Grashoff Number Research Articles

On the effect of flow direction on mixed convection from a horizontal cylinder

AbstractThe influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two‐dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re2. The results are compared with the available experimental data and the agreement is satisfactory.

Convective heat transfer in an inclined cavity with heated from bottom surface in a forced laminar flow.

This study deals numerically with a convective heat transfer in an inclined rectangular cavity with heated from bottom heating surface in a forced laminar Flow. Flow patterns and temperature profiles in the cavity and local and average heat transfer coefficients on the bottom heating surface are presented by Up-Wind difference numerical method for various Reynolds numbers ReH, Grashoff numbers Grw and inclination angles θ. It is clarified that the inclination angle has an important role in estimating the Flow pattern and heat transfer in the inclined cavity. It is also understood that the Nusselt number is not increased monotonically with increasing ReH at Grw = 2×103 at low ReH.

An application of a boundary element method to natural convection

The direct boundary element method is applied to the numerical modelling of thermal fluid flow in a transient state. The Navier-Stokes equations are considered under the Boussinesq approximation and the viscous thermal flow equations are expressed in terms of stream function, vorticity, and temperature in two dimensions. Boundary integral equations are derived using logarithmic potential and time-dependent heat potential as fundamental solutions. Boundary unknowns are discretized by linear boundary elements and flow domains are divided into a series of triangular cells. Charged points are translated upstream in the numerical evaluation of convective terms. Unknown stream function, vorticity, and temperature are staggered in the computational scheme. Simple iteration is found to converge to the quasi steady-state flow. Boundary solutions for two-dimensional examples at a Reynolds number 100 and Grashoff number 10 7 are obtained.

Magnetohydrodynamic free convective effect for an incompressible viscous fluid past an infinite limiting surface

An analysis of the effect of a magnetic field on the free convective flow of an incompressible, electrically conducting and viscous fluid past an infinite vertical limiting surface, has been carried out. Also the limiting surface are unmoving, we have constant heat flux at the limiting surface, the free velocity is constant and the magnetic Reynolds number is not small. The effects of the magnetic parameter and the Grashoff number on the flow are discussed.

Unsteady free convective flow and mass transfer through a porous medium bounded by an infinite vertical limiting surface with constant suction and time-dependent temperature

In this work an analysis of the two-dimensional unsteady free convective flow and mass transfer is given, for an incompressible viscous fluid through a porous medium bounded by an infinite vertical limiting surface. The suction velocity perpendicular to the limiting surface is constant and the temperature of the limiting surface fluctuates with time about a non-zero constant mean. Expressions for the velocity, temperature and concentration fields are obtained and the effects of the various parameters of the problem, e.g. modified Grashoff number, permeability of the porous medium and the frequency on the velocity field are discussed.

Natural convection heat transfer in air about a horizontal circular nonisothermal cylinder

Results are presented of a numerical investigation of laminar free convection heat transfer in air about a horizontal circular cylinder in the moderate Grashoff number range (104 ⩽ Grm ⩽ 109), for linear and quadratic laws of surface temperature variation.

Transient hydromagnetic convective flow in a rotating channel with porous boundaries

The paper studies the combined free and forced convection in a rotating, viscous, incompressible fluid confined between two parallel porous plates. Assuming that the temperature varies linearly along the plates and the pressure gradient maintained uniform over the planes parallel to the plates, the velocity, temperature and the stresses are calculated analytically. Their behaviours for different values of the parameters viz., the Hartmann number, the Grashoff number and the suction parameter etc., are discussed graphically giving out the interplay between the various forces.

Exotische Lösungen des Bénardschen Problems

AbstractA bifurcation analysis is given for the generalized Bénard problem near the critical value of the Grashoff number. In contrast to earlier investigations where symmetry arguments were used to reduce the boundary‐value‐problem to a simple‐eigenvalue‐bifurcation, we only require double periodicity and treat high multiplicity bifurcation. It is shown that solutions of a yet unknown type exist.

Free convection of heat generating fluids in cylindrical tanks

Laminar, axisymmetric free convection of a uniform heat generating fluid which fills or partially fills a vertical cylindrical tank has been investigated theoretically, using finite difference methods to compute steady state non-dimensional maximum temperatures and velocities. Tables of maximum temperatures and velocities are presented together with isotherm distributions and velocity vector diagrams for a range of Prandtl numbers (0.1 ⩽ Pr⩽ 10), modified Grashoff numbers (10 ⩽ Gr'⩽ 10 4) and fluid height to radius ratios ( L R ) of 2:1 and 1:1.

Numerical Solutions of Heat and Mass Transfer Effects of an Unsteady MHD Free Convective Flow past an Infinite Vertical Plate with Constant Suction

The objective of this work is to study heat and mass transfer in an unsteady MHD free convective flow past an infinite vertical plate with constant suction numerically. Dimensionless governing equations of the problem have been solved by using finite difference technique. Numerical solutions for temperature, velocity, concentration have been obtained for suitable parameters like Grashoff number, mass Grashoff number, Prandtl number and Schmidt number. Rate of heat transfer and mass transfer are studied. The results obtained are discussed with the help of graphs and tables to observe effect of various parameters concerned in the problem under investigation. Stability and convergence of the finite difference scheme is established. Key words: MHD, unsteady, constant suction, finite difference technique, Heat and mass transfer. doi:10.3329/jname.v5i1.1785 Journal of Naval Architecture and Marine Engineering Vol. 5, No. 1 (June, 2008) 27-36

Free Convection in a Rotating Medium

Numerical techniques have been used to study natural convection in a fluid subjected to axial rotation. Axisymmetrical flows were studied in two different geometries for a variety of rotational speeds. For case I (R1 = 1.0, R2 = 2.5, H = 3.0), the computed flow patterns were qualitatively compared with those which would be expected from the basic rules of physics, and good agreement was obtained. Rotational speeds between Ω = 0, and Ω = 20 were studied for a Grashoff number of 3000. Increased rotational speed was found to decrease the over-all heat transfer rate. For case II (R1 = 1.0, R2 = 4.0, H = 1.0), rotational speeds of Ω = 0.0 to Ω = 40.0 were studied at a Grashoff number of 400. At low rotational speeds, a single convection cell was found, however, at higher rotational speeds, the single cell became unstable, and changed to a two-celled pattern. This transition resulted in a slight increase in the over-all heat transfer rate.

An Attempt on the Analysis of the Vortex Streets Developed in a Free-Convection Boundary Layer

Preliminarily it was pointed out, for the case of free convection phenomena, that the transition point from laminar flow to vortex streets flow would not be given by the critical Reynolds number. Then we divided the laminar boundary layer by an imaginary wave length along the flow direction, made the ratio of the momentum energy of the imaginarily divided part in the case that the part would move en bloc independently to the increase of the momentum energy of the same part in the case that the part would move still one more wave length, maintaining the laminar state continuously, and supposed that the transition would happen when the ratio reaches a critical number. The critical Grashoff number was given from that ratio, and also the wave length and the frequency of the vortex streets were calculated with the same ratio, under the assumption of the continuity of the vorticity flow before and behind the transition. Nearly good coincidence was observed between the theoretical relations and the experimental data measured by the author with water and ethylene-glycol and Eckert-Soehngen with air.

Heat Transfer Resistance of Air Layer (1st Report)

Heat transfer resistance of the air layer is severely influenced by the state of motion in the air layer. In this report, the state of motion is observed by using both TiCl4 and NH3OH, and the coefficient of heat transfer through the air layer is measured as the first report. According to our experiments, the convective motion in the air layer is cellular motion and the breadth of a cell is about twice of the thickness of the air layer and the ratio between the thickness of the air layer and the breadth of a cell increases with Grashoff number. And then the heat transfer is theoretically analyzed and it is found that theoretical results agree well with the experimental data.

Experimental Researches on Heat Transfer from Vertical Flat Plate by Natural Convection (1st Report)

This report presents the heat transfer from a vertical flat plate by natural convection in the case where the surface-temperature of the plate is not uniform. The flat plate, whose thickness, length and breadth are about 0.6 cm, 31 cm and 16 cm, respectively, and which has a wooden frame surrounding the iron plate which is electrically heated and has a size 0.6×25×12 cm3, is suspended verically in the wooden cubic box whose edge is 120 cm long. The local coefficient of heat transfer is measured on the center line of the plate. In this esperiments, the distribution of surface-temperature T1 is approximately given by the following equation : T1=T0+Bxβ Where T0 : temperature of surrounding air, x : height of plate, B and β : constants, and β is about 0.13. The relation between non-dimensional numbers, Nu and Cγ, becomes as follows : Nu=0.393 Gr0.251 (105<Gr<108) where Nu : Nusselt number, using local coefficient of heat transfer, Gr : Grashoff number. This relation agrees very well with our theoretical results, Nu=3/2[(5β+3)/630]1/4Pr1/4Gr1/4

Heat Transfer Resistance of Air Layer (2nd Report)

Heat transfer resistance of the air layer is severely influenced by the state of motion in the air layer. In this report, the state of motion is observed by using both TiCl4 and NH3OH, and the coefficient of heat transfer through the air layer is measured as the first report. According to our experiments, the convective motion in the air layer is cellular motion and the breadth of a cell is about twice of the thickness of the air layer and the ratio between the thickness of the air layer and the breadth of a cell increases with Grashoff number. And then the heat transfer is theoretically analyzed and it is found that theoretical results agree well with the experimental data.