Analytical Study of Transient Heat Transfer in a Triangular Moving Porous Fin with Temperature Dependant Thermal Properties

2019 ◽  
Vol 393 ◽  
pp. 31-46
Author(s):  
Partner Luyanda Ndlovu
Keyword(s):  
Analytical Study ◽  
Closed Form Solution ◽  
Transformation Method ◽  
Form Solution ◽  
Solution Technique ◽  
Porous Fin ◽  
Approximate Analytical Solutions ◽  
Numerical Solver ◽  
The Impact ◽  
Darcy’S Model

The present work investigates heat enhancement through a moving porous fin of trangular profile. The interaction between the fluid and the porous media in not locally thermodynamic equilibrium. The transport through the porous medium is derived using Darcy’s model. The calculations are carried out using the two-dimensional Differential Transformation Method (2D DTM), which is an analytical solution technique that can be applied to various types of differential equations. The approximate analytical solutions are validated using the numerical solution obtained via the inbuilt numerical solver in MATLAB (pdepe). The results reveal that the 2D DTM can achieve accurate results in predicting the solution of such problems. The impact of the thermal parameters on temperature distribution is performed using the closed-form solution generated by DTM.

Improved Dynamic Model of the Human Knee Joint and Its Response to Impact Loading on the Lower Leg

1993 ◽  
Vol 115 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Ali Erkan Engin ◽  
Sami Turgut Tu¨mer
Keyword(s):  
Knee Joint ◽  
Impact Loading ◽  
Closed Form Solution ◽  
Lower Leg ◽  
Form Solution ◽  
Solution Technique ◽  
Human Knee ◽  
Human Knee Joint ◽  
Impact Theory ◽  
The Impact

Almost a decade ago, three-dimensional formulation for the dynamic modeling of an articulating human joint was introduced. Two-dimensional version of this fomulation was subsequently applied to the knee joint. However, because of the iterative nature of the solution technique, this model cannot handle impact conditions. In this paper, alternative solution methods are introduced which enable investigation of the response of the human knee to impact loading on the lower leg via an anatomically based model. In addition, the classical impact theory is applied to the same model and a closed-form solution is obtained. The shortcomings of the classical impact theory as applied to the impact problem of the knee joint are delineated.

scholarly journals On the impact of antenna diversity in IEEE 802.11b DCF with capture

2004 ◽  
Vol 17 (1) ◽  
pp. 41-52
Author(s):  
Zoran Velkov-Hadzi ◽  
Boris Spasenovski
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Access Point ◽  
Form Solution ◽  
Capture Probability ◽  
Antenna Diversity ◽  
Ieee 802.11B ◽  
Selection Diversity ◽  
Maximum Selection ◽  
The Impact

In this paper, we examined the influence of capture effect with L-fold antenna diversity at the Access Point over IEEE 802.11b DCF. We obtained an exact closed-form solution for the conditional capture probability in case of ideal selection diversity, and an approximate closed-form solution for the conditional capture probability in case of maximum selection diversity in a Rayleigh-faded channel. Obtained analytical expressions have general significance and can be applied for any other multiple access wireless network. We also analytically evaluated saturation throughput increase of the IEEE 802.11b DCF protocol exposed to capture.

New continuum surgical robot based on hybrid concentric tube-tendon driven mechanism

2021 ◽  
pp. 095440622110424
Author(s):  
Mohammed Abdel-Nasser ◽  
Omar Salah
Keyword(s):  
Inverse Kinematics ◽  
High Performance ◽  
Analytical Study ◽  
Fuzzy Inference ◽  
Closed Form Solution ◽  
Form Solution ◽  
Robot Arm ◽  
Inference System ◽  
Neuro Fuzzy ◽  
Intelligent Approach

Robotics technology is used widely in minimally invasive surgery (MIS) which provides high performance and accuracy. The most famous robot arm mechanisms, which are used in MIS, are tendon-driven mechanism (TDM), and concentric tube mechanism (CTM). Unfortunately, these mechanisms until now have some limitations, i.e. making friction with the tissue during extracting and retracting and strain limits, for TDM and CTM respectively. A new hybrid concentric tube-tendon driven mechanism (HCTDM) is proposed to overcome these limitations. HCTDM enables the end-effector to get close to and get away from the surgical area during the operation without harming the tissue and with more flexibility. In addition to that, the workspace increases as a result of this combination, too. This benefit serves MIS, especially endoscopic surgeries (ESs). We did an analytical study of this idea and got the forward kinematics. In the inverse kinematics, an intelligent approach which is called an adaptive neuro-fuzzy inference system (ANFIS) is used because the closed-form solution is more complicated for such these mechanisms. Finally, HCTDM is analyzed and evaluated by using a computer simulation. The simulation results show that the workspace becomes wider and has more dexterity than use TDM or CTM individually. Furthermore, various trajectories are used to test the mechanism and the kinematic analysis, which show the mechanism can follow and track the trajectories with maximum mean error 1.279, 0.7027, and [Formula: see text] for X, Y, and Z axes respectively.

Analysis of Simply-Supported Orthotropic Cylindrical Shells Subject to Lateral Impact Loads

1990 ◽  
Vol 57 (2) ◽  
pp. 376-382 ◽  
Author(s):  
A. P. Christoforou ◽  
S. R. Swanson
Keyword(s):  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Double Fourier Series ◽  
Form Solution ◽  
Lateral Impact ◽  
Simply Supported ◽  
Response Characteristics ◽  
Simple Support ◽  
The Impact ◽  
Approximate Procedure

An analytic solution is given for the problem of simply-supported orthotropic cylindrical shells subject to impact loading. The closed-form solution has not been obtained previously. The analysis is based on an expansion of the loads, displacements, and rotations in a double Fourier series which satisfies the end boundary conditions of simple support. Each expansion is assumed to be separable into a function of time and a function of position. By neglecting in-plane and rotary inertia the problem becomes a second-order ordinary differential equation in time for the Fourier coefficients of the radial deflection. For a given loading impulse the solution can be found by invoking the convolution integral. The results show that for impact by a heavy mass, the solution is equivalent to that obtained by an approximate procedure of neglecting the mass of the shell, which leads to a simple simple-degree-of-freedom analysis. For problems of impact by smaller masses, the higher response frequencies of the cylinder become important. The results show the importance of dynamic effects in the predicted impact duration, peak force, and peak deflection relative to the quasi-static response. The results show that the response amplitude varies linearly with the impact velocity, but the response characteristics depend on the mass of the impactor and the mass and stiffness of the cylinder.

A closed-form solution to eye-to-hand calibration towards visual grasping

2014 ◽  
Vol 41 (6) ◽  
pp. 567-574 ◽  
Author(s):  
Hui Pan ◽  
Na Li Wang ◽  
Yin Shi Qin
Keyword(s):  
Closed Form ◽  
Design Methodology ◽  
Closed Form Solution ◽  
Form Solution ◽  
Content Type ◽  
The Impact ◽  
Calibration Plane

Purpose – The purpose of this paper is to propose a method that calibrates the hand-eye relationship for eye-to-hand configuration and afterwards a rectification to improve the accuracy of general calibration. Design/methodology/approach – The hand-eye calibration of eye-to-hand configuration is summarized as a equation AX = XB which is the same as in eye-in-hand calibration. A closed-form solution is derived. To abate the impact of noise, a rectification is conducted after the general calibration. Findings – Simulation and actual experiments confirm that the accuracy of calibration is obviously improved. Originality/value – Only a calibration plane is required for the hand-eye calibration. Taking the impact of noise into account, a rectification is carried out after the general calibration and, as a result, that the accuracy is obviously improved. The method can be applied in many actual applications.

scholarly journals Optimal control of an inventory system under whole sale price changes

2019 ◽  
Author(s):  
Ata Allah Taleizadeh ◽  
Hamidreza Zarei ◽  
Shib Sankar Sana
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Price Changes ◽  
Total Saving ◽  
Ordering Policy ◽  
Decision Variables ◽  
Optimal Ordering Policy ◽  
Optimal Ordering ◽  
The Impact ◽  
Special Order

Nowadays business owners use lots of incentive schemes to make customers buy more products. In this paper optimal ordering policy for customers is obtained when the manufacturer increases the purchasing price or temporary decreases it. Offering a special sale from the manufacturer is probabilistic and shortage occurs as partial backlogging. In this paper, the initial level of inventory when the purchasing price changes is not equal to zero. With respect to the assumptions, the amount of special order quantity, the shortage quantity, and the expected total saving from making an special order is optimized for the customer. The optimal amount of decision variables are obtained by maximizing the expected total saving function and a closed-form solution is derived. Several numerical examples are solved and sensitivity analysis is performed to prove the applicability of the proposed model. Finally, the impact of some parameters of the model including the demand, the probability of making a special order, the future prices, and the initial inventory is investigated. Optimal ordering policy for the customers is obtained in cases when an announced price increase occurs and when the prices temporarily decrease.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

scholarly journals Performance Evaluation of Alternative Relative Orientation Procedures for UAV-based Imagery with Prior Flight Trajectory Information

2016 ◽  
Vol XLI-B3 ◽  
pp. 21-25 ◽  
Author(s):  
F. He ◽  
A. Habib
Keyword(s):  
Low Cost ◽  
Closed Form Solution ◽  
Experimental Tests ◽  
Form Solution ◽  
Relative Orientation ◽  
Conjugate Points ◽  
Flying Height ◽  
Reliable Estimate ◽  
Comparative Performance ◽  
The Impact

Thanks to recent advances at the hardware (e.g., emergence of reliable platforms at low cost) and software (e.g., automated identification of conjugate points in overlapping images) levels, UAV-based 3D reconstruction has been widely used in various applications. However, mitigating the impact of outliers in automatically matched points in UAV imagery, especially when dealing with scenes that has poor and/or repetitive texture, remains to be a challenging task. In spite of the fact that existing literature has already demonstrated that incorporating prior motion information can play an important role in increasing the reliability of the matching process, there is a lack of methodologies that are mainly suited for UAV imagery. Assuming the availability of prior information regarding the trajectory of a UAV-platform, this paper presents a two-point approach for reliable estimation of Relative Orientation Parameters (ROPs) of UAV-based images. This approach is based on the assumption that the UAV platform is moving at a constant flying height while maintaining the camera in a nadir-looking orientation. For this flight scenario, a closed-form solution that can be derived using a minimum of two pairs of conjugate points is established. In order to evaluate the performance of the proposed approach, experimental tests using real stereo-pairs acquired from different UAV platforms have been conducted. The derived results from the comparative performance analysis against the Nistér five-point approach demonstrate that the proposed two-point approach is capable of providing reliable estimate of the ROPs from UAV-based imagery in the presence of poor and/or repetitive texture with high percentage of matching outliers.

scholarly journals Analytical Solution to Improper Integral of Divergent Power Functions Using The Riemann Zeta Function

2019 ◽  
Author(s):  
Siamak Tafazoli ◽  
Farhad Aghili
Keyword(s):  
Closed Form Solution ◽  
Zeta Functions ◽  
Bernoulli Numbers ◽  
Form Solution ◽  
Binomial Coefficients ◽  
Solution Technique ◽  
Power Functions ◽  
Definite Integrals ◽  
Improper Integral ◽  
Riemann Zeta

This paper presents an analytical closed-form solution to improper integral $\mu(r)=\int_0^{\infty} x^r dx$, where $r \geq 0$. The solution technique is based on splitting the improper integral into an infinite sum of definite integrals with successive integer limits. The exact solution of every definite integral is obtained by making use of the binomial polynomial expansion, which then allows expression of the entire summation equivalently in terms of a weighted sum of Riemann zeta functions. It turns out that the solution fundamentally depends on whether or not $r$ is an integer. If $r$ is a non-negative integer, then the solution is manifested in a finite series of weighted Bernoulli numbers, which is then drastically simplified to a second order rational function $\mu(r)=(-1)^{r+1}/(r+1)(r+2)$. This is achieved by taking advantage of the relationships between Bernoulli numbers and binomial coefficients. On the other hand, if $r$ is a non-integer real-valued number, then we prove $\mu(r)=0$ by the virtue of the elegant relationships between zeta and gamma functions and their properties.

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