Determine the total heat transfer from the vertical wall described in Problem 19.4 to the surrounding air per meter of width if the wall is 2.5 m high.

Problem 19.4

Using the relations from Problem 19.19, determine, for the case of air at 310 K adjacent to a vertical wall with its surface at 420 K,

a. the thickness of the boundary layer at x = 15 cm, 30 cm, 1.5 m,

b. the magnitude of h_x at 15 cm, 30 cm, 1.5 m.

Problem 19.19

Using the integral relations from Problem 19.8, and assuming the velocity and temperature profiles of the form

And

where d is the thickness of both the hydrodynamic and thermal boundary layers, show that the solution in terms of δ and v_x from each integral equation reduce to

Next, assuming that both δ and v_x vary with x according to

show that the resulting expression for δ becomes

and that the local Nusselt number is

Problem 19.8

In a thermal heat sink the heat flux variation along the axis of a cooling passage is approximated as

where x is measured along the passage axis and L is its total length.

A large installation involves a stack of plates with a 3-mm air space between them. The flow passages are 1.22 m long, and the heat flux in the plates varies according to the above equation where a = 900 W/m² and v = 2500 W/m². Air enters at 100°C with a mass velocity (the product of ρV) of 7:5 kg/s m². The surface coefficient along the flow passage can be considered constant with a value of 56 W/m² K: Generate a plot of heat flux, mean air temperature, and plate surface temperature as functions of x. Where does the maximum surface temperature occur and what is its value?