**7. Numerical methods**

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 depicted in this section.

#### **7.1 Heat conduction**

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

#### **7.2 Inverse analysis**

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].

**11**

*Applications of Heat Transfer Enhancement Techniques: A State-of-the-Art Review*

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].

Numerical methods can also be utilized to predict the turbulent flow. k-ϵ and LES model were used to study turbulent flow field around rows of tree and building, turbulence in flow field and temperature can be predicted, renormalization is used to determine the eddy diffusion in turbulence flow, intermittency model was developed for studying the laminar boundary transition at supersonic and hypersonic condition, and LES is used to forecast the heat transfer coefficient and blade

The sheer variety of heat transfer operations has been demonstrated by a number of researchers in their works dealing with thermoacoustic and thermoelectric devices, rotating heat exchangers, commercial blood oxygenators, soil and deep bore heat exchangers, space craft radiators, and pressurized bubble columns.

The procedure to ease heat transfer has been stated by many researchers. The fin technology of extension is quite prevalent in the recent times. An investigation was carried out with fin tubes using liquid crystal display technology and plate finned tube exchanger by infrared thermal imaging, and performance measurement has been reported for a finned tube surface and annular fins. Fins having curly surfaces are examined for humid airflow. In addition to this film-wise condensation on plane low finned tubes, transient conduction in a fin, performance of extruded-serrated and extruded-finned tube bundles, and the features of a multi-pass heat exchanger

A number of applications now employ miniaturization of heat transfer devices: micro-heat pipe arrays, electronic cooling, microturbine, evaporation and boiling in microfin, microheat pipes, microscale temperature measurements, and modeling of

An investigation has been done to study the effect of gas-side fouling in cross flow. Calcium carbonate fouling effect was studied with a microscale image; mineral fouling in extended tube heat exchangers was studied; the use of polyacrylic

acid as anti-scaling and antifouling agent was studied [94–96].

*DOI: http://dx.doi.org/10.5772/intechopen.92873*

**7.3 Fluid flow**

**7.4 Turbulent flow**

metal temperature [92].

**8.1 Applications**

**8. Heat exchanger and thermosyphons**

**8.2 Enhancement of heat transfer**

have also been reported.

microchannel flows [93].

**8.4 Effect of fouling**

**8.3 Microscale heat transfer**

*Applications of Heat Transfer Enhancement Techniques: A State-of-the-Art Review DOI: http://dx.doi.org/10.5772/intechopen.92873*
