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In this paper, we propose a class of high-order time integration schemes combined with high-order IsoGeometric Analysis (IGA) in three space dimensions. The combined methods offer robust solutions of nonlinear heat diffusion in three-dimensional composites that pose numerical challenges. This tailored strategy significantly enhances computational efficiency, especially crucial when addressing nonlinear heat transfer in three-dimensional enclosures. Leveraging precise geometry representation and seamless high-order element continuity of the IGA, this method effectively exploits these advantages. It emphasizes the vital synergy between high-order spatial discretization and an equivalent high-order time integration scheme. This study also highlights the risks of overlooking this pairing, which can lead to a degradation of the overall high-order accuracy and increased computational demands due to the complexity of high-order nonuniform rational B-splines. Numerical examples, such as applications involving a furnace wall segment and a rail wheel heat transfer, are used to validate the efficiency and accuracy of the combined approach. Consistently surpassing the conventional methods in both aspects, the proposed method notably excels in providing precise solutions for steep heat gradients even on coarse meshes. Consequently, this approach constitutes a substantial advancement in the field of transient heat transfer analysis within composite domains.

In this paper, two dimensional unsteady flow and energy equations are employed for simulating the fluid flow, heat transfer and solidification during direct chill continuous casting of Al-Mg alloy billet. In these processes, the formation of some macro defects such as thermal cracking, hot tearing, surface cracking, etc, has been found to initiate during the starting phase of the operation. In this paper, a numerical study of these developing fluid flow and thermal phenomena from the beginning of casting operation to a steady-state is presented. The computations are based on an iterative deforming finite volume method and a single-domain enthalpy formulation to solve the growth of metal being solidified and the accompanying dynamic fluid flow and thermal behavior. The effect of phase change on convection is accounted for using a Darcy's law-type porous media treatment. The results indicate that the fluid flow and temperature fields change drastically at the initial stage but evolve slowly afterwards.

There has been a growing research interest in the melting and solidification technology among mathematicians and engineers. The topic has obvious practical importance in a wide range of applications. Natural convection may play a significant role in heat transfer and hence affect the progress of the solidification. A fixed-grid finite volume numerical approach is developed and used to simulate physical details of convection flow in the solidification problems. This approach is based on the enthalpy–porosity method that is traditionally used to track the motion of the liquid–solid front and to obtain the temperature distribution and the velocity profiles in the liquid phase. The enthalpy–porosity model treats the mushy region as a porous medium.

In this paper, the numerical and experimental studies of unsteady natural convection during solidification of cylindrical ingots are presented. The aim of the study consists of the numerical determination of the fluid flow, the temperature evolution, and the solidification front versus time. To validate the numerical model, an experimental study of the simple casting of cylindrical ingots was undertaken within the laboratory of metallurgy. The measured temperature was compared with values calculated numerically. A good agreement was obtained.

The heat and mass transfer in an unsteady boundary layer flow of an incompressible, laminar, natural convective third-grade fluid is studied. The flow is taken over a semi-infinite vertical porous plate with the temperature-dependent fluid properties by taking into account the effect of viscous dissipation and variable suction. The partial differential equations governing the problem are reduced into the nonlinear, coupled, nondimensional ordinary differential equations with the help of suitable similarity transformations. The Galerkin Finite Element Method is implemented to solve this acquired system. The effects of various significant parameters such as Grashof number, Prandtl number, Eckert number, Solutal Grashof number and Schmidt number on dimensionless velocity, temperature and concentration profiles are presented graphically. The Nusselt number is found to be depressed whereas the Sherwood number is observed to be enhanced with the increasing values of Grashof number and Prandtl number. The study has important applications in chemical process industries such as filtration in food industry, production of drinking water and recovering salts from solutions.

To study the effect of enhanced surface geometries on nucleate boiling heat transfer, the numerical simulation of nucleate boiling on enhanced surfaces are performed by lattice Boltzmann method. For validation of the present model, a vapor bubble growth on and departure from plain surface is simulated and compared to experimental results. The numerical results are in good agreement with existing experimental results. By means of present model, the processes of bubble growth on and departure from triangular and rectangular structure surface are simulated, respectively. The numerical results demonstrate that the rectangular structure surface possesses the highest performance for heat transfer during nucleate boiling. The plain surface has the lowest heat transfer efficiency. The mechanisms contributing to the high thermal performance of enhanced surfaces are discussed. In addition, through the analysis of bubble shapes and temperature fields, it is found that the simulation results support the transient micro-convection model and the thin film evaporation model.

The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms are also included. The direct problem is solved by using Galerkin finite element method (FEM) with mixed finite elements and the control problem approach is the discretize-then-optimize procedure. The control formulations with the flow index parameter and the Hartmann number are given to regain the desired velocity profile and temperature isolines of the MHD flow.

This paper presents a hybrid approach to enhance heat transfer (HT) within a copper square duct for gas turbine (GT) blade cooling systems. The proposed method combines the gannet optimization algorithm (GOA) with the Spiking Deep Residual Network (SDRN), referred to as the GOA–SDRN technique. Since GTs operate at temperatures exceeding metal melting points, internal cooling is crucial to safeguard the blades and extend their lifespan. This study’s main goal is to apply rib tubular or turbulence promoters in internal cooling turbine blades, with a focus on managing temperature and maximizing HT to enhance GT blade-cooling systems. To achieve this, the proposed method analyzes the effectiveness of ribs by employing internal rib configurations, subsequently coated with composite nanomaterials such as thermal polymer and titanium carbide powder. The study investigates turbulent flow through the square passage at various Reynolds Numbers (Re), maintains constant ambient hot air temperature, and evaluates the performance of ribs. Specifically, the flow and HT within a square channel, resembling the air-cooled turbine blade cross-section, will be examined. The effectiveness of the GOA–SDRN method will then be assessed using MATLAB and compared against existing methodologies. The proposed method outperforms existing optimization methods significantly, achieving the highest efficiency of 94%, compared to 62% for SSA, 70% for CSA, and 84% for HBO. Additionally, the proposed method exhibits the lowest cost of $35, compared to $67 for SSA, $55 for CSA, and $48 for HBO. In summary, the proposed method offers superior efficiency and cost-effectiveness, making it the preferred choice for the application.

Applications for heat exchangers are many and include power plants, air conditioning, chemical and chemical engineering, and other scientific fields. The cost of materials and energy has increased recently, placing pressure on heat exchangers to become even more efficient. In mechanical design, this work proposes a hybrid method for heat transfer optimization and thermal analysis. The proposed hybrid method is the joint execution of both the Wild Horse Optimizer (WHO) and Multi Fidelity Deep Neural Network (MFDNN). It is hence known as the WHO–MFDNN approach. This proposed technique’s goal is to minimize the system’s overall operating costs while optimizing the system’s efficacy. The MFDNN technique is used to forecast the system’s ideal solution, while the proposed WHO approach is employed to minimize the system’s overall operating costs. By then, the proposed approach has been implemented into the MATLAB working platform, and the existing technique is used to compute the execution. In every system now in use, like Artificial Neural Network (ANN), Wild Border Collie Optimization (BCO) and Particle Swarm Optimization (PSO) the proposed approaches produce superior results. It concludes that the proposed method offers superior performance by achieving a cost of $40, converging in just 200 iterations, and requiring only 10 s of computational time, significantly outperforming existing methods with higher costs and longer convergence and computation times.