The Two-Dimensional Heat Transfer Analysis in Arrayed Fins with the Thermal Dissipation Substrate

The aim of the present study is to investigate the two-dimensional heat transfer analysis in arrayed fins with thermal dissipation substrate. The governing equations for the fins and the substrate are expressed with Laplace equations, and the boundary conditions around the fins and substrate are Robin conditions. The present investigation first aims to provide a solution with regard to the geometry models by a series truncation method. Then the research will compare the results of the series truncation method with the point-matching method. Furthermore, the present study will also discuss the effects of dimension and Biot number of the fins on local dimensionless temperature, mean temperature, and heat transfer rate.

Forced Convection Past an Oblate Spheroid at Low to Moderate Reynolds Numbers

Forced convection past a heated oblate spheroid is studied in an attempt to investigate the effect of the axis ratio on the heat transfer rate. The time-dependent full Navier–Stokes and energy equations are solved using a series truncation method. The axis ratios considered range from 1∕2 to 1 (a perfect sphere). The results for the flow and thermal fields are satisfactorily compared with relevant published research. The results are presented in the form of streamlines, isotherms, and the local and averaged Nusselt number distributions.

A model for the free-surface flow due to a submerged source in water of infinite depth

We consider a free-surface flow due to a source submerged in a fluid of infinite depth. It is assumed that there is a stagnation point on the free surface just above the source. The free-surface condition is linearized around the rigid-lid solution, and the resulting equations are solved numerically by a series truncation method with a nonuniform distribution of collocation points. Solutions are presented for various values of the Froude number. It is shown that for sufficiently large values of the Froude number, there is a train of waves on the free surface. The wavelength of these waves decreases as the distance from the source increases.

Free-surface flow due to a source submerged in a fluid of infinite depth with two stagnant regions

Two-dimensional free-surface flows produced by a submerged source in a fluid of infinite depth are considered. It is assumed that the point on the free surface just above the source is a stagnation point and that the fluid outside two shear layers is at rest. The free-surface profile and the shape of the shear layers are determined numerically by using a series-truncation method. It is shown that there is a solution for each value of the Froude number F > 0. When F tends to infinity, the flow also describes a thin jet impinging in a fluid at rest.

Steady flows inside and around a fluid sphere at low Reynolds numbers

The effects of internal circulation in bubbles and droplets have been analysed by means of a semi-analytical series-truncation method. The equations of motion are transformed into a series of coupled, ordinary, nonlinear differential equations by use of orthogonal sets. These infinite-series equations are then truncated adequately and solved numerically. Using this series-truncation method, we have evaluated the effects of different ratios (between the continuous and dispersed phases) of both density and viscosity for the flows of low Reynolds numbers. For all the density ratios investigated, the density difference has almost no effect on the drag coefficient at low Reynolds numbers. The shear stress and the drag coefficient increase with increasing viscosity ratio of droplet to ambience and decrease with increasing Reynolds number.