Heat Transfer to a Nonisothermal Rotating Disk With a Turbulent Boundary Layer

1965 ◽  
Vol 87 (3) ◽  
pp. 362-368 ◽  
Author(s):  
J. P. Hartnett ◽  
Shing-Hwa Tsai ◽  
H. N. Jantscher
Keyword(s):  
Heat Transfer ◽  
Additional Data ◽  
Rotating Disk ◽  
Eddy Diffusivity ◽  
Nonisothermal Condition ◽  
High Speeds ◽  
Infinite Extent ◽  
Tangential Momentum ◽  
Induced Flow ◽  
Nonisothermal Conditions

Three approaches are presented for the prediction of heat transfer from a nonisothermal disk rotating in a fluid of infinite extent at such high speeds that the induced flow is turbulent. These include the analysis of Dorfman, the analysis of Davies (extended to nonisothermal conditions) assuming the eddy diffusivity of radial momentum is equal to the eddy diffusivity of heat, and a modified Davies analysis assuming the eddy diffusivity of tangential momentum is equal to the eddy diffusivity of heat. A comparison of these three predictions with available heat and mass transfer data suggests that Dorfman’s analysis when appropriately modified gives the best representation for the isothermal rotating disk. For the nonisothermal disk having a power-function wall-temperature distribution, Tw − Te = Brm, both the Dorfman analysis and the tangential momentum analogy give what appears to be a reasonable estimate of the influence of the nonisothermal condition, while the radial momentum analogy overestimates the influence. Until additional data are obtained, it is recommended that the modified Dorfman prediction be used to estimate heat transfer from a nonisothermal disk in the presence of turbulent flow.

Use of Fin Equation to Calculate Nusselt Numbers for Rotating Disks

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Hui Tang ◽  
Tony Shardlow ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Circular Disk ◽  
Rotating Disk ◽  
Conjugate Problem ◽  
Temperature Measurements ◽  
Rotating Disks ◽  
Nusselt Numbers ◽  
Induced Flow ◽  
Thin Disks

Conduction in thin disks can be modeled using the fin equation, and there are analytical solutions of this equation for a circular disk with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disk systems is a conjugate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number,  Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disk temperature is known then Bi  can be determined numerically. But the determination of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this paper, Bayesian statistics are applied to the inverse solution of the circular fin equation to produce reliable estimates of Bi for rotating disks, and numerical experiments using simulated noisy temperature measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating compressor disks.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

scholarly journals A sensitivity study on carbon nanotubes significance in Darcy–Forchheimer flow towards a rotating disk by response surface methodology

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anum Shafiq ◽  
Tabassum Naz Sindhu ◽  
Qasem M. Al-Mdallal
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Ethylene Glycol ◽  
Biot Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Rotating Disk ◽  
Sensitivity Study ◽  
Basic Fluid ◽  
Walled Cnts

AbstractThe current research explores incremental effect of thermal radiation on heat transfer improvement corresponds to Darcy–Forchheimer (DF) flow of carbon nanotubes along a stretched rotating surface using RSM. Casson carbon nanotubes’ constructed model in boundary layer flow is being investigated with implications of both single-walled CNTs and multi-walled CNTs. Water and Ethylene glycol are considered a basic fluid. The heat transfer rate is scrutinized via convective condition. Outcomes are observed and evaluated for both SWCNTs and MWCNTs. The Runge–Kutta Fehlberg technique of shooting is utilized to numerically solve transformed nonlinear ordinary differential system. The output parameters of interest are presumed to depend on governing input variables. In addition, sensitivity study is incorporated. It is noted that sensitivity of SFC via SWCNT-Water becomes higher by increasing values of permeability number. Additionaly, sensitivity of SFC via SWCNT-water towards the permeability number is higher than the solid volume fraction for medium and higher permeability levels. It is also noted that sensitivity of SFC (SWCNT-Ethylene-glycol) towards volume fraction is higher for increasing permeability as well as inertia coefficient. Additionally, the sensitivity of LNN towards the Solid volume fraction is higher than the radiation and Biot number for all levels of Biot number. The findings will provide initial direction for future device manufacturing.

scholarly journals Color Response Modification of Encapsulated Liquid Crystals Used in Rotating Disk Heat Transfer Studies

1995 ◽  
Author(s):  
Cengiz Camci ◽  
Boris Glezer
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Rotational Speed ◽  
Rotating Disk ◽  
Point Of View ◽  
Centrifugal Acceleration ◽  
Relative Shift ◽  
Color Response ◽  
Stationary Conditions

The liquid crystal thermography can be successfully used in both transient and steady-state heat transfer experiments with excellent spatial resolution and good accuracy. Although most of the past liquid crystal based heat transfer studies are reported in the stationary frame, measurements from the rotating frame of turbomachinery systems exist The main objective of the present investigation is to determine the influence of rotation on the color calibration of encapsulated liquid crystals sprayed on the flat surface of a rotating aluminum disk. The investigation is performed for a rotational speed range from 0 rpm to 7500 rpm using three different liquid crystal coatings displaying red at 30, 35 and 45° C, under stationary conditions. An immediate observation from the present study is that the color response of liquid crystals is strongly modified by the centrifugal acceleration of the rotating environment. It is consistently and repeatedly observed that the hue versus temperature curve is continuously shifted toward lower temperatures by increasing rotational speed. The relative shift of the display temperature of the green can be as high as 7°C at 7500 rpm when compared to the temperature of the green observed under stationary conditions. The present study shows that relative shift of the liquid crystal color has a well-defined functional dependency to rotational speed. The shift is linearly proportional to the centrifugal acceleration. It is interesting to note that the individual shift curves of the green for all three liquid crystal coatings collapse into a single curve when they are normalized with respect to their own stationary green values. When the color attribute is selected as “intensity” instead of “hue”, very similar shifts of the temperature corresponding to the intensity maximum value appearing around green is observed. An interpretation of the observed color shift is made from a thermodynamics energy balance point of view.

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