## 1 Introduction  
Heat exchangers are the apparatus used in many industries for heat transfer among fluids. In the design process of heat equipment, such as boilers, nuclear-reactor cores, radiators, condensers, and air conditioners, heat transfer engineering analysis is necessary [1]. Heat transfer enhancement in heat exchangers results in thermal efficiency and energy saving. A double-pipe heat exchanger (DPHE) is a special kind of heat exchanger with two concentric pipes, one inside the other. There are two different fluid flows in a DPHE, such that one fluid flows inside the inner pipe and the other fluid flows in the annulus region outside of the inner pipe. There is a growing need to decrease the cost and size of heat exchangers and increase the heat transfer characteristics. The performance of heat exchangers can be enhanced by adopting appropriate techniques. These techniques include the use of extended surfaces, surface vibration, rough surfaces, and coiled tubes. The present work deals with the technique of using the extended fins. These fins are extended surfaces and employed to increase the heated surface. A brief survey of some existing forms of heat exchanger extended fins is presented below. The authors of [2, 3] proposed increasing the heat transfer using triangular fins in straight pipes. They adopted the finite element (FE) technique for numerical results. Theydecomposed the problem into two parts. In the first part [2], they presented the analysis for the following parameters: the number, thickness, and height of the fins. They also suggested empirical relationships for the friction factor. In the second part [3], they analyzed the heat transfer characteristics by assuming the condition of axially uniform heat flux. This type of thermal boundary condition is known as the H1 boundary condition ([PERSON] and [PERSON] [4]). They reported an optimum number of fins for enhanced values of the Nusselt number (Nu). [PERSON] et al. [5] reported the increase of the coefficient of heat transfer using the tapered longitudinal fins in tubes. They applied the condition of constant wall temperature. They also compared their suggested results with a finless pipe. The thermal boundary condition considered in [5] is known as the T1 boundary condition. [PERSON] and [PERSON] [6] performed the analysis of heat enhancement in a pipe with annular fins. These fins were augmented externally and arranged in arrays with regular space. They employed the Biot number for heat analysis. They reported a substantial rise in the Biot number as compared to the finless tube. [PERSON] and [PERSON] [7] carried out the study of heat enhancement of laminar flow at the entry section of a duct. They assumed radial fins of zero thickness. They presented results for a number of radial fins varying from 8 to 24. [PERSON] [8] discussed the combined convection and conduction heat exchange analysis in a finned pipe. He reported that fins augmented internally cause a significant effect on heat exchange. [PERSON] and [PERSON] [9] investigated the heat and flow analysis in a pipe with augmented periodic fins. They considered the values of fin-gap, fin-height, and radii ratio in the range of 2 to 5, 0.33 to 0.67, and 0.3 to 0.5, respectively. They reported that recirculating flow was observed in the whole fin-inter spacing for the Reynolds number (Re) greater than 500, and a 3.1 times rise in heat transfer for specific parametric values. [PERSON] and [PERSON] [10] experimentally investigated the pressure drop in terms of pumping power in a DPHE. They considered rectangular fins having interruptions. They reported that the coefficient of heat exchange rises with an increasing number of interruptions. [PERSON] [11] investigated the heat exchange numerically in a DPHE with rectangular fins. He proposed that the height and thickness of the fins may also be considered along with hydraulic diameter to form the correlation of coefficient of heat exchange.