Approximate Solution to a Class of Transient Forced Convection Problems

1977 ◽  
Vol 99 (4) ◽  
pp. 567-574 ◽  
Author(s):  
J. Sucec
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Surface Temperature ◽  
Forced Convection ◽  
Free Stream ◽  
The Body ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Response Curves ◽  
Constant Property

Approximate solutions using integral methods and the method of characteristics are found for the case of laminar, low speed, constant property, two-dimensional planar boundary layer type flow over a body which is initially at the constant temperature of the fluid passing over it and then, suddenly, has its surface temperature changed to a new constant value or has a constant heat flux imposed at the surface. The free stream velocity is variable with position along the body and the entire velocity field is assumed to be in the steady state. Response curves for surface heat flux or of surface temperature as a function of position and time are presented for power law variations of free stream velocity (the “wedge” type flows) and also for one particular nonsimilar (nonwedge) case. The relative ease with which the nonsimilar cases can be handled is thought to make the approach, advanced herein, a useful tool for the engineer to attack other nonsimilar cases. It was also found that the use of an “equivalent” wedge variable gives reasonably satisfactory results for the nonsimilar case chosen. Hence the application of the equivalent wedge methods is valid for transient forced convection problems just as it is, as is well known, for steady-state forced convection.

Bioconvection in Casson nanofluid flow with Gyrotactic microorganisms and variable surface heat flux

2019 ◽  
Vol 12 (04) ◽  
pp. 1950041 ◽  
Author(s):  
I. S. Oyelakin ◽  
S. Mondal ◽  
P. Sibanda ◽  
D. Sibanda
Keyword(s):  
Heat Flux ◽  
Vertical Plate ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Convection Flow ◽  
Stream Velocity ◽  
Constant Density ◽  
Gyrotactic Microorganisms ◽  
Casson Nanofluid ◽  
Variable Surface

This paper presents a two-dimensional unsteady laminar boundary layer mixed convection flow heat and mass transfer along a vertical plate filled with Casson nanofluid located in a porous quiescent medium that contains both nanoparticles and gyrotactic microorganisms. This permeable vertical plate is assumed to be moving in the same direction as the free stream velocity. The flow is subject to a variable heat flux, a zero nanoparticle flux and a constant density of motile microorganisms on the surface. The free stream velocity is time-dependent resulting in a non-similar solution. The transport equations are solved using the bivariate spectral quasilinearization method. A grid independence test for the validity of the result is given. The significance of the inclusion of motile microorganisms to heat transfer processes is discussed. We show, inter alia, that introducing motile microorganisms into the flow reduces the skin friction coefficient and that the random motion of the nanoparticles improves the rate of transfer of the motile microorganisms.

Effect of Free-Stream Velocity Vector and Aspect Ratio on the Output of a Free-Standing Circular Disk Heat Flux Gage

1984 ◽  
Vol 106 (1) ◽  
pp. 229-233 ◽  
Author(s):  
M. F. Young
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Free Stream ◽  
Angle Of Attack ◽  
Circular Disk ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Free Standing

The effects of free-stream velocity, angle of attack, and aspect ratio on the output of a free-standing circular disk heat flux gage subjected to a combined radiative and convective heat flux are reported. The Reynolds number range investigated extends from 6000 to 25,000, while the gage angle of attack was varied from 0 to 90 deg. Results for three gage aspect ratios, 5.85, 8.77, and 11.76, are presented. The Nusselt number is used to represent the effects of convection on the gage output. The Nusselt number was found to increase with increasing Reynolds number and angles of attack. At an angle of attack of about 90 deg, however, a significant reduction in the Nusselt number was noted. A correlation relating the Nusselt number (based on the disk diameter) to the Reynolds number (based on the gage outside diameter) and the angle of attack is reported. This correlation represents the data to within ±5 percent.

scholarly journals Boundary-Layer Type Solutions for Initial Platelet Activation and Deposition

2002 ◽  
Vol 4 (2) ◽  
pp. 95-108 ◽  
Author(s):  
T. David ◽  
P. G. de Groot ◽  
P. G. Walker
Keyword(s):  
Platelet Activation ◽  
Peclet Number ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Bulk Fluid ◽  
Péclet Number ◽  
Activated Platelets ◽  
Activation Rate ◽  
Initial Adhesion

This paper presents, on the basis of high Peclet number, a mathematical model for the activation and initial adhesion of flowing platelets onto a surface. In contrast to past work, the model is applicable to general 2D and axi-symmetric flows where the wall shear stress is knowna priori. Results indicate that for high activation reaction rates there exist two layers, one containing only activated platelets and the other both activated and non-activated platelets. Fundamental relationships are proposed between the adhesion rate of platelets to the surface and the characteristic parameters of Peclet number and Reynolds number. Activation in the bulk fluid (blood) is characterised by the Damkohler number, which is a function of activation rate and the free-stream velocity. It is shown that, as the free-stream velocity varies, there exists a maximum of activated platelet flux to the wall for particular values of the velocity. These values, at which the maximum occur, are themselves functions of the platelet activation rate. As the free-stream velocity increases the activation of platelets ceases altogether and adhesion is reduced to a very small value strengthening the hypothesis of the correlation between atherogenesis/thrombogenesis and areas of low shear.

scholarly journals Surface temperature and free-stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 13-23
Author(s):  
Zia Ullah ◽  
Muammad Ashraf ◽  
Saqib Zia ◽  
Ishtiaq Ali
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Surface Temperature ◽  
Skin Friction ◽  
Slip Velocity ◽  
Free Stream ◽  
Slip Flow ◽  
Stream Velocity ◽  
Velocity Oscillation

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 position but maximum amplitude of oscillation in heat transfer is observed at each position ? = ?/4 and 2?/3. It is further noticed that a fluid velocity increas?es sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physi?cally in good agreement.

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