## 1 Introduction
The BEMT combines a CV conservation of momentum analysis with the blade sectional analysis [11]. The BEMT is an upshot of the general momentum theory developed by [PERSON] and [PERSON] [5; 12]. Although interesting solutions of the general momentum equations were developed for special cases with simplifying assumptions, these researchers were not able to provide closure with an analytically determined axial force equation; later researchers determined that there was not enough information to account for an axial force balance [12]. According to the BEMT, the axial induction factor varies radially and azimuthally across the rotor [9]. Another numerical model is the actuator line model (ALM). The ALM represents the three rotor blades of a HAWT by a rotating body of forces. The force per unit span on a rotor blade is estimated and the total force on the rotor is calculated by multiplying the integral of the force per unit span by the number of rotor blades [13]. Typically, the overall forces on a WT rotor are calculated by adding up the aerodynamic forces of each cross-section using the strip or blade element theory. The centrifugal and Coriolis forces that appear in the laminar boundary layer (LBL) increase the aerodynamic lift forces as compared to those in a similar two-dimensional non-rotating disk. Centrifugal forces produce a span-wise outward velocity, which gives rise to the Coriolis forces that act as favorable pressure gradients in the chord-wise direction. They also tend to reduce the thickness of the LBL due to the outward movement of the fluid, viz, the centrifugal pumping effect. This secondary flow postpones the appearance of the separation point, allowing the airfoil to reach a higher angle of attack before stalling [14]. [PERSON] assumed that the angular speed of the wake is never greater than the angular speed of the rotor [12] but gave no justification for this assumption. On the contrary, in real life, even static rotors impart swirl on their wakes [12]. A setback of the ADT is the fact that it results in a discontinuity in pressure as air flows past the actuator disk. The Betz-Joukowsky limit was derived using a simple balance of axial momentum and remains the basis for the maximum power extracted by an ideal HAWT rotor [15]. [PERSON] et al. [16] modified the ADT in their bid to account for the effects of the atmospheric boundary layer (ABL) on the maximum efficiency of an ideal HAWT by introducing modification factor \(\beta\) to account for the effects of Coriolis forces on the average KE per unit mass passing through the rotor and modification factor \(\gamma\) to account for the effects of velocity changes over a cross-section of the CV on the average momentum. They claimed that because of the effects of the ABL, the maximum power coefficient calculated is slightly higher than the Betz-Joukowsky limit--i.e., a 1-2% increase in the Betz limit was observed. [PERSON] et al. [17] in their study of the analytical methods for WT wake developed independently by [PERSON] and [PERSON], discovered that though these models are fast in calculating wake velocity deficit, they rely solely on empirical coefficients that are case specific. For instance, [PERSON]'s model requires a wake expansion coefficient to be determined. These two models are modifications of the ADT. [PERSON] considered a turbulent wake state in developing his model, while [PERSON] used a steady wake state. Power predictions by the latter are higher than those of the former. By revisiting the ALM discussed in a foregoing paragraph, it was first developed by [PERSON] and [PERSON] in 2002. It represents the HAWT rotor blades by a series of point forces acting along the span of each rotor blade at the quarter chord. The ALM allows for the flow effects on the rotor blades to be modeled using discrete rotor blades without requiring the discretization of the blade boundary layer, resulting in lower computational requirements than three-dimensional blade-resolved models, while preserving the principal effects of the rotor on the flow.