to vary according to a power-law form, that is, u w (x)=Cx p . Two conditions of surface heating were considered, a variable wall temperature (VWT) in the form T w (x)−T ∞=Ax n and a variable surface heat flux (VHF) in the form q w (x)=Bx m . The governing differential equations are transformed by introducing proper nonsimilarity variables and solved numerically using a procedure based on finite difference approximations. Results for the local Nusselt number and the local friction coefficient are obtained for a wide range of governing parameters, such as the surface velocity parameter p, the wall temperature exponent n, the surface heat flux exponent m, the buoyancy force parameters (ξ for the VWT case and χ for the VHF case), and Prandtl number of the fluid. It is found that the local Nusselt number is increased with increasing the velocity exponent parameter p for the VWT case, while the opposite trend is observed for the VHF case. The local friction coefficient is increased for a decelerated stretching surface, while it is decreased for an accelerated stretching surface. Also, appreciable effects of the buoyancy force on the local Nusselt number and the local friction coefficient are observed for both VWT and VHF cases, as expected.

Combined convection in non‐Newtonian fluids along a nonisothermal vertical plate in a porous medium

The problem of combined convection from vertical surfaces in a porous medium saturated with power‐law type non‐Newtonian fluids along a non‐isothermal vertical plate is investigated. The transformed conservation laws were solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented.

Nonsimilar Solutions for Mixed Convection in Non-Newtonian Fluids Along a Wedge with Variable Surface Heat Flux in a Porous Medium

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non Newtonian fluids along a vertical wedge with variable wall temperature distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Mixed convection in non-Newtonian fluids along a vertical plate with variable surface heat flux in a porous medium

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along a vertical plate with power-law surface heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Mass transfer effects on impulsively with variable surface heat flux

Numerical Solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with variable surface heat flux and mass transfer is presented here. The governing equations are solved using implicit finite-difference scheme of Crank-Nicolson type. The velocity profiles are compared with exact Solution and are found to be in good agreement. The transient and steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that there is a rise in the velocity due to the presence of a mass diffusion. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.

Heat transfer over a stretching surface with variable surface heat flux

Heat transfer over a stretching surface with variable surface heat flux and uniform surface heat flux subject to injection and suction is examined. The boundary layer equations are transformed to ordinary differential equations, containing an injection parameter I, velocity exponent parameter M, heat flux exponent parameter and Prandtl number . The effect of these parameters is studied. Suction increases the heat transfer from the surface, whereas injection causes a decrease in the heat transfer.

Mixed convection heat transfer from a horizontal plate with variable surface heat flux in a porous medium

In this article nonsimilarity solution for mixed convection from a horizontal surface in a saturated porous medium was obtained for the case of variable surface heat flux. The entire mixed convection regime, ranging from pure forced convection to pure free convection, is considered by introducing a single nonsimilarity parameter. Heat transfer results are predicted by employing four different flow models, namely, Darcy's law, the Ergun model, and the Brinkman-Forchheimer-extended Darcy model with constant and variable porosity. The variable porosity effect is approximated by an exponential function. Effects of transverse thermal dispersion are taken into consideration in the energy equation, along with variable stagnant thermal conductivities. The formulation of the present problem shows that the flow and heat transfer characteristics depend on five parameters, that is, the power in the variation of surface heat flux, the nonsimilarity mixed-convection parameter, the inertia effect parameter, the boundary effect parameter, and the ratio of thermal conductivity of the fluid phase to that of the solid phase. Numerical results for the local Nusselt number variations, based on the various flow models, are presented for the entire mixed convection regime. The impacts␣of different governing parameters on the heat transfer results are thoroughly investigated.

Non-Darcy mixed convection from a vertical plate in saturated porous media-variable surface heat flux

Nonsimilarity solutions for non-Darcy mixed convection from a vertical impermeable surface embedded in a saturated porous medium are presented for variable surface heat flux (VHF) of the power-law form. The entire mixed convection region is divided into two regimes. One region covers the forced convection dominated regime and the other one covers the natural convection dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finite-difference scheme. Computations are based on Keller Box method and a tolerance of iteration of 10−5 as a criterion for convergence.

Darcian mixed convection along slender vertical cylinders with variable surface heat flux embedded in a porous medium

The problem of mixed convection flow along a vertical slender circular cylinder with variable surface heat flux embedded ina fluid-porous medium has been studied. The effects of mixed convection, surface curvature and buoyancy parameters are analyzed for the case of power-law variation in surface heat flux. The numerical solution of the transformed governing equations has been obtained using the Keller box method to demonstrate the important influence of these parameters on the flow and heat transfer characteristics

MIXED CONVECTION BOUNDARY LAYER FLOW OF A MICROPOLAR FLUID ON A HORIZONTAL PLATE

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid past a semi-infinite horizontal fiat plate with variable surface heat flux. A nonsimilar mixed convection parameter £ and a pseudosimilarity variable v are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using the finite difference method. A single mixed convection parameter is used to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameters, the power-law variation of surface heat flux, nonsimilar mixed convection parameter and Prandtl number are considered. The micropolar fluids are observed to display drag reduction and reduced surface heat transfer rate when compared to Newtonian fluids. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress.

Nonsimilarity solutions for non-Darcy mixed convection from horizontal surfaces in a porous medium

Non-Darcy mixed convection in a porous medium from horizontal surfaces with variable surface heat flux of the power-law distribution is analyzed. The entire mixed convection regime is divided into two regions. The first region covers the forced convection dominated regime where the dimensionless parameter ζ f =Ra* x /Pe2 x is found to characterize the effect of buoyancy forces on the forced convection with K′U∞/ν characterizing the effect of inertia resistance. The second region covers the natural convection dominated regime where the dimensionless parameter ζ n =Pe x /Ra*1/2 x is found to characterize the effect of the forced flow on the natural convection, with (K′U∞/ν)Ra*1/2 x /Pe x characterizing the effect of inertia resistance. To obtain the solution that covers the entire mixed convection regime the solution of the first regime is carried out for ζ f =0, the pure forced convection limit, to ζ f =1 and the solution of the second is carried out for ζ n =0, the pure natural convection limit, to ζ n =1. The two solutions meet and match at ζ f =ζ n =1, and R* h =G* h .