**7.3 Fluid flow**

*Inverse Heat Conduction and Heat Exchangers*

process of AISI 304 stainless steel [79].

**6.6 Globules, spray, and plunge cooling**

the flow of heat in the granular materials [88].

**6.5 Crystal growth**

process [80, 81].

**7. Numerical methods**

depicted in this section.

**7.1 Heat conduction**

**7.2 Inverse analysis**

freezing time significantly [77].

packed bed of spheres has been developed using graphite/PCM composite for increasing the thermal conductivity which resulted in reduction in melting and

It has been observed that the supercooling properties of sodium acetate trihydrate can be improved by addition of nano-Cu [78]. A simulation model of melting and solidification of PCM in metallic porous foam has been investigated in the heat exchanger. The Hunt-Trivedi model has been used to simulate the solidification

The crystal growth involves controlled growth of microstructure using optical heating, modeling of mass crystallization in magma chamber, effect of crystal growth on solute distribution, and simulation of crystal growth for binary melting

This subsection deals with the deposition of metal droplets on the premolten pool and wavy surfaces, numerical analysis using FEM to study fluid mechanics and heat transfer of solder droplet on flat surface, numerical analysis of microdroplet deposition over a novel micromanufacturing process, and utilization of impulse

Numerical methods are used to develop the mathematical models to solve complex numerical problems. The technique is used widely in research for modeling and optimization of the physical work which otherwise required rigorous work. The research work done in the field of heat transfer using numerical methods has been

A hybrid 3D model has been developed for the analysis of transient heat conduction in a functionally graded material (FGM) using generalized finite difference method [85], Cattaneo-Vernotte model (CV model) was used to develop numerical simulation of non-Fourier heat conduction for a fin attached to a microelectronic surface [86], Galerkin-vector theory and numerical method are used to develop a mathematical model to study heat conduction in nonhomogenous materials [87], and heat conduction model was developed using numerical methods to understand

Systematic and local error has been identified using WKB method through numerical analysis [89], numerical inverse Laplace transform was used to solve nonlinear differential Equation [90], and numerical inverse method has been

developed to extract heat flux in heat-sensitive coating region [91].

atomization technique to produce controlled size droplets [82–84].

**6.4 Melting and solidification of metals, non-metals, and composites**

**10**

The lattice Boltzmann method is used for simulation model of non-Newtonian fluid flow, two fluid method, and discrete particle method used for simulating the gas-solid flow of rough particles. A CFD model can be used effectively to study the hydrofluidization freezing, and a numerical simulation of fluid flow with thermal hydraulic mechanical coupling method on an uneven surface was developed [89].
