Question

Consider an open flat ground. The surface of this ground gets heated every day due to solar radiation, and cools every evening. Assume that the top surface of the ground has a temperature given as TI + T sin(t), where T (temperature variation) and  (frequency) are constants, where TI is the "nominal" temperature of the ground, viz. the ground temperature deep inside is TI. The ground has a thermal diffusivity = . Please solve for the ground temperature, assuming "periodic steady state" conditions. a. Write down the governing equations for energy transfer, simplify these and write down suitable boundary conditions.

Answer 1

The governing equation for energy transfer in this case is the heat conduction equation, which can be simplified for the periodic steady state conditions as d^2T/dx^2 = (1/α)(dT/dt). The specific boundary conditions for the open flat ground should be provided to proceed with solving the problem.

Step-by-step explanation:

Governing Equations and Boundary Conditions

The governing equation for energy transfer in this case is the heat conduction equation, which can be simplified for the periodic steady state conditions as follows:

d2T/dx2 = (1/α)(dT/dt)

The boundary conditions for this problem depend on the specifics of the situation. Please provide additional information about the boundary conditions of the open flat ground to proceed with solving the problem.