Air is heated as it flows subsonically through a duct. When the amount of heat transfer reaches

Air is heated as it flows subsonically through a duct. When...

Key Concepts

Stagnation versus Static Properties

Stagnation properties, such as total (or stagnation) temperature and pressure, represent the conditions a fluid would experience if it were brought to rest isentropically, while static properties describe the conditions of the moving fluid. In the context of heat addition and choked flow, understanding the relation between these two sets of properties is essential, as energy added to the flow alters the relation between the static state and the total state.

Conservation of Energy in Compressible Flows

Conservation of energy in compressible flows involves the interplay between kinetic energy and the fluid's internal energy (through specific enthalpy). When heat is added in a duct, the energy equation is used to relate changes in velocity, temperature, and pressure between different sections of the duct. This concept is key to predicting the evolution of flow properties when thermal energy is introduced into a moving fluid.

Subsonic Flow Dynamics

Subsonic flow dynamics concerns the behavior of fluids moving at speeds lower than the speed of sound, particularly in ducts or channels where flow characteristics are influenced by geometry, pressure gradients, and thermal effects. Analysis of subsonic flow is important when assessing the impact of heat addition, which can accelerate the flow towards sonic conditions and induce choking phenomena.

Rayleigh Flow

Rayleigh flow describes the behavior of a compressible fluid in a duct when heat is added or removed, leading to changes in the thermodynamic properties of the fluid. It is particularly significant when analyzing how added heat influences properties such as temperature, pressure, and velocity, and when assessing the conditions under which the flow may choke. This concept helps in understanding the coupling between heat transfer and compressible effects in constant-area ducts.

Choked Flow

Choked flow occurs when the fluid velocity reaches the local speed of sound, setting a maximum limit on the mass flow rate through a duct. In such conditions, further modifications in the downstream or upstream conditions do not alter the mass flow due to the sonic conditions at the critical point. This concept is crucial in analyzing the operation limits of ducts subjected to heat addition or extraction.

Transcript

00:01 So, in this question if you see, air is heated in a duct during subsonic flow until it is choked.

00:14 For specified pressure and velocity at the exit, the temperature, the pressure and the velocity at the inlet have to be found out.

00:29 These are the three quantities that we need to find out.

00:34 So let's see how does it go? so in order to carry forward this question, we have to take certain assumptions here.

00:40 So the first assumptions associated with relay flow is that it should be a steady flow.

00:53 It should be a one -dimensional flow of an ideal gas.

00:56 Ideal gas should be there.

00:58 That is important with constant properties.

01:02 Constant properties should be there.

01:06 Then we should have a constant cross -sectional.

01:12 Area this is also very important first area of duct and negligible friction should be there and that is only valid for this case so we take here certain properties also and the property of air that you have to take is k is equal to 1 .4 cp equals to 1 .005 kilojoule per kg kelvin and our r equals to 0 .287 kilojoule per kg kelp.

02:09 So now when we are doing the analysis of this question, we'll see that the sonic conditions exist at the exit.

02:20 So sonic conditions are there at the exit.

02:25 So the exit temperature, we have to find that out.

02:31 So how will we find out the exit temperature? with the formula c2 equals to v2 upon m82 which is equals to 680 meter per second.

02:42 So c2 here is equal to root of krt2 and that is equal to 68t right.

02:51 So from here we find out that t2 is 11551k.

02:57 So this is the exit temperature that we have.

03:02 1151k.

03:03 This is the first thing that we require...