Determine the temperature distribution at the five discrete points shown ( x = 3 0 mm) with time (with time steps t = 3 0 0 seconds) from the time of the surface temperature change until 4 5 …

The basic differential equation of the elastic curve for a uniformly loaded beam is given as where E = 30,000 ksi, I = 800 in4, w = 0.08333 kip/in, L = 120 in. Solve for the deflection of the beam using the …

The measured temperatures at selected points of the outer surfaces are as shown. The thermal conductivity of the body is k = 45 W/m. degree C, and there is no heat generation. Using the finite …

Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The measured temperatures at selected points of the outer surfaces are as shown. The …

A very thick plate with thermal diffusivity 5.6 x 10-6 m/s and thermal conductivity Initially at a uniform temperature of 325 C. Suddenly, the surface is exposed to a coolant at 15 C for which the convection …

Apply the finite difference method ( central Difference Formulas) with the given step size h to generate a linear system of equations to be solved for solution estimates.

A bridge is subjected to dynamic loading due to passing vehicles.The vertical displacement of a specific point on the bridge deck is measured over time and recorded in the table below.Using the data, …

Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state conductive heat transfer through a metal rod and convection to the surrounding air, which are …

Backward differencing scheme (a.k.a. Backward Euler method) Assume a time Consider the exponential decay (or growth) equation (encountered in radioactive decay, unchecked population growth (or …

Also, we can replace the symmetry lines with insulation and utilize the mirror-image concept when writing the finite difference equations for the interior nodes. Using the finite difference method with a …