Every summer we get tons of cooling system threads, which often get polluted with less-than-perfectly-correct information and advice so I took some time today to type up a bunch of stuff that goes through my head when I'm thinking about fixing or improving a cooling system.
I'm a mechanical engineer approaching 19 years of experience in the HVACR industry with time spent in heat exchanger design, controls, system (chiller) design, and more recently directing a sales and service/commissioning team where all the most troublesome and confusing performance issues bubble up to me.
The goal here is to share some of the equations behind how heat exchanger performance is modeled, in a way that someone who isn't an engineer or a calculus expert but has at least some exposure to basic algebra can apply to their thought process.
I don't want to talk down to people but at the same time I don't want to talk over people's heads and with such a wide range of backgrounds here of people most of which I've never met, both are bound to happen. I'm happy to answer any clarifying questions that come up.
Let’s start from the beginning.
The internal combustion engine is not a highly efficient device. They obviously vary and the manufacturers have found ways to make them better over the years, but it’s pretty safe to estimate that about 30% of the energy that comes out of the combustion of gasoline will end up available at the crankshaft. The other 70% will be converted to heat – some through friction, such as the rings sliding up and down in the cylinders and the lifters following the cam under valve spring pressure, and of course crank and camshaft journals rotating within their bearings. The biggest part of it however, goes out as heat that the engine can’t use mechanically and instead gets absorbed into the cylinder walls, piston crown, combustion chamber roof, and exhaust port before getting blown out to the catalyst and on.
The heat that gets absorbed by those components before it escapes is what we’re concerned with in a discussion of the cooling system. If it were absorbed and not carried away, the materials comprising the block and head would simply heat up until they melted, or more likely until stresses from uneven heating and thermal expansion caused them to fracture or expand to a size that is too large for the space they occupied and became mechanically joined with another component that they were intended to move against. Instead, engines are given means to rid themselves of that heat and maintain a temperature safe for their materials and components.
Equation 1
This expression quantifies the heat transfer rate in a heat exchanger.
U=overall heat transfer coefficient (subscript indicates radiator or engine). This is a quantifier of the capabilities of the heat exchanger and the fluid being used, on a per-unit-area basis and independent of temperature difference. It is unique to a given heat exchanger and a given set of fluid properties and within it is implied the convective or film coefficient h, an expression of the heat transfer through the boundary layer. The boundary layer is a layer of fluid which is not moving as quickly due to friction against the wall surface and ends up approaching the surface temperature, which adds a thermal resistance between the surface and the fluid stream, like a thin layer of insulation. The thickness of this boundary layer is a function of the viscosity of the fluid and the velocity at which it is moving, up to a point. Once the inertial forces (from velocity) are large enough that the viscous forces are negligible (thermal-fluids nerds will recognize this ratio as the Reynolds Number), the flow is considered fully turbulent and the boundary layer thickness hits an effective minimum where increasing velocity no longer meaningfully impacts heat transfer. Heat transfer in laminar flow sucks because the boundary layer is THICC, so no one designs for velocities that low in something they want to transfer heat, but it may occur in specific situations like in a radiator when the thermostat is closed.
A=surface area. This seems fairly self explanatory as the surface area of the heat exchanger. It’s pretty simple when you have a contained heat exchanger like a plate or shell-in-tube but gets complicated to calculate when you have enhanced surfaces like fins, let alone very deep ones like on an air cooled engine so for the purposes of this discussion it’s best thought of conceptually and in the context of the impacts of increasing or reducing it.
ΔTlm = logarithmic mean temperature difference. T1 and T2 represent the temperature difference between the hot and cold fluids at each end of the heat exchanger. Like Area, it’s pretty straightforward for heat exchangers that fit neatly into a counterflow or parallel flow box, but an engine isn’t exactly that, so again we can just think about this as the temperature difference between the combustion chamber temperature and the ambient air.
And importantly;
Qout = Qin for steady state conditions, meaning, if the heat input (proportional to engine load) is held constant, then the other variables will adjust themselves as needed to ensure that the heat rejected to the environment will equal the heat input.
The result of all this math is that for a given engine load, we have to reject a particular amount of heat to keep the engine happy, and that there are a small number of easily understood parameters that make that happen.
I'm a mechanical engineer approaching 19 years of experience in the HVACR industry with time spent in heat exchanger design, controls, system (chiller) design, and more recently directing a sales and service/commissioning team where all the most troublesome and confusing performance issues bubble up to me.
The goal here is to share some of the equations behind how heat exchanger performance is modeled, in a way that someone who isn't an engineer or a calculus expert but has at least some exposure to basic algebra can apply to their thought process.
I don't want to talk down to people but at the same time I don't want to talk over people's heads and with such a wide range of backgrounds here of people most of which I've never met, both are bound to happen. I'm happy to answer any clarifying questions that come up.
Let’s start from the beginning.
The internal combustion engine is not a highly efficient device. They obviously vary and the manufacturers have found ways to make them better over the years, but it’s pretty safe to estimate that about 30% of the energy that comes out of the combustion of gasoline will end up available at the crankshaft. The other 70% will be converted to heat – some through friction, such as the rings sliding up and down in the cylinders and the lifters following the cam under valve spring pressure, and of course crank and camshaft journals rotating within their bearings. The biggest part of it however, goes out as heat that the engine can’t use mechanically and instead gets absorbed into the cylinder walls, piston crown, combustion chamber roof, and exhaust port before getting blown out to the catalyst and on.
The heat that gets absorbed by those components before it escapes is what we’re concerned with in a discussion of the cooling system. If it were absorbed and not carried away, the materials comprising the block and head would simply heat up until they melted, or more likely until stresses from uneven heating and thermal expansion caused them to fracture or expand to a size that is too large for the space they occupied and became mechanically joined with another component that they were intended to move against. Instead, engines are given means to rid themselves of that heat and maintain a temperature safe for their materials and components.
Equation 1
This expression quantifies the heat transfer rate in a heat exchanger.
U=overall heat transfer coefficient (subscript indicates radiator or engine). This is a quantifier of the capabilities of the heat exchanger and the fluid being used, on a per-unit-area basis and independent of temperature difference. It is unique to a given heat exchanger and a given set of fluid properties and within it is implied the convective or film coefficient h, an expression of the heat transfer through the boundary layer. The boundary layer is a layer of fluid which is not moving as quickly due to friction against the wall surface and ends up approaching the surface temperature, which adds a thermal resistance between the surface and the fluid stream, like a thin layer of insulation. The thickness of this boundary layer is a function of the viscosity of the fluid and the velocity at which it is moving, up to a point. Once the inertial forces (from velocity) are large enough that the viscous forces are negligible (thermal-fluids nerds will recognize this ratio as the Reynolds Number), the flow is considered fully turbulent and the boundary layer thickness hits an effective minimum where increasing velocity no longer meaningfully impacts heat transfer. Heat transfer in laminar flow sucks because the boundary layer is THICC, so no one designs for velocities that low in something they want to transfer heat, but it may occur in specific situations like in a radiator when the thermostat is closed.
A=surface area. This seems fairly self explanatory as the surface area of the heat exchanger. It’s pretty simple when you have a contained heat exchanger like a plate or shell-in-tube but gets complicated to calculate when you have enhanced surfaces like fins, let alone very deep ones like on an air cooled engine so for the purposes of this discussion it’s best thought of conceptually and in the context of the impacts of increasing or reducing it.
ΔTlm = logarithmic mean temperature difference. T1 and T2 represent the temperature difference between the hot and cold fluids at each end of the heat exchanger. Like Area, it’s pretty straightforward for heat exchangers that fit neatly into a counterflow or parallel flow box, but an engine isn’t exactly that, so again we can just think about this as the temperature difference between the combustion chamber temperature and the ambient air.
And importantly;
Qout = Qin for steady state conditions, meaning, if the heat input (proportional to engine load) is held constant, then the other variables will adjust themselves as needed to ensure that the heat rejected to the environment will equal the heat input.
The result of all this math is that for a given engine load, we have to reject a particular amount of heat to keep the engine happy, and that there are a small number of easily understood parameters that make that happen.
).
