The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Ali J. Chamkha - One of the best experts on this subject based on the ideXlab platform.
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simulation of cattaneo christov heat flux on the flow of single and multi walled carbon nanotubes between two stretchable coaxial Rotating Disks
Journal of Thermal Analysis and Calorimetry, 2020Co-Authors: A. Bhattacharyya, G. S. Seth, Ali J. Chamkha, R KumarAbstract:With an objective to unfold the flow and heat transfer characteristics of carbon nanotubes between two stretchable coaxial Rotating Disks, the present investigation has been carried out. The behavior of single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs) taking water as the base fluid is analyzed. To formulate the energy equation, we have incorporated Cattaneo–Christov heat flux model. Consideration of such kind of model accounts the contribution by thermal relaxation. von Karman transformation has been implemented in order to reconstruct the governing partial differential equations into a system of ordinary differential equations. Employing optimal homotopy analysis method series solutions are obtained. Error analysis has also been performed and presented in tabular form. The physical clarifications for the behavior of fluid velocity, temperature, skin friction coefficient and Nusselt number are well demonstrated with the help of graphs and contour plots. One of the major outcomes of the present study signifies that water-based SWCNTs have a tendency to cause less drag and higher rate of heat transfer as compared to water-based MWCNTs. This investigation finds numerous applications in different mechanisms of thermal conversion for nuclear propulsion and spacecraft.
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Simulation of Cattaneo–Christov heat flux on the flow of single and multi-walled carbon nanotubes between two stretchable coaxial Rotating Disks
Journal of Thermal Analysis and Calorimetry, 2019Co-Authors: A. Bhattacharyya, G. S. Seth, R Kumar, Ali J. ChamkhaAbstract:With an objective to unfold the flow and heat transfer characteristics of carbon nanotubes between two stretchable coaxial Rotating Disks, the present investigation has been carried out. The behavior of single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs) taking water as the base fluid is analyzed. To formulate the energy equation, we have incorporated Cattaneo–Christov heat flux model. Consideration of such kind of model accounts the contribution by thermal relaxation. von Karman transformation has been implemented in order to reconstruct the governing partial differential equations into a system of ordinary differential equations. Employing optimal homotopy analysis method series solutions are obtained. Error analysis has also been performed and presented in tabular form. The physical clarifications for the behavior of fluid velocity, temperature, skin friction coefficient and Nusselt number are well demonstrated with the help of graphs and contour plots. One of the major outcomes of the present study signifies that water-based SWCNTs have a tendency to cause less drag and higher rate of heat transfer as compared to water-based MWCNTs. This investigation finds numerous applications in different mechanisms of thermal conversion for nuclear propulsion and spacecraft.
Tasawar Hayat - One of the best experts on this subject based on the ideXlab platform.
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entropy optimization in cnts based nanomaterial flow induced by Rotating Disks a study on the accuracy of statistical declaration and probable error
Computer Methods and Programs in Biomedicine, 2020Co-Authors: Tasawar Hayat, Ijaz M Khan, Waqar M Ahmad, A AlsaediAbstract:Abstract Background CNTs (Carbon nanotubes) being allotropes of carbon, made of graphene and diameters of single and multi-walls carbon nanotubes are typically 0.8 to 2 nm and 5 to 20 mn, although diameter of MWCNTs can exceed 100 nm. Carbon nanotubes lengths range from less than 100 nm to 0.5 m. Their impressive structural, electronic and mechanical attributes subject to their small size and mass, their high electrical and thermal conductivities, and their strong mechanical potency. CNTs based materials are successfully applied in medicine and pharmacy subject to their huge surface area that is proficient of conjugating or adsorbing with a wide variety of genes, drugs, antibodies, vaccines and biosensors etc. Therefore, we have presented a theoretical study about mathematical modeling of CNTs based viscous material flow between two Rotating Disks. Both types of nanotubes i.e., SWCNTs and MWCNTs are considered. Xue model is used for the mathematical modeling. Fluid flow is due to Rotating Disks. Main focus here is given to probable error and statistical declaration. Entropy is calculated for both single and multi-walls nanotubes. Method Nonlinear PDEs are first converted into ODEs and then computed for homotopy convergent solutions. Results and conclusion Statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at both Disks surface for higher values of Reynolds number, lower stretching parameter and porosity parameter while it decays for both of Disks versus larger rotation parameter. Nusselt number or heat transfer rate also enhances at both Disks in the presence of radiation and Reynolds number while it decays against Eckert number.
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entropy optimized cnts based darcy forchheimer nanomaterial flow between two stretchable Rotating Disks
International Journal of Hydrogen Energy, 2019Co-Authors: Sohail A Khan, Tasawar Hayat, Ijaz M Khan, Tareq Saeed, Imran M Khan, A AlsaediAbstract:Abstract Here entropy optimized CNTs based flow of viscous liquid is addressed between two stretchable surfaces of Disks. Both upper and lower Disks stretch and rotate with different rates and angular frequencies. Carbon nanotubes (single and multi-walls) are considered as a nanoparticles and water as continuous phase liquid. Xue model is utilized in the mathematical modeling for the transport of nanoparticles. Energy expression is developed through first law of thermodynamics and discussed in the presence of viscous dissipation. Main attention is given to the modeling of entropy generation subject to CNTs nanoparticles. Total entropy rate is calculated. Average residual error is calculated through implementation of optimal homotopy analysis method. Flow parameters are graphically discussed for both single and multi-walls carbon nanotubes. Furthermore, engineering quantities like skin friction and Nusselt number are numerical calculated and discussed through Tables. From obtained outcomes it is examined that entropy rate boosts up versus larger Brinkman number and nanoparticles volume friction. No such attempt is yet done by the researchers on entropy optimized Darcy-Forchheimer CNTs based nanomaterial flow between two Rotating Disks. The obtained outcomes are compared with published literature and found good agreement.
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transportation of cnts based nanomaterial flow confined between two coaxially Rotating Disks with entropy generation
Physica A-statistical Mechanics and Its Applications, 2019Co-Authors: Ijaz M Khan, Tasawar Hayat, Faqir Shah, A AlsaediAbstract:Abstract The mechanical characteristics of CNTs disclose them as one of the sturdiest materials in nature. CNTs are long empty graphene cylinders. Although graphene sheets have two-dimensional symmetry, CNTs by geometry have diverse characteristics in radial and axial directions. In axial directions CNTs are very strong. There are various characteristics and applications of CNTs which take full consideration of CNTs mechanical strength, aspect ratio, thermal and electrical conductivity. Keeping such proficiency of CNTs base materials in mind we here target to scrutinize entropy generation subject to CNTs in dissipative flow between two coaxially Rotating Disks. Viscous dissipation, heat source/sink and radiative flux are used to develop the energy equation. Main attention is given to the total entropy rate with CNTs. Nonlinear partial differential equations are converted to ordinary ones via appropriate transformations. Built-in-Shooting technique (Bvp4c) is used for solution. Flow parameters are discussed graphically. Engineering quantities like Nusselt number and surface drag force are examined numerically. Brinkman number plays a vital role in controlling the entropy rate. Rise in entropy rate is seen for increasing values of Brinkman number and radiation parameter.
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theoretical investigation of ree eyring nanofluid flow with entropy optimization and arrhenius activation energy between two Rotating Disks
Computer Methods and Programs in Biomedicine, 2019Co-Authors: Tasawar Hayat, Ijaz M Khan, Sohail A Khan, A AlsaediAbstract:Abstract Background and objective Improvement of high performance thermal systems for heat transport augmentation has become quite prevalent nowadays. Various works have been performed to pick up a comprehension of the heat transport execution for their practical utilization to heat transport augmentation. Therefore, the nanomaterial has been used in flow of Ree-Eyring fluid between two Rotating Disks for thermal conductivity enhancement of base fluid. Heat transfer characteristics are discussed through viscous dissipation and heat source/sink. Behaviors of Brownian motion and thermophoresis are also examinted. Physical behaviors of irreversibility in nanofluid with Arrhenius activation energy are also accounted. Methods The nonlinear systems lead to ordinary differential problems through implementation of appropriate transformations. The relevant problems are tackled by (OHAM) Optimal homotopic method for series solutions. Results Effects of various physical parameters on the velocity, entropy rate, Bejan number, concentration and temperature are discussed graphically. Skin friction coefficient and gradient of temperature are numerically examined and discussed with various parameters. Conclusions Entropy generation rate is control by minimizing the values of Brinkman number and stretching parameter. Entropy rate and Bejan number show the dual behaviors against Eckert number. Both decay near the lower disk while reverse holds near the upper disk. Entropy rate and Bejan number show similar behaviors for Weissenberg number.
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entropy generation in radiative flow of ree eyring fluid due to due Rotating Disks
International Journal of Numerical Methods for Heat & Fluid Flow, 2019Co-Authors: Muhammad Ijaz Khan, Tasawar Hayat, Sohail A Khan, Muhammad Faisal Javed, Ahmed AlsaediAbstract:This study aims to examine the flow characteristics of Ree–Eyring fluid between two Rotating Disks. The characteristics of heat transfer are discussed in presence of viscous dissipation, heat source/sink and nonlinear radiative heat flux.,Nonlinear flow expressions lead to ordinary ones through adequate similarity transformations. The ordinary differential system has been tackled through optimal homotopic method. The impact of different flow variables on the velocity field, entropy generation rate and temperature fields is graphically discussed. The surface drag force and heat transfer rate are numerically examined via various pertinent parameters.,By minimization of values of stretching parameter and Brinkman number, the entropy generation rate can be controlled. The entropy generation rate enhances for higher values of magnetic parameter, while the Bejan number is decreased via magnetic parameter.,No such work is yet published in the literature.
A Alsaedi - One of the best experts on this subject based on the ideXlab platform.
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entropy optimization in cnts based nanomaterial flow induced by Rotating Disks a study on the accuracy of statistical declaration and probable error
Computer Methods and Programs in Biomedicine, 2020Co-Authors: Tasawar Hayat, Ijaz M Khan, Waqar M Ahmad, A AlsaediAbstract:Abstract Background CNTs (Carbon nanotubes) being allotropes of carbon, made of graphene and diameters of single and multi-walls carbon nanotubes are typically 0.8 to 2 nm and 5 to 20 mn, although diameter of MWCNTs can exceed 100 nm. Carbon nanotubes lengths range from less than 100 nm to 0.5 m. Their impressive structural, electronic and mechanical attributes subject to their small size and mass, their high electrical and thermal conductivities, and their strong mechanical potency. CNTs based materials are successfully applied in medicine and pharmacy subject to their huge surface area that is proficient of conjugating or adsorbing with a wide variety of genes, drugs, antibodies, vaccines and biosensors etc. Therefore, we have presented a theoretical study about mathematical modeling of CNTs based viscous material flow between two Rotating Disks. Both types of nanotubes i.e., SWCNTs and MWCNTs are considered. Xue model is used for the mathematical modeling. Fluid flow is due to Rotating Disks. Main focus here is given to probable error and statistical declaration. Entropy is calculated for both single and multi-walls nanotubes. Method Nonlinear PDEs are first converted into ODEs and then computed for homotopy convergent solutions. Results and conclusion Statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at both Disks surface for higher values of Reynolds number, lower stretching parameter and porosity parameter while it decays for both of Disks versus larger rotation parameter. Nusselt number or heat transfer rate also enhances at both Disks in the presence of radiation and Reynolds number while it decays against Eckert number.
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entropy optimized cnts based darcy forchheimer nanomaterial flow between two stretchable Rotating Disks
International Journal of Hydrogen Energy, 2019Co-Authors: Sohail A Khan, Tasawar Hayat, Ijaz M Khan, Tareq Saeed, Imran M Khan, A AlsaediAbstract:Abstract Here entropy optimized CNTs based flow of viscous liquid is addressed between two stretchable surfaces of Disks. Both upper and lower Disks stretch and rotate with different rates and angular frequencies. Carbon nanotubes (single and multi-walls) are considered as a nanoparticles and water as continuous phase liquid. Xue model is utilized in the mathematical modeling for the transport of nanoparticles. Energy expression is developed through first law of thermodynamics and discussed in the presence of viscous dissipation. Main attention is given to the modeling of entropy generation subject to CNTs nanoparticles. Total entropy rate is calculated. Average residual error is calculated through implementation of optimal homotopy analysis method. Flow parameters are graphically discussed for both single and multi-walls carbon nanotubes. Furthermore, engineering quantities like skin friction and Nusselt number are numerical calculated and discussed through Tables. From obtained outcomes it is examined that entropy rate boosts up versus larger Brinkman number and nanoparticles volume friction. No such attempt is yet done by the researchers on entropy optimized Darcy-Forchheimer CNTs based nanomaterial flow between two Rotating Disks. The obtained outcomes are compared with published literature and found good agreement.
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transportation of cnts based nanomaterial flow confined between two coaxially Rotating Disks with entropy generation
Physica A-statistical Mechanics and Its Applications, 2019Co-Authors: Ijaz M Khan, Tasawar Hayat, Faqir Shah, A AlsaediAbstract:Abstract The mechanical characteristics of CNTs disclose them as one of the sturdiest materials in nature. CNTs are long empty graphene cylinders. Although graphene sheets have two-dimensional symmetry, CNTs by geometry have diverse characteristics in radial and axial directions. In axial directions CNTs are very strong. There are various characteristics and applications of CNTs which take full consideration of CNTs mechanical strength, aspect ratio, thermal and electrical conductivity. Keeping such proficiency of CNTs base materials in mind we here target to scrutinize entropy generation subject to CNTs in dissipative flow between two coaxially Rotating Disks. Viscous dissipation, heat source/sink and radiative flux are used to develop the energy equation. Main attention is given to the total entropy rate with CNTs. Nonlinear partial differential equations are converted to ordinary ones via appropriate transformations. Built-in-Shooting technique (Bvp4c) is used for solution. Flow parameters are discussed graphically. Engineering quantities like Nusselt number and surface drag force are examined numerically. Brinkman number plays a vital role in controlling the entropy rate. Rise in entropy rate is seen for increasing values of Brinkman number and radiation parameter.
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theoretical investigation of ree eyring nanofluid flow with entropy optimization and arrhenius activation energy between two Rotating Disks
Computer Methods and Programs in Biomedicine, 2019Co-Authors: Tasawar Hayat, Ijaz M Khan, Sohail A Khan, A AlsaediAbstract:Abstract Background and objective Improvement of high performance thermal systems for heat transport augmentation has become quite prevalent nowadays. Various works have been performed to pick up a comprehension of the heat transport execution for their practical utilization to heat transport augmentation. Therefore, the nanomaterial has been used in flow of Ree-Eyring fluid between two Rotating Disks for thermal conductivity enhancement of base fluid. Heat transfer characteristics are discussed through viscous dissipation and heat source/sink. Behaviors of Brownian motion and thermophoresis are also examinted. Physical behaviors of irreversibility in nanofluid with Arrhenius activation energy are also accounted. Methods The nonlinear systems lead to ordinary differential problems through implementation of appropriate transformations. The relevant problems are tackled by (OHAM) Optimal homotopic method for series solutions. Results Effects of various physical parameters on the velocity, entropy rate, Bejan number, concentration and temperature are discussed graphically. Skin friction coefficient and gradient of temperature are numerically examined and discussed with various parameters. Conclusions Entropy generation rate is control by minimizing the values of Brinkman number and stretching parameter. Entropy rate and Bejan number show the dual behaviors against Eckert number. Both decay near the lower disk while reverse holds near the upper disk. Entropy rate and Bejan number show similar behaviors for Weissenberg number.
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entropy generation in dissipative flow of williamson fluid between two Rotating Disks
International Journal of Heat and Mass Transfer, 2018Co-Authors: Sumaira Qayyum, Tasawar Hayat, Ijaz M Khan, A Alsaedi, M TamoorAbstract:Abstract This communication addresses flow characteristics of Williamson fluid between two Rotating Disks. Electrically conducting fluid is considered. Total entropy generation rate is calculated through implementation of second law of thermodynamics. The lower and upper Disks have different stretching rates and angular velocities for rotation. Characteristics of heat transport are expressed through dissipation, heat generation/absorption and thermal radiation. Von Karman transformations are utilized to convert the dimensional flow expressions into dimensionless form. Convergent series solutions are constructed. Influence of different pertinent variables on velocity, temperature, entropy number, skin friction coefficients and Nusselt numbers are studied. It is observed that the axial and tangential velocities increase for higher Weissenberg number while radial velocity decays. Further entropy number remarkably increases for magnetic, radiation and Brinkman number. Bejan number is less for higher magnetic parameter, stretching parameter, Brinkman number and Weissenberg number.
A. Bhattacharyya - One of the best experts on this subject based on the ideXlab platform.
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simulation of cattaneo christov heat flux on the flow of single and multi walled carbon nanotubes between two stretchable coaxial Rotating Disks
Journal of Thermal Analysis and Calorimetry, 2020Co-Authors: A. Bhattacharyya, G. S. Seth, Ali J. Chamkha, R KumarAbstract:With an objective to unfold the flow and heat transfer characteristics of carbon nanotubes between two stretchable coaxial Rotating Disks, the present investigation has been carried out. The behavior of single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs) taking water as the base fluid is analyzed. To formulate the energy equation, we have incorporated Cattaneo–Christov heat flux model. Consideration of such kind of model accounts the contribution by thermal relaxation. von Karman transformation has been implemented in order to reconstruct the governing partial differential equations into a system of ordinary differential equations. Employing optimal homotopy analysis method series solutions are obtained. Error analysis has also been performed and presented in tabular form. The physical clarifications for the behavior of fluid velocity, temperature, skin friction coefficient and Nusselt number are well demonstrated with the help of graphs and contour plots. One of the major outcomes of the present study signifies that water-based SWCNTs have a tendency to cause less drag and higher rate of heat transfer as compared to water-based MWCNTs. This investigation finds numerous applications in different mechanisms of thermal conversion for nuclear propulsion and spacecraft.
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Entropy generation of von Karman's radiative flow with Al_2O_3 and Cu nanoparticles between two coaxial Rotating Disks: A finite-element analysis
The European Physical Journal Plus, 2019Co-Authors: R Kumar, G. S. Seth, A. BhattacharyyaAbstract:This article explores the entropy generation of von Karman's radiative hydromagnetic nanofluid flow i.e. alumina (Al_2O_3) and copper (Cu) nanoparticles and water as base fluid between two co-axial Rotating porous Disks. The governing boundary layer equations of a magnetohydrodynamic (MHD) laminar flow between two stretchable Rotating Disks are formulated under the influence of a magnetic field. Using the von Karman transformation, the governing equations for fluid flow, heat and mass transfer are converted into a number of coupled differential equations. The calculations are performed by the hp-Galerkin finite-element analysis (FEA). The physical clarification of fluid velocity, temperature and concentration for several regulatory flow parameters which characterize the physics of the flow, are discussed graphically, while the physical parameters such as skin friction coefficient, the rate of heat and mass transfers in the lower and upper Disks, are presented through tables. The minimal percentage errors are calculated between the previous published result and current result. The thermal radiation, nanoparticle volume fraction, magnetic field and Brinkmann number have an important influence on the irreversibility of thermal energy in terms of Bejan number. This study has numerous applications in thermal transformation mechanisms for nuclear propulsion devices and spacecraft.
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Simulation of Cattaneo–Christov heat flux on the flow of single and multi-walled carbon nanotubes between two stretchable coaxial Rotating Disks
Journal of Thermal Analysis and Calorimetry, 2019Co-Authors: A. Bhattacharyya, G. S. Seth, R Kumar, Ali J. ChamkhaAbstract:With an objective to unfold the flow and heat transfer characteristics of carbon nanotubes between two stretchable coaxial Rotating Disks, the present investigation has been carried out. The behavior of single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs) taking water as the base fluid is analyzed. To formulate the energy equation, we have incorporated Cattaneo–Christov heat flux model. Consideration of such kind of model accounts the contribution by thermal relaxation. von Karman transformation has been implemented in order to reconstruct the governing partial differential equations into a system of ordinary differential equations. Employing optimal homotopy analysis method series solutions are obtained. Error analysis has also been performed and presented in tabular form. The physical clarifications for the behavior of fluid velocity, temperature, skin friction coefficient and Nusselt number are well demonstrated with the help of graphs and contour plots. One of the major outcomes of the present study signifies that water-based SWCNTs have a tendency to cause less drag and higher rate of heat transfer as compared to water-based MWCNTs. This investigation finds numerous applications in different mechanisms of thermal conversion for nuclear propulsion and spacecraft.
Albert C. J. Luo - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Vibration of Heated Co-Rotating Disks
Journal of Vibration and Control, 2007Co-Authors: Nader Saniei, Albert C. J. LuoAbstract:Nonlinear vibrations of co-Rotating Disks with thermal effects are investigated under non-uniform temperature distributions relative to airflow induced by disk rotation. For analytical investigation of thermal effects, the temperature distribution patterns are obtained through the heat transfer coefficients measurements. The natural frequencies for symmetric and asymmetric responses of an 86 mm diameter computer memory disk are computed. When the disk is heated, its stiffness becomes larger for the two lowest nodal diameter numbers and smaller for the other nodal diameter numbers. This implies that the vibration of heated, Rotating Disks for the higher nodal diameter numbers may be induced more easily than the cooled one.
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Thermal Effects on the Natural Frequency of Nonlinear, Co-Rotating Disks
Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise Parts A B and C, 2005Co-Authors: Albert C. J. Luo, Nader Saniei, William Ray HarpAbstract:Thermal effects on the natural frequency for the nonlinear free vibration of co-Rotating Disks are investigated for non-uniform temperature distributions relative to airflow induced by disk rotation. The natural frequencies for symmetric and asymmetric responses of a 3.5 inch diameter computer memory disk are calculated. When the disk is heated, its stiffness becomes larger for the two lowest nodal diameter numbers and smaller for the other nodal diameter numbers. It implies that the vibration of heated, Rotating Disks for the higher nodal diameter numbers may be induced more easily than the cooled one.
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Thermally Induced, Nonlinear Vibrations of Rotating Disks
Nonlinear Dynamics, 2001Co-Authors: Nader Saniei, Albert C. J. LuoAbstract:The natural frequency and responses for the nonlinear free vibration ofheated Rotating Disks are presented analytically when nonuniformtemperature distributions pertaining to the laminar and turbulentairflow induced by disk rotation are considered. The nonuniformtemperature distributions on the disk are highly dependent on itsrotation speed. The natural frequencies for symmetric and asymmetricresponses of a 3.5 inch diameter computer memory disk are calculated.When the disk is heated, its stiffness becomes larger for the two lowestnodal diameter numbers and smaller for the other nodal diameter numbers.It implies that the vibration of heated, Rotating Disks for the highernodal diameter numbers may be induced more easily than the cooled one.The results for the nonlinear vibration can reduce to those for thelinear vibration when the nonlinear effects vanish. To furtherinvestigate of the interaction of thermal and nonlinearity of RotatingDisks, the temperature distribution for such a Rotating disk needs to bedeveloped.
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Resonant and Stationary Waves in Rotating Disks
Nonlinear Dynamics, 2001Co-Authors: Albert C. J. Luo, Chin An TanAbstract:The analytical conditions for resonant and stationary waves inRotating Disks are presented. These conditions are derived from anonlinear plate theory pertaining to initial configurations and areapplicable to Rotating Disks with initial waviness and/or undergoinglarge-amplitude displacements. The rotational speeds at which theresonant and stationary waves occur for a 3.5-inch diameter computermemory disk are computed. The resonant waves for linear and nonlinear,Rotating Disks are simulated numerically. It is found that some diskmodes exhibit a hardening effect under which the rotational speeds forthe resonant and stationary waves increase with increasing waveamplitude, while other modes experience a softening effect with thoserotational speeds decreasing with increasing wave amplitude. TheRotating-disk resonant spectrum presented in this paper is relevant tothe disk drive industry for determining the range of operationalrotation speed.
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Nonlinear resonant traveling waves in Rotating Disks
Communications in Nonlinear Science and Numerical Simulation, 2000Co-Authors: Albert C. J. Luo, Chin An TanAbstract:Abstract The resonant conditions for traveling waves in Rotating Disks are derived. The nonlinear resonant spectrum of a Rotating disk is computed from the resonant conditions. Such a resonant spectrum is useful for the disk drive industry to determine the range of operational rotation speed. The resonant wave motions for linear and nonlinear, Rotating Disks are simulated numerically for a 3.5-inch diameter computer memory disk.
