 Okay, in the last segment what we said was that we're looking at convective heat transfer and trying to determine the value of the convective heat transfer coefficient. We said that convective heat transfer really does come down to being a fluid mechanics problem. So what we're going to do we're going to begin looking at one of those basic flows within fluid mechanics and that is the flow over a flat plate and what we'll be doing is taking a look at the boundary layer which is the flow that is adjacent to a flat plate and that will kind of become the basis of a lot of the things we're going to be looking at in terms of being able to estimate the convective heat transfer coefficient H. So we'll begin I'll draw out a schematic of the boundary layer going from laminar through transition to turbulent. Okay, so what we have here is a schematic representation of what is going on in the boundary layer starting from the leading edge of a flat plate and so this is the leading edge up here and the flow starts off on the flat plate growing in what we call a laminar boundary layer and so that is where the flow is relatively smooth there are not a lot of significant fluctuations within the flow and then what happens is the flow undergoes instabilities and growth of these instabilities and it transitions from laminar into a turbulent boundary layer and turbulent boundary layer has very very different characteristics from the laminar boundary layer growth rate is very different as well as heat transfer characteristics to be very very different but this transition process begins at Reynolds number and we use Reynolds number to characterize many many different fluid mechanic flows and and the boundary layer flow is one of those and the way that we define the Reynolds number is U infinity which would be the free stream velocity times some characteristic length scale and for a flat plate boundary layer it's usually the distance from the leading edge and then we divide that by the kinematic viscosity nu and remember that nu is just mu our dynamic viscosity divided by the density of the fluid flowing over the flat plate so what happens is we have this transition region boundary layer thickness is showing here and that basically represents how thick the boundary layer is and we'll be defining that in a moment it's basically where the velocity goes up to being about 99% of the free stream velocity so that is what is happening in the boundary layer and the main thing to take away from this is just to understand that laminar boundary layer characteristics are very different from turbulent and consequently there'll be very very different heat transfer characteristics and what else should we take away from this we'll be looking at the growth rate we'll be looking at the heat transfer characteristics in both regions so those are probably the main things to take away at this point so let's take a look at the boundary layer thickness itself one other thing that we should take away we can perform analysis on the laminar boundary layer however we cannot perform analysis on the turbulent boundary layer for that we try to do it using numerical methods direct numerical simulation is really the only one that truly is able to replicate it but for the most part we end up using different experimental values that are kind of tweaking a numerical solution or we just go and do experiments directly so laminar boundary layer we can come up with solutions for but turbulent is hard even laminar it can be hard depending upon the external pressure gradient that might be with our flow but it's looking at the boundary layer thickness delta x so there are different definitions for the boundary layer thickness but we'll use this one 99% of the free stream velocity we already introduced the Reynolds number but I'll write that out again and in a generic sense Reynolds number for the flat plate boundary layer is you infinity the characteristic length scale which is distance from the leading edge divided by our kinematic viscosity okay and the last thing well another thing that I want to say about this we talked here about this critical Reynolds number and that is the Reynolds number typically where we would expect the boundary layer to start going through a transition process where it goes from laminar to turbulent and the value of that there are different values that you'll find in the literature but typically one that is often uses five times ten to the five and the reason why there are different values is the transition process is dependent upon a number of different things one of them is the baseline turbulence in the flow coming in to begin with we always assume that this flow is perfectly laminar coming in but there there's always residual turbulence in any kind of flow field that you'll have and consequently it would be dependent upon that and it would also be dependent upon surface roughness how how rough the flat plate is and and that can have an impact on this critical Reynolds number there's a field called hydrodynamic stability and that is involved with studying the process of transition from laminar to turbulent but rule of thumb and typically five times ten to the five is the number that you'll often see quoted in the literature and this is the point where and sometimes you'll see the acronym LBL that stands for laminar boundary layer transitions to a TBL and that stands for the turbulent boundary layer so if you see LBL or TBL that is what that is referring to so that is the boundary layer flow and that is a flow that we will be studying in the next this lecture and in the next lecture and it kind of forms the basis for a lot of the heat transfer relationships that we'll be coming up with because even with a rounded object let's say you have flow over an object like this what we can do is we can zoom in to parts of that object and treat this as being almost like a flat plate there will be a pressure gradient external which will have an impact on the boundary layer but at any point you can piecewise look at the flow over any kind of object in the manner of looking at it like a boundary layer unless you get to a separation point when you have separation then you're going to get the boundary layer lifting off and and the flow in here is very very non-stationary and very very complex and consequently the boundary layer you would not be able to really apply it in that region and we'll be seeing that when we look at flow over bluff bodies such as cylinders and then the heat transfer characteristics of a cylinder but that is the flat plate boundary layer and that's something that we'll be looking at as we go along