A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall ...A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (<em>Rot</em> = 0<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span> - 90<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span>) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed <em>U</em><sub>0</sub>. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ <em>Pr</em> ≤ 2), Reynolds number (60 ≤ <em>Re</em> ≤ 120), Rayleigh number (<em>Ra</em> = 10<sup>3</sup>) and Hartmann number (<em>Ha</em> = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of <em>Nu</em><sub>av</sub> of hot bottom wall and <em>θ</em><sub>av</sub> in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.展开更多
This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The...This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.展开更多
文摘A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (<em>Rot</em> = 0<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span> - 90<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span>) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed <em>U</em><sub>0</sub>. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ <em>Pr</em> ≤ 2), Reynolds number (60 ≤ <em>Re</em> ≤ 120), Rayleigh number (<em>Ra</em> = 10<sup>3</sup>) and Hartmann number (<em>Ha</em> = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of <em>Nu</em><sub>av</sub> of hot bottom wall and <em>θ</em><sub>av</sub> in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.
文摘This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.
