The role of thermal radiation on the boundary layer past a stationary flat plate with constant surface boundary condition

This study is devoted to investigating the importance of thermal radiation on the boundary layer over a horizontal surface considering classical constant surface boundary condition. The mathematical model consists of coupled two-dimensional partial differential equations which are transformed to the set of ordinary differential equations via the similarity transformation. The final set of dimensionless equations is solved numerically using Runge Kutta Fehlberg (RKF45) method in Maple software. The significant effect of the thermal radiation is examined using four fluids namely; water, Sulphur oxide, air and mercury whose respective Prandtl numbers are 7, 2, 0.72 and 0.044. The influence of other prominent parameters affecting the flow formation and temperature profile is demonstrated using tables and graphs. The results indicated that the thermal boundary layer thickness could be increase by reducing the Prandtl number. The results also showed that increasing the thermal radiation parameter has a positive impact on the boundary layer thickness. The heat transfer rate could be improved by increasing thermal radiation or decreased by increasing the values of the Prandtl number. Regarding the temperature gradient, an observable increasing is seen far from the flat plate with the growing of thermal radiation whereas the opposite trend is true near the plate surface.

New Weighted Total Acceleration on Momentum Euler Equation for Formulating Water Wave Dispersion Equation

In this present study, weighted total acceleration for Kinematic Free Surface Boundary Condition (KFSBC) and in momentum Euler equation was formulated. Furthermore, by using both aforementioned equations, the nonlinear water wave dispersion equation was then formulated. The wavelength obtained from dispersion equation is determined by weighting coefficient. The weighting coefficient value was determined by using the maximum wave height and critical wave steepness criteria which have been obtained from the previous studies.

Thermal performance analysis of a Solar parabolic dish concentrator system with modified cavity receiver

Purpose This paper aims to present the numerical models and experimental outcomes pertain to the performance of the parabolic dish concentrator system with a modified cavity-type receiver (hemispherical-shaped). Design/methodology/approach The numerical models were evolved based on two types of boundary conditions; isothermal receiver surface and non-isothermal receiver surface. For validation of the numerical models with experimental results, three statistical terms were used: mean of absolute deviation, R2 and root mean square error. Findings The thermal efficiency of the receiver values obtained using the numerical model with a non-isothermal receiver surface found agreeing well with experimental results. The numerical model with non-isothermal surface boundary condition exhibited more accurate results as compared to that with isothermal surface boundary condition. The receiver heat loss analysis based on the experimental outcomes is also carried out to estimate the contributions of various modes of heat transfer. The losses by radiation, convection and conduction contribute about 27.47%, 70.89% and 1.83%, in the total receiver loss, respectively. Practical implications An empirical correlation based on experimental data is also presented to anticipate the effect of studied parameters on the receiver collection efficiency. The anticipations may help to adopt the technology for practical use. Social implications The developed models would help to design and anticipating the performance of the dish concentrator system with a modified cavity receiver that may be used for applications e.g. power generation, water heating, air-conditioning, solar cooking, solar drying, energy storage, etc. Originality/value The originality of this manuscript comprising presenting a differential-mathematical analysis/modeling of hemispherical shaped modified cavity receiver with non-uniform surface temperature boundary condition. It can estimate the variation of temperature of heat transfer fluid (water) along with the receiver height, by taking into account the receiver cavity losses by means of radiation and convection modes. The model also considers the radiative heat exchange among the internal ring-surface elements of the cavity.

Analytical Analysis of Effects of Buoyancy, Internal Heat Generation, Magnetic Field, and Thermal Radiation on a Boundary Layer over a Vertical Plate with a Convective Surface Boundary Condition

In this paper, the effects of magnetic field, thermal radiation, buoyancy force, and internal heat generation on the laminar boundary layer flow about a vertical plate in the presence of a convective surface boundary condition have been investigated. In the analysis, it is assumed that the left surface of the plate is in contact with a hot fluid, whereas a stream of cold fluid flows steadily over the right surface, and the heat source decays exponentially outwards from the surface of the plate. The governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations with the help of similarity transformation which were solved analytically by applying the optimal homotopy asymptotic method. The variations of fluid velocity and surface temperature for different values of the Grashof number, magnetic parameter, Prandtl number, internal heat generation parameter, Biot number, and radiation absorption parameter are tabulated, graphed, and interpreted in physical terms. A comparison with previously published results on similar special cases of the problem shows an excellent agreement.

Improvement of Non-Hydrostatic Hydrodynamic Solution Using a Novel Free-Surface Boundary Condition

Hydrodynamic models based on the RANS equation are well-established tools to simulate three-dimensional free surface flows in large aquatic ecosystems. However, when the ratio of vertical to horizontal motion scales is not small, a non-hydrostatic approximation is needed to represent these processes accurately. Increasing efforts have been made to improve the efficiency of non-hydrostatic hydrodynamic models, but these improvements require higher implementation and computational costs. In this paper, we proposed a novel free-surface boundary condition based on a fictional sublayer at the free-surface (FSFS). We applied the FSFS approach at a finite difference numerical discretization with a fractional step framework, which uses a Neumann type of boundary condition to apply a hydrostatic relation in the top layer. To evaluate the model performance, we compared the Classic Boundary Condition Approach (CBA) and the FSFS approach using two numerical experiments. The experiments tested the model’s phase error, capability in solving wave celerity and simulate non-linear wave propagation under different vertical resolution scenarios. Our results showed that the FSFS approach had a lower phase error (2 to 5 times smaller) than CBA with a little additional computational cost (ca. 7% higher). Moreover, it can better represent wave celerity and frequency dispersion with 2 times fewer layers and low mean computational cost (CBA δ t = 2.62 s and FSFS δ t = 1.22 s).

A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane

We derive a second-order correction to an existing leading-order model for surface waves in linear elasticity. The same hyperbolic–elliptic equation form is obtained with a correction term added to the surface boundary condition. The validity of the correction term is shown by re-examining problems which the leading-order model has been applied to previously, namely a harmonic forcing, a moving point load and a periodic array of compressional resonators.