 We're now going to take a look at a heat transfer coefficient that is used for heat exchangers and that is what we refer to as being the overall heat transfer coefficient. So when we're looking at heat exchangers we're exchanging thermal energy between two different fluid streams it could be liquid or gas and typically what we have we will have convective force convective heat transfer on one side conduction through whatever the interface is and then force convective heat transfer on the other side and and consequently the overall heat transfer coefficient characterizes all three of those processes and then you get to have other things going on you can have fins on the heat exchanger that you would then model you can have fouling going on which is build up of deposits which negatively impacts the heat exchange between the two fluid streams but what we're going to do we're going to derive an expression or come up with the expression for the overall heat transfer coefficient and we're going to begin by looking at a double pipe heat exchanger so if you recall that was this would be a parallel flow configuration but what I'm going to do I'm going to label the fluid on the inside as being ta that's the temperature of the fluid and I'm going to assume that the convective heat transfer coefficient on the inside is hi and then for the fluid in the outer pipe what I'll do there is I will label the temperature tb and h outer and that would then characterize the force convective heat transfer on the outside of the tube now what we're going to do we want to express this we're going to use thermal resistances and so if you recall we looked at that quite a long time ago in the course but we're going to pull that out now and we're going to use it so let's draw our thermal resistance circuit and then the different thermal resistance values okay so what we have here we have three different thermal resistances one is for convective heat transfer and a and if we look back a was being our internal fluid so that is the internal then we have conduction through the wall and then we have convection on the fluid on the in the outer pipe and consequently we can also write here that if we look at the wall temperatures on the pipe the inner pipe it would go from ti to to and q is flowing through and so let's write out our thermal resistances now okay so those are the three thermal resistances that we have within this system now what we're going to do we're going to combine those together and we're going to solve for the heat flow very much like what we did when we looked at thermal resistances earlier on so in this what we're now going to do we are going to rewrite the equation so q is equal to and the form that we're looking at here you'll recognize it is this here and that's what we've seen before so what i am now going to do is i'm going to rewrite this in terms of this overall heat transfer coefficient and we'll have a ua delta t and in this what i am doing is i am assuming that the sum of the thermal resistances is equal to the inverse of this overall heat transfer coefficient times an area that we have not yet defined so u this is defined as being our overall heat transfer coefficient and it can be defined either in terms of the inner or the outer area of our double pipe heat exchanger so what am i referring to well if you look at your wall that this is the inner pipe and we have that's the wall thickness so area inner would be here and area outer would be there so it depends if you use your internal or your external radius or diameter of the interior pipe so what we're going to do we're going to write out two different overall heat transfer coefficients so those are two different ways of expressing the overall heat transfer coefficient depending if you use your inner or outer tube area now typical values that we find in heat exchangers are as follows so you can see a range of values if we're going through a phase change it's going to be quite high if we have water to air the water will have the higher convective heat transfer the liquid will have a higher convective heat transfer coefficient as shown there and then at the lower end if you have gas gas gas you recall the convective heat transfer coefficient is we know it as far high as a liquid and consequently the overall value is going to drop somewhat there so these are numbers that are quite often well will be used in the analysis sometimes it's given to you sometimes you're trying to solve it and so a lot of what we're going to be doing when we're doing heat exchanger analysis is trying to estimate a unit's overall heat transfer coefficient now one thing is let's say you know the value of u so maybe you've determined this empirically and if you know the geometry a thing should be good right but let's take a look at what our equation looked like we had q is equal to u a delta t so usually we're after the amount of heat transfer maybe we know the amount of heat transfer that's usually what we're after but looking at this equation so let's say you know you you've determined that you know your area and you've been asked to find q well what delta t are you going to use and and this is what we're going to be looking at in the next segment uh in the next lecture actually because this is not a simple trivial solution if you even just look at the simple double pipete exchanger like this uh what is happening is as the fluid is coming through uh one fluid stream is heating while the other is cooling and consequently you are going to have different values of delta t and that is going to be delta t as a function of position and we did look at this earlier on in the course when we looked at pipe flow internal force convection and we came up with an expression we're going to come up with a very similar expression in the next lecture but that is in order to enable us to figure out how to express delta t given that delta t changes as a function of position within the unit so anyways that's a bit of an introduction to heat exchangers we looked at different types of heat exchangers we looked at how to model the temperature distribution or at least schematically represented and then we've just looked at the overall heat transfer coefficient which is something that we'll carry through when we're doing the analysis but we're going in the next lecture we're going to try to figure out how to estimate this value of delta t