How to Solve the Heat Equation With Galerkin's

Galerkin’s Method is a complicated series of equations used to measure the thermal properties of different materials. When solving heat equations, Galerkin’s Method uses Fourier’s Law to compare the heat flux and heat conductivity of a given material, according to the Vietnamese-German University website. In order to use Galerkin’s Method, you will need to know an object’s thermal conductivity – or ability to transfer heat from one object to another.

Instructions

    • 1

      Determine the thermal conductivity of your object or material by multiplying its temperature by the distance of its heat variable. Start by multiplying the area of the object in inches by the temperature gradient, using the formula (A × ΔT). For example: if your area is 16 inches and the temperature gradient is 10 degrees per minute, you would receive 160.

    • 2

      Divide this number into your total distance value in inches, as expressed by the formula L / (A × ΔT). Multiply this final number by the heat of your object in degrees Fahrenheit to receive your thermal conductivity. For example: if the object is 150 degrees Fahrenheit, with a heat distance of 20 inches, your variable for thermal conductivity will be 18.75, as expressed by the formula Q × L / (A × ΔT).

    • 3

      Multiply the thermal conductivity of your object by -1 to receive the variable for your heat flux, as explained in the formula q = -Δ u. Multiply this number by the heat gradient to receive your final variable for the heat equation. You can apply this final number to a variety of different variables and heat factors using other methods and formulas.

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