## 1 Introduction  
In the past few years, scientists have faced a consequential issue of thermal efficiency in different engineering and industrial applications. Technological advances, like high speed microelectronics, chemical synthesis, transportation, optical, microfluidics, microsystems including mechanical and electrical components bears high thermal loads. The cooling of these devices is a major concern in these days. Traditionally, the rate of heat transfer is increased by increasing the area available for heat exchange. Another way is to use a thermally efficient fluid, which is usually dispersed the nano-sized structures within the conventional heat transfer fluids (fluids bearing poor thermal properties), like water, propylene glycol, ethylene glycol, etc. [1]. The pioneer behind the discovery of these thermally efficient fluids, called 'nanofluids', was [PERSON] [2, 3]. This discovery further opens the door to a new research era. Many experimentalists would opt for this idea and as a result, several subsequent models have been successfully proposed. [PERSON] [4] took a first step and suggested a model to analyze the effective thermal conductivity of nanofluids. This model involves the nanoparticles concentration and the thermal conductivity of the base fluid and nanoparticles. Besides, it only takes the spherical inclusions of nanoparticles. To overcome this deficiency, [PERSON] and crosser [5] proposed a model which is applicable for non-spherical shaped nanoparticles. More studies in this area introduce a variety of models which examined the effects of nanoparticles type [6; 7; 8], particle shapes [9] and particles size [10; 11] etc. Moreover, various heat transfer mechanisms including Brownian movement of particles [12], particles agglomeration [13; 14] and liquid layering [15] would also gain the attention of many scientists. Even though nanofluids have a lot of potential to meet the growing thirst of thermal efficiency, still scientists are eagerly looking for different varieties of fluids. Hybrid nanofluids are an advanced type of nanofluids, which exhibit a remarkable thermal efficiency as compared to nanofluids. These fluids came into existence by dispersing two or more kinds of tiny particles within the base fluid or composite nanostructures in a base fluid. This implies a homogeneous mixture possessing physicochemical properties of various substances that can hardly be imagined to exist in an individual substance [16]. Hybrid nanofluids play an active role in a wide range of heat transfer applications such as electronic cooling, automobile radiators, generator cooling, nuclear system cooling, coolant in machining, lubrication, welding, solar heating, thermal storage, heating and cooling in buildings, biomedical, drug reduction, refrigeration and defense etc. At the industrial level, there are positive features like chemical stability and high thermal efficiency, which enables them to perform efficiently as compared to nanofluids. In the last few decades, many experimental studies have been conducted to explore the properties of hybrid nanofluids. [PERSON] et al. [17] employed the two-step method to study the synthesis of hybrid Al\({}_{2}\)O\({}_{3}\)-Cu/water nanofluids. The rate of heat transfer influenced by H\({}_{2}\)O-based Al\({}_{2}\)O\({}_{3}\)-Cu hybrid nanofluids was examined by [PERSON] et al. [18]. [PERSON] [19] experimentally investigates the laminar flow of a hybrid nanofluid along with mixed convection inside an inclined tube. Later on, the magnetohydrodynamic (MHD) flow of a hybrid Al\({}_{2}\)O\({}_{3}\)-Cu/water nanofluid over a permeable expanding sheet along with suction has been numerically considered by [PERSON] and [PERSON] [20]. Recently, to analyze the entropy generation, [PERSON] et al. [21] takes into account the magnetohydrodynamic Cu-Al\({}_{2}\)O\({}_{3}\)/water-based hybrid nanofluid flow between porous walls. [PERSON] and [PERSON] [22] analyze the Blasius hybrid nanofluid flow over a heated surface combined with convection.