الكهرومغناطيسية والكهرومغناطيسات

يُعد المُجدِّد، أو "المُقتصد"، أهم إسهامات روبرت ستيرلنغ، وهو سرُّ الكفاءة العالية للمحرك. وهو مبادل حراري داخلي يُخزِّن الطاقة الحرارية ويُطلقها مؤقتًا خلال الدورة. عندما ينتقل الغاز الساخن إلى الجانب البارد، يُرسِّب الحرارة في مصفوفة المُجدِّد، والتي يلتقطها الغاز البارد في رحلة عودته إلى الجانب الساخن.

Engineering stress ([latex]\sigma[/latex]) is the applied load divided by the original cross-sectional area ([latex]A_0[/latex]), while engineering strain ([latex]\epsilon[/latex]) is the change in length ([latex]\Delta L[/latex]) divided by the original length ([latex]L_0[/latex]). These definitions, [latex]\sigma = \frac{F}{A_0}[/latex] and [latex]\epsilon = \frac{\Delta L}{L_0}[/latex], are fundamental for plotting stress-strain curves but assume the specimen's dimensions remain constant during the test.

The Navier–Stokes equations are a set of non-linear partial differential equations describing the motion of viscous fluid substances. They are a statement of Newton's second law, balancing momentum changes with pressure gradients, viscous forces, and external forces. For an incompressible fluid, the equation is [latex]\rho (\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f}[/latex].

الحماية الكاثودية (CP) هي تقنية تُستخدم للتحكم في تآكل سطح المعدن بجعله مهبطًا لخلية كهروكيميائية. يتحقق ذلك بتزويد تيار كهربائي خارجي يُثبط تيارات التآكل الطبيعية. يُستقطب جهد المعدن المحمي إلى قيمة سالبة، مما يُحوّله إلى منطقة مناعة أو سلبية.

For continuous systems like fluids or solids, momentum conservation is expressed in a differential form. The rate of change of momentum density [latex]\rho \vec{v}[/latex] at a point is governed by the divergence of the Cauchy stress tensor [latex]\sigma[/latex] and body forces [latex]\vec{f}[/latex]. This is described by the Cauchy momentum equation: [latex]\frac{\partial (\rho \vec{v})}{\partial t} + \nabla \cdot (\rho \vec{v} \otimes \vec{v}) = \nabla \cdot \sigma + \vec{f}[/latex].

The ideal Stirling cycle is a closed regenerative thermodynamic cycle comprising four distinct processes: isothermal expansion, isochoric heat removal, isothermal compression, and isochoric heat addition. The working fluid is permanently contained. Its theoretical thermal efficiency equals the Carnot cycle efficiency, given by [latex]\eta_{th} = 1 - \frac{T_C}{T_H}[/latex], where [latex]T_H[/latex] and [latex]T_C[/latex] are the absolute temperatures of the hot and cold reservoirs.

يُعامل افتراض الاستمرارية السوائل كمادة متصلة، لا كجزيئات منفصلة. ويُطبّق هذا التبسيط عندما يكون مقياس طول المسألة أكبر بكثير من المسافة بين الجزيئات، مما يسمح بتحديد خصائص مثل الكثافة والسرعة عند نقاط متناهية الصغر. وهذا يُمكّن من استخدام المعادلات التفاضلية لوصف السلوك العياني لتدفق السوائل.

A magnet's magnetic moment is a vector quantity that characterizes its overall magnetic properties. It can be visualized as a magnetic dipole, a hypothetical pair of north and south poles separated by a distance. The moment points from the south to the north pole. For a current loop, the magnetic moment [latex]\vec{\mu} = I \vec{A}[/latex], where I is the current and A is the area vector.

The Cauchy stress tensor, denoted [latex]\boldsymbol{\sigma}[/latex], is a second-order tensor that completely defines the state of stress at a point inside a material. It relates the traction vector (force per unit area) [latex]\mathbf{T}[/latex] on any surface passing through that point to the surface's normal vector [latex]\mathbf{n}[/latex] via the linear relationship [latex]\mathbf{T} = \boldsymbol{\sigma} \cdot \mathbf{n}[/latex].

The work-energy theorem states that the net work ([latex]W[/latex]) done by all forces acting on a particle equals the change in its kinetic energy ([latex]\Delta E_k[/latex]). Mathematically, [latex]W = \Delta E_k = E_{k,f} - E_{k,i}[/latex]. This principle directly links the concepts of force, displacement, and energy, providing a powerful tool for analyzing motion without directly using Newton's second law.