Free and Forced Convection Flow Past a Cylinder with Slip Boundary Conditions (original) (raw)
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Abstract and Applied Analysis, 2015
The objective of this study is to explore the influence of wall slip condition on a free convection flow of an incompressible viscous fluid with heat transfer and ramped wall temperature. Exact solution of the problem is obtained by using Laplace transform technique. Graphical results to see the effects of Prandtl number Pr, timet, and slip parameterηon velocity and skin friction for the case of ramped and constant temperature of the plate are provided and discussed.
Unsteady forced convection laminar boundary layer flow over a moving longitudinal cylinder
Acta Mechanica, 1992
The unsteady nonsimilar forced convection flow over a longitudinal cylinder, which is moving in the same or in the opposite direction to the free stream, has been investigated. The unsteadiness is due to the free stream velocity, cylinder velocity, surface temperature of the cylinder and the mass transfer, and nonsimilarity is due to the transverse curvature. The partial differential equations, governing the flow, have been solved numerically, using an implicit finite-difference scheme in combination with a quasilinearization technique. The results show that both, skin friction and heat-transfer, are appreciably affected by the free stream velocity distributions and by the cylinder velocity. Also, skin friction as well as heat-transfer are found to increase as the transverse curvature or the suction increases, but the effect of injection is just the opposite. The heat-transfer is significantly affected by the viscous dissipation and variation of surface temperature with time. It is observed that results of this problem are crucially dependent on the parameter c~, which is the ratio of the velocity of the cylinder to the velocity of the free stream. In particular, it is found that solutions for the upstream moving cylinder exist only for a certain range of this parameter (c0, and they are nonunique in a small range of c~ too.
Aim of this paper is to investigate the boundary layer flow and heat transfer of unsteady laminar free convection flow past a semi-infinite isothermal vertical cylinder immersed in air. The fluid viscosity is adopted to vary the temperature. An explicit finite difference method has been devoted to solve the governing non-dimensional boundary layer equations. A parametric study is accomplished to interpret the influence of variable viscosity on the velocity and temperature profiles. The numerical consequences disclose that the viscosity has significant influence on transient velocity and temperature profiles, average skin friction coefficient and average heat transfer rate. The conclusion indicates that when the viscosity parameter increases the temperature and skin friction coefficient increases but the velocity near the wall and Nusselt number decreases. We have also shown the effect of viscosity variation parameter on isotherms and streamlines.
Thermal Science, 2020
The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite dif?ference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are exam?ined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and cur?rent density for various emerging parameters magnetic force parameter, ?, mixed convection parameter, ?, magnetic Prandtl number, ?, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each ...
Boundary-Layer Separations of Mixed Convection Flow Past an Isothermal Circular Cylinder
International Journal of Applied and Computational Mathematics, 2019
This study reveals the boundary-layer separations of unsteady mixed convection flow of incompressible fluid past a circular cylinder which is kept at a constant temperature. The governing equations are made dimensionless using an appropriate transformation. These equations are solved with the use of finite difference method. We also solve the problem using perturbation method for small time and local non-similarity method for long time. Results show that numerical solutions agree well with the series solutions obtained by perturbation method for small time and asymptotic method for long time. For an increase of Richardson number and Prandtl number, the local friction factor and the rate of heat transfer increases. Besides, the streamlines and isotherms reveal that when the Richardson number and the Prandtl number are increased, the point of separation of boundary-layer reduces and the size of vortex decreases. Moreover, the larger values of Richardson number thicken the thermal boundary layer whereas the reverse characteristic is observed for higher Prandtl numbers.
Korean Journal of Chemical Engineering, 2008
A numerical analysis is performed to study the influence of temperature-dependent viscosity and Prandtl number on unsteady laminar free convection flow over a vertical cylinder. The governing boundary layer equations are converted into a non-dimensional form and a Crank-Nicolson type of implicit finite-difference method is used to solve the governing non-linear set of equations. Numerical results are obtained and presented for different viscosityvariation parameters and Prandtl numbers. Transient effects of velocity and temperature are analyzed. The heat transfer characteristics against the viscosity-variation parameter are analyzed with the help of average skin-friction and Nusselt number and are shown graphically.
Slip effects on unsteady free convective heat and mass transfer flow with Newtonian heating
Thermal Science, 2016
This article investigates the effects of slip condition on free convection flow of viscous incompressible fluid past an oscillating vertical plate with Newtonian heating and constant mass diffusion. The governing equations together with imposed initial and boundary conditions are solved using the Laplace transform technique. The results for velocity, temperature and concentration are obtained and plotted for the embedded parameters. The results for skin friction, Nusselt number and Sherwood number are computed in table. It is investigated that the presence of slip parameter reduces the fluid velocity.
Momentum and Heat Transfer in Laminar Slip Flow over a Cylinder
The vorticity transport and energy equations are solved numerically in a laminar gas flow past a circular cylinder. The slip boundary condition and temperature jump are applied at the cylinder wall. The changes in heat transfer and slip velocity at the cylinder wall due to Knudsen and Reynolds number variations are calculated. The velocity at the wall increases as the Knudsen number increases due to the slip condition. The separation point moves downstream as slip increases. As the Knudsen number increases, the slip increases at the wall and the heat flux between the cylinder wall and the flow decreases. These results show that the heat transfer coefficient and the Nusselt number decrease as the slip increases. When hot wires are used for temperature measurements, failure to include a slip boundary condition will also lead to an error in the temperature measurement. Nomenclature c p = specific heat, J∕kg-K d = effective diameter of the gas molecule, m g = correction factor for rarefaction i = radial node location j = tangential node location k = air conductivity, W∕m-K k b = Boltzmann constant, 1.3806503 × 10 −23 m 2 kgs −2 K −1 Kn D = Knudsen number based on the cylinder diameter Nu D = Nusselt number based on the cylinder diameter P = pressure, Pa Pr = nondimensional Prandtl number r = radius, m Re D = Reynolds number based on the cylinder diameter R out = outer radius, m r wall = cylinder radius, m r = nondimensional radius r wall = nondimensional cylinder radius r out = nondimensional outer radius T = temperature, K t = time, s T gas = gas temperature at the wall, K T surf = cylinder wall temperature, K T wall = gas temperature at the wall, K T = nondimensional temperature t = nondimensional time T ∞ = ambient temperature, K U = far-stream velocity, m∕s u r = radial velocity, m∕s u slip = slip velocity at the wall, m∕s u θ = angular velocity, m∕s x = horizontal direction, m y = vertical direction, m
Transient free convection flow past vertical cylinder with constant heat flux and mass transfer
Ain Shams Engineering Journal, 2015
This paper describes a one dimensional unsteady natural convection flow past an infinite vertical cylinder with heat and mass transfer under the effect of constant heat flux at the surface of the cylinder. Closed form solutions of the dimensionless unsteady linear governing boundary layer equations are obtained in terms of Bessel functions and modified Bessel functions by Laplace transform method. The numerical values of velocity, temperature and concentration profiles are obtained for different values of the physical parameters namely, thermal Grashof number, mass Grashof number, Prandtl number, Schmidt number and time and presented in graphs. Also, skin friction and Sherwood number are shown graphically and discussed. It is observed that the velocity and temperature increase unboundedly with time, while the concentration approaches steady state at larger times.
Journal of Applied Fluid Mechanics
An unsteady two-dimensional forced convection over a square cylinder with sharp and rounded corner edge is numerically analyzed for the low Reynolds number laminar flow regime. In this study, the analysis is carried out for Reynolds number (Re) in the range of 80 to 180 with Prandtl number (Pr) variation from 0.01 to 1000 for various corner radius (r=0.50, 0.51, 0.54, 0.59, 0.64 and 0.71). The lateral sides of the computational domain are kept constant to maintain the blockage as 5%. Heat transfer due to unsteady forced convection has been predicted by Artificial Neural network (ANN). The present ANN is trained by the input and output data which has been acquired from the numerical simulation, performed in finite volume based Computational Fluid Dynamics (CFD) commercial software FLUENT. The heat transfer characteristics over the sharp and rounded corner square cylinder are evaluated by analyzing the local Nusselt number (Nu local), average Nusselt number (Nu avg) at various Reynolds number, Prandtl numbers and for various corner radii. It is found that the heat transfer rate of a circular cylinder can be enhanced by 12% when Re is varying and 14% when Prandtl number is varying by introducing a new cylinder geometry of corner radius r=0.51. It is found that the unsteady forced convection heat transfer over a cylinder can be predicted appropriately by ANN. It is also observed that the back propagation ANN can predict the heat transfer characteristics of forced convection very quickly compared to a standard CFD method.