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The purpose of this paper is to present novel search formulations in gradient‐type methods for prediction of boundary heat flux distribution in two‐dimensional nonlinear heat conduction problems.

The performance of gradient‐type methods is strongly contingent upon the effective determination of the search direction. Based on the definition of this parameter, gradient‐based methods such as steepest descent, various versions of both conjugate gradient and quasi‐Newton can be distinguished. By introducing new search techniques, several examples in the presence of noise in data are studied and discussed to verify the accuracy and efficiency of the present strategies.

The verification of the proposed methods for recovering time and space varying heat flux. The performance of the proposed methods via comparisons with the classical methods involved in its derivation.

The innovation of the present method is to use a hybridization of a conjugate gradient and a quasi‐Newton method to determine the search directions in gradient‐based approaches.

Fluid mixing plays a critical role in the success or failure of industrial processes which call for the addition of small quantities of chemicals to working fluid. This paper aims to describe how mixing processes of liquids in turbulent flow regime can be simulated numerically, present the flow pattern through a helical static mixer, and provide useful information that can be extracted from the simulation results.

The performance of a helical static mixer under turbulent flow conditions is numerically studied. The model solves the 3D Reynolds‐averaged Navier‐Stokes equations, closed with the Spalart‐Allmaras turbulence model, using a second‐order‐accurate finite‐volume numerical method. Numerical simulations are carried out for a six‐element mixer. Using a variety of predictive tools, mixing results are obtained and the performance of static mixer under turbulent flow condition is studied.

The upstream mixing elements increase the mixing more effectively compared to the downstream mixing elements; and also, the rate of mixing is higher in the regions close to the edges of mixing elements.

Static mixers have been widely used in the following industries: chemicals, food processing, heating, ventilation, and air conditioning, mineral processing, paints and resins, petrochemicals and refining, pharmaceuticals, polymers and plastics, pulp and paper, and water and waste treatment.

This paper fulfils an identified information need and offers practical help to an individual researcher in academia as well as industry.

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used for the first time to solve phase change problems. Several isothermal phase change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate and robust for the numerical modeling of phase change problems.