Pengubahsuaian ke Atas Kaedah Kecerunan Konjugat untuk Peminimuman Tak Berkekangan

Penumpuan utama tesis ini adalab dalam usaba mencari penyelesaian berangka untuk masalab pengoptimuman tak linear tak berkekangan. Kami mempertimbangkan suatu kaedab pengoptimu man yang terkenal disebut kaedab kecerunan konjugat. Khususnya, satu kelas kaedab kecerunan konjugat bemama kaedab Fletcher-Reeves akan difokuskan. Kami lanjutkan analisis kami kepada tatacara gelintaran gans baru yang diperkenalkan oleh (Potra dan Shi, 1995). Kami seterusnya menerbitkan dua teknik pembaikan: yang pertama kami menggunakan satu kriteria penukaran di antara arab kecerunan konjugat dan kuasi-Newton dan untuk yang kedua, kami memperkenalkan penggunaan arab kelengkungan negatif dalam gabungan linear bagi kaedab kecerunan konjugat dan kuasi-Newton. Tesis ini akan meliputi keputusan-keputusan yang menghuraikan persembaban berangka bagi kaedahkaedab terubahsuai ke atas suatu set fungsi ujian yang dipilih. Kesimpulan dan beberapa kemungkinan kajian lanjutan akan diberi untuk mengakhiri tesis ini. Penggunaan tatacara gelintaran garis baru, penukaran di antara arab kecerunan konjugat dan kuasi-Newton dan penggunaan arab kelengkungan negatif dalam gabungan linear bagi kaedah kecerunan konjugat dan kuasi-Newton memberikan keputusan berangka yang lebih baik

Similarity solutions for the stagnation-point flow and heat transfer over a nonlinearly stretching/shrinking sheet

This paper presents a numerical analysis of a stagnation-point flow towards a nonlinearly stretching/shrinking sheet immersed in a viscous fluid. The stretching/shrinking velocity and the external flow velocity impinges normal to the stretching/shrinking sheet are assumed to be in the form U ~ xm, where m is a constant and x is the distance from the stagnation point. The governing partial differential equations are converted into ordinary ones by a similarity transformation, before being solved numerically. The variations of the skin friction coefficient and the heat transfer rate at the surface with the governing parameters are graphed and tabulated. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique for m > 1/3

MHD stagnation-point flow of a micropolar fluid with prescribed wall heat flux.

The steady magnetohydrodynamic (MHD) mixed convection stagnation point flow towards a vertical surface immersed in an incompressible micropolar fluid with prescribed wall heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. Numerical results are obtained for the skin-friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely, the mixed convection parameter, material parameter, and Prandtl number. Dual solutions are found to exist for the opposing flow

Mixed convection boundary layer flow over a permeable vertical cylinder with prescribed surface heat flux.

In this study we investigate the steady mixed convection boundary layer flow along a permeable vertical cylinder with prescribed surface heat flux. The free stream velocity and the surface heat flux are assumed to vary linearly with the distance from the leading edge. The governing system of partial differential equations is first transformed into a system of ordinary differential equations, and the transformed equations are solved numerically for both assisting and opposing flow regimes using two different methods, namely the Keller-box method and the NAG routine D02HAF. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Dual solutions for the previously studied mixed convection boundary layer flow over an impermeable surface of the cylinder are shown to exist also in the present problem for aiding and opposing flow situations

The effects of suction and injection on a moving flat plate in a parallel stream with prescribed surface heat flux

The effect of surface mass flux on a moving flat plate in a moving fluid with prescribed surface heat flux is studied. The governing partial differential boundary layer equations are first transformed into ordinary differential equations before being solved numerically by a finite difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist when the plate and the free stream move in the opposite directions. The results indicate that the range of known dual solutions increases with suction and decreases with injection and the rate of heat transfer increases with increasing heat flux exponent parameter

Power-law fluid flow on a moving wall

The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a moving flat plate in a moving fluid is studied. The transformed boundary-layer equation is solved numerically for some values of the power-law index n and velocity ratio parameter ε. The effects of these parameters on the skin friction coefficient are analyzed and discussed. It is found that dual solutions exist when the plate and the fluid move in the opposite directions, near the region of separation. It is also found that the drag force is reduced for dilatant fluids compared to pseudo-plastic fluids

Feedback control of the Marangoni-Bénard convection in a horizontal fluid layer with internal heat generation

Feedback control is applied to the steady Marangoni-Bénard convection in a horizontal layer of fluid with internal heat generation heated from below and cooled from above. The analytical technique is used to obtain the close form analytical expression for the onset of Marangoni-Bénard convection when the lower boundary is conducting. The effects of feedback control are studied by examining the critical Marangoni numbers and wave numbers. It is shown that the critical Marangoni number decreases as the value of internal heat generation but the critical Marangoni number can be increased through the use of feedback control

Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid.

The unsteady laminar flow of an incompressible micropolar fluid over a stretching sheet is investigated. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. Effects of the unsteadiness parameter, material parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined

Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid with prescribed surface heat flux.

The unsteady laminar flow of an incompressible micropolar fluid over a stretching sheet with prescribed surface heat flux is investigated. The governing partial differential boundary layer equations are first transformed into ordinary differential equations before being solved numerically by a finite-difference m 'hod. The effects of the unsteadiness parameter and Prandtl number on the flow and heat transfer characteristics are studied. It is found that the surface shear stress and the heat transfer rate at the surface are higher for micropolar fluids compared to Newtonian fluids

Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet.

An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow to a melting stretching/shrinking sheet. The governing partial differential equations are converted into ordinary differential equations by similarity transformation, before being solved numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, stretching/shrinking parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique