Steady Flow Energy Equation (SFEE) is the application of conservation of energy on to an open system. Figure shown below is a schematic of open system in which fluid enters at 𝑖 and exits at 𝑒. The red broken line represents the control surface (CS) of the control volume (CV). ... Read More

Simpson's rule is a very powerful tool to perform numerical integration. To maximise accuracy while requiring fewer divisions, Simpson's rules calculate the integrals using weighting factors. The trapezoidal rule only considers two points, 𝑥𝑖 and 𝑥𝑖+1, to estimate a trapezoid's area, but Simpson's rules use more than two points (or ... Read More

In this tutorial, we will see how to model 2D heat conduction equation using Python. A 2D, steady, heat conduction equation with heat generation can be written in Cartesian coordinates as follows − $$\mathrm{\triangledown^{2} T \: + \: \frac{q_{g}}{k} \: = \: \frac{\partial^{2}T}{\partial x^{2}} \: + \: \frac{\partial^{2}T}{\partial y^{2}} \: ... Read More

The Taylor Table method is a very efficient and elegant method of obtaining a finite difference scheme for a particular derivative considering a specific stencil size. To understand it one should be very much clear about what is a stencil. Suppose one wants to evaluate $\mathrm{\frac{d^{2}f}{dx^{2}}}$ then in finite difference ... Read More

Entropy is a property of a thermodynamic system that remains constant during a reversible adiabatic process. Moreover, we can also say that it is the degree of randomness or disorder in the system. If a system exchanges dQ heat from its surroundings at temperature T, then the chance in the ... Read More

The purpose of integration (definite) is to calculate the area under a curve of a function between two limits, a and b. The plot shown below will clear this concept further. Quadrature, which is also commonly called as numerical integration, is a method for evaluating the area under the ... Read More

Stirling Cycle Four processes—two reversible isochoric and two reversible isothermal—make up the Stirling cycle. In the same temperature range, the efficiency of the ideal regenerative Stirling cycle is equivalent to that of the Carnot cycle. Heat interaction takes place throughout the cycle, whereas work interaction only happens in processes 1-2 ... Read More

Otto Cycle An air standard cycle called the Otto Cycle is employed in spark ignition (SI) engines. It comprises of two reversible adiabatic processes and two isochoric processes (constant volume), totaling four processes. When the work interactions take place in reversible adiabatic processes, the heat addition (2-3) and rejection (4-1) ... Read More

Gauss Seidel Method is the iterative method to solve any system of linear equations. Though the method is very much similar to the Jacobi's method but the values of unknown (x) obtained in an iteration are used in the same iteration in Gauss Seidel whereas, in Jacobi's method they are ... Read More

When an object at very high temperature is suddenly dropped in a cooler liquid and if it is assumed that the conductive resistance of the solid is very small in comparison to the surrounding convective resistance then the heat transfer analysis is called as lumped capacitance analysis (as shown in ... Read More