Showing papers on "Film temperature published in 2010"

Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating

Abstract: The steady boundary layer flow and heat transfer over a stretching sheet with Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered in this study. The transformed governing nonlinear boundary layer equations are solved numerically by a finite-difference method. Numerical solutions are obtained for the heat transfer from the stretching sheet and the wall temperature for a large range of values of the Prandtl number Pr. The Newtonian heating is controlled by a dimensionless conjugate parameter, which varies between zero (insulated wall) and infinity (wall temperature remains constant). The important findings in this study are the variation of the surface temperature and heat flux from the stretching surface with the conjugate parameter and Prandtl number. It is found that these parameters have essential effects on the heat transfer characteristics.

Transitional and turbulent boundary layer with heat transfer

Abstract: We report on our direct numerical simulation of an incompressible, nominally zero-pressure-gradient flat-plate boundary layer from momentum thickness Reynolds number 80–1950. Heat transfer between the constant-temperature solid surface and the free-stream is also simulated with molecular Prandtl number Pr=1. Skin-friction coefficient and other boundary layer parameters follow the Blasius solutions prior to the onset of turbulent spots. Throughout the entire flat-plate, the ratio of Stanton number and skin-friction St/Cf deviates from the exact Reynolds analogy value of 0.5 by less than 1.5%. Mean velocity and Reynolds stresses agree with experimental data over an extended turbulent region downstream of transition. Normalized rms wall-pressure fluctuation increases gradually with the streamwise growth of the turbulent boundary layer. Wall shear stress fluctuation, τw,rms′+, on the other hand, remains constant at approximately 0.44 over the range, 800

Thermal boundary layers over a shrinking sheet: an analytical solution

Abstract: In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.

Viscous dissipation effects of power-law fluid flow within parallel plates with constant heat fluxes

Abstract: Both hydro-dynamically and thermally fully developed laminar heat transfer of non-Newtonian fluids between fixed parallel plates has been analyzed taking into account the effect of viscous dissipation of the flowing fluid. Thermal boundary condition considered is that both the plates kept at different constant heat fluxes. The energy equation, and in turn the Nusselt number, were solved analytically in terms of Brinkman number and power-law index. The findings show that the heat transfer depends on the power-law index of the flowing fluid. Pseudo-plastic and dilatant fluids manifest themselves differently in the heat transfer characteristics under the influence of viscous dissipation. Under certain conditions, the viscous dissipation effects on heat transfer between parallel plates are significant and should not be neglected.

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

Abstract: This article presents a numerical solution for the steady two-dimensional mixed convection MHD flow of an electrically conducting viscous fluid over a vertical stretching sheet, in its own plane. The stretching velocity and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function of the temperature and a linear function of the temperature. A generalized similarity transformation is introduced to study the influence of temperature dependent fluid properties. The transformed boundary layer equations are solved numerically, using a finite difference scheme known as Keller Box method, for several sets of values of the physical parameters, namely, the stretching parameter, the temperature dependent viscosity parameter, the magnetic parameter, the mixed convection parameter, the temperature dependent thermal conductivity parameter and the Prandtl number. The numerical results thus obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of the physical parameters on the flow and heat transfer characteristics. Here it may be noted that, in the case of the classical Navier–Stokes fluid flowing past a horizontal stretching sheet, McLeod and Rajagopal (1987) [42] showed that there exist an unique solution to the problem. This may not be true in the present case. Hence we would like to explore the non-uniqueness of the solution and present the findings in the subsequent paper.

Unsteady MHD flow and heat transfer on a stretching sheet in a rotating fluid

Abstract: This study deals the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer analysis in an incompressible rotating viscous fluid over a stretching continuous sheet. A similar solution is developed numerically using the Keller-box method. The effects of the involving physical parameters on the velocity field, the temperature distribution, the local skin friction coefficients and the local Nusselt number are graphically shown and discussed. Comparison of the present results for hydrodynamic flow ( M = 0) is given and found in excellent agreement with the existing results in the literature.

Convective heat transfer in planetary dynamo models

Abstract: [1] The magnetic fields of planets and stars are generated by the motions of electrically conducting fluids within them. These fluid motions are thought to be driven by convective processes, as internal heat is transported outward. The efficiency with which heat is transferred by convection is integral in understanding dynamo processes. Several heat transfer scaling laws have been proposed, but the range of parameter space to which they apply has not been firmly established. Following the plane layer convection study by King et al. (2009), we explore a broad range of buoyancy forcing (Ra) and rotation strength (E−1) to show that heat transfer (Nu) in spherical dynamo simulations occurs in two distinct regimes. We argue that heat transfer scales as Nu ∼ Ra6/5 in the rapidly rotating regime and Nu ∼ Ra2/7 in the weakly rotating regime. The transition between these two regimes is controlled by the competition between the thermal and viscous boundary layers. Boundary layer scaling theory allows us to predict that the transition between the regimes occurs at a transitional Rayleigh number, Rat = E−7/4. Furthermore, boundary layer control of heat transfer is shown to relate to the interior temperature profiles of the models. In the weakly rotating regime, the interior fluid is nearly adiabatic. In the rapidly rotating regime, adverse mean temperature gradients abide, irrespective of the Reynolds number (Re). Extrapolating our results to Earth's core, we estimate that core convection resides in the rapidly rotating regime, with Ra ≈ 2 × 1024 (Ra/Rat ≈ 0.02), corresponding to a superadiabatic density variation of Δρ/ρo ≈ 10−7, which is significantly below the sensitivity of present seismic observations.