Let (X,d,μ) be a space of homogeneous type and L be a nonnegative self-adjoint operator on L2(X) whose heat kernels satisfy Gaussian upper bounds. In this article, we introduce the weighted variable Besov space associated with the operator L and demonstrate that Peetre maximal functions can be used to characterize this space. Furthermore, we provide a detailed study of its atomic decompositions.

Let (X,d,μ) be a space of homogeneous type and L be a nonnegative self-adjoint operator on L2(X) whose heat kernels satisfy Gaussian upper bounds. In this article, we introduce the weighted variable Besov space associated with the operator L and demonstrate that Peetre maximal functions can be used to characterize this space. Furthermore, we provide a detailed study of its atomic decompositions.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

Heat transfer by convection is widely used in many engineering applications such as in heat exchangers, combustion devices or gas processing. In Buildings, the use of rough surfaces allows enhancing heat transfer rates. Practically, in this study, a rough surface is obtained by using protuberances on the vertical left wall. In this perspective, the originality of this research is to study the influence of the protuberance geometric shapes on the heat transfer using 2D numerical simulations as a tool investigation. The homotopic transformation is used to reach a flat plate. The system of equations with the boundary conditions is solved using the finite volume method. A simple algorithm is chosen for the integration of algebraic equations. The governing equations are figured out using ANSYS FLUENT commercial software with SIMPLE algorithm in order to solve pressure-velocity coupling. The numerical simulations have been performed for different shapes of the protuberances (battlement, triangular and sinusoidal). The boundary conditions are based on a uniform heat flux applied to the vertical wall. On the other hand, the horizontal walls are subject to the adiabatic condition. It can be noticed that the effect of the wavy geometry induces a noticeable improvement of the heat transfer rate compared to an enclosure without protuberances. It can also conclude that the wavy configuration exhibits a Nusselt average slightly higher than that of the square cavity, particularly the triangular configuration, by approximately 20%.

The significance of the Black female identity in the stratified predominantly White American society have been under scrutiny for the past half a century. Affiliated with two socially persecuted groups, African American women felt unavoidably compelled to fall under certain societal patterns and paradigms, which expectedly fail to represent their authentic sense of self. The conundrum encountered by Black females in “The Bluest Eye” is in fact aesthetically rooted; Toni Morrison vividly portrayed the destructive outcome of blindingly conforming to the standardized beauty concepts created by a dominant social group, and systematically masterminded for everyone to embrace and adapt to regardless of their cultural backgrounds and skin color. The novel exemplifies Morrison’s unswerving fight against the underestimation of Black women’s existence and the devaluation of their self-worth and identity.

The significance of the Black female identity in the stratified predominantly White American society have been under scrutiny for the past half a century. Affiliated with two socially persecuted groups, African American women felt unavoidably compelled to fall under certain societal patterns and paradigms, which expectedly fail to represent their authentic sense of self. The conundrum encountered by Black females in “The Bluest Eye” is in fact aesthetically rooted; Toni Morrison vividly portrayed the destructive outcome of blindingly conforming to the standardized beauty concepts created by a dominant social group, and systematically masterminded for everyone to embrace and adapt to regardless of their cultural backgrounds and skin color. The novel exemplifies Morrison’s unswerving fight against the underestimation of Black women’s existence and the devaluation of their self-worth and identity.

The knee osteoarthritis requires the latter joint replacement by a total knee prosthesis (TKP). Generally, this prosthesis consists of three parts; a femoral component in CoCrMo cobalt alloy, a tibial insert in polyethylene, and a tibial tray in titanium a loy Ti6AL4V. This type of prosthesis is not 100 % comfortable, after years of implantation, the tibial insert (polyethylene) degrades and gives more wear debris, which affects the bio-functionality of this prosthesis and the patient life. In this study, two models of total knee prosthesis are designed and analyzed using SolidWorks and Ansys software, the first model is the existing three-part prosthesis, and the second model is based on the theory of Mooney – Rivlin method prosthesis with a new layer of silicone component. In this paper, shock simulation of a free fall from a height of 75 cm is studied. The results of the displace ment comparison between the first model 0.039 mm, and the second model 1.41 mm. In compar ison with the contraction of the biological knee joint show that the second model has a contraction closer to the biological knee. It can be deduced that this total knee prosthesis has a hyper-elastic behavior closer to the behavior of a biological knee as well, which gives more stability and provides a cushioning role for the knee compared to the existing TKP.

The knee osteoarthritis requires the latter joint replacement by a total knee prosthesis (TKP). Generally, this prosthesis consists of three parts; a femoral component in CoCrMo cobalt alloy, a tibial insert in polyethylene, and a tibial tray in titanium a loy Ti6AL4V. This type of prosthesis is not 100 % comfortable, after years of implantation, the tibial insert (polyethylene) degrades and gives more wear debris, which affects the bio-functionality of this prosthesis and the patient life. In this study, two models of total knee prosthesis are designed and analyzed using SolidWorks and Ansys software, the first model is the existing three-part prosthesis, and the second model is based on the theory of Mooney – Rivlin method prosthesis with a new layer of silicone component. In this paper, shock simulation of a free fall from a height of 75 cm is studied. The results of the displace ment comparison between the first model 0.039 mm, and the second model 1.41 mm. In compar ison with the contraction of the biological knee joint show that the second model has a contraction closer to the biological knee. It can be deduced that this total knee prosthesis has a hyper-elastic behavior closer to the behavior of a biological knee as well, which gives more stability and provides a cushioning role for the knee compared to the existing TKP.

The knee osteoarthritis requires the latter joint replacement by a total knee prosthesis (TKP). Generally, this prosthesis consists of three parts; a femoral component in CoCrMo cobalt alloy, a tibial insert in polyethylene, and a tibial tray in titanium a loy Ti6AL4V. This type of prosthesis is not 100 % comfortable, after years of implantation, the tibial insert (polyethylene) degrades and gives more wear debris, which affects the bio-functionality of this prosthesis and the patient life. In this study, two models of total knee prosthesis are designed and analyzed using SolidWorks and Ansys software, the first model is the existing three-part prosthesis, and the second model is based on the theory of Mooney – Rivlin method prosthesis with a new layer of silicone component. In this paper, shock simulation of a free fall from a height of 75 cm is studied. The results of the displace ment comparison between the first model 0.039 mm, and the second model 1.41 mm. In compar ison with the contraction of the biological knee joint show that the second model has a contraction closer to the biological knee. It can be deduced that this total knee prosthesis has a hyper-elastic behavior closer to the behavior of a biological knee as well, which gives more stability and provides a cushioning role for the knee compared to the existing TKP.

The knee osteoarthritis requires the latter joint replacement by a total knee prosthesis (TKP). Generally, this prosthesis consists of three parts; a femoral component in CoCrMo cobalt alloy, a tibial insert in polyethylene, and a tibial tray in titanium a loy Ti6AL4V. This type of prosthesis is not 100 % comfortable, after years of implantation, the tibial insert (polyethylene) degrades and gives more wear debris, which affects the bio-functionality of this prosthesis and the patient life. In this study, two models of total knee prosthesis are designed and analyzed using SolidWorks and Ansys software, the first model is the existing three-part prosthesis, and the second model is based on the theory of Mooney – Rivlin method prosthesis with a new layer of silicone component. In this paper, shock simulation of a free fall from a height of 75 cm is studied. The results of the displace ment comparison between the first model 0.039 mm, and the second model 1.41 mm. In compar ison with the contraction of the biological knee joint show that the second model has a contraction closer to the biological knee. It can be deduced that this total knee prosthesis has a hyper-elastic behavior closer to the behavior of a biological knee as well, which gives more stability and provides a cushioning role for the knee compared to the existing TKP.