Calculating heat lost

How To Calculate Heat Loss?

Author: Skip Schaefer

Heat is energy and heat can affect molecules, recall Bill Nye the Science Guy (you dont need to sing along to his music videos). Now everyting is made up of molecules. Air, water, walls, tanks, and metal are all particles where heat can be transferred or lost. There are 3 types of heat transfer: Conduction, Convection & Radiation which I will cover below. Everything has heat, whether it is hot or cold. It's important to understand the movement of molecules and its relationship to temperature. Warmer water will rise while cooler water will sink because the atoms become closer together adding density. If you heat something up too much, the matter will vibrate so fast they vaporize. This is why you learn how to calculate heat loss.

Understanding Heat Transfer Types

Now that we have middle school science covered, lets move on to the types of heat transfer or movement. Some might call it heat loss. Click below for definitions and examples of thermal energy phase changes.

hot coffee mug spoon

Conduction is the transfer of heat or electricity through a substance by direct contact. The heat transfer rate is dependent upon how much resistance exists between objects of differing temperatures. (That's insulation) A good example of conduction is placing a spoon in a glass of hot coffee. The metal spoon warms up because it touched the hot molecules. The coffee solution actually had heat loss.

Now not all objects are good conductors of heat. Metal is a good conductor, so it heats up fast in hot coffee. Glass is a poor conductor. The outside of the glass is cooler than the metal spoon, even though they are both touching hot coffee.

Whether a substance acts as a thermal conductor or insulator depends on the thermal resistive properties of the matter. Thermal resistance (R) is a measure of an object's ability to decrease heat transfer by way of conduction through a given thickness of the substance. Mathematically, R is: Calculating Heat Loss from Industrial Systems to determine heat tracing where L is the insulation thickness in inches, k is thermal conductivity, (BTU)(in)/(ft2)(oF)(hr) As the thickness (L) changes, it affects the R value, or thermal resistance of an insulation. K values are constants that are specific to the physical properties of a given material. They measure thermal conductivity.

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ $$ R = {L \over k}$$

iced coffee with straw

Convection is the transfer of heat through fluids (gases or liquids) from a warmer spot to a cooler spot. Place an ice cube in hot coffee and the molecules on top become cooler and dense therefore moving to the bottom.

If you heated the bottom of the coffee mug the opposite would happen. The more dense liquid on bottom would expand becoming lighter and would move to the top. This movement of heat is called convection.

radiation waves penetration

Radiation is the transition of energy (heat) from one body in the form of waves or particles.

Sounds simple but radiation can come in different forms and energy strengths, here are some examples of radiation:

  • •  ultraviolet light from the sun
  • •  heat from a camp fire
  • •  light from a candle
  • •  x-rays from an x-ray device
  • •  alpha particles emitted from radioactive decay of uranium
  • •  cooking waves from a microwave oven
  • •  electromagnetic radiation from your mobile phone

Heat Loss Calculations

In most low-to-medium temperature applications, radiation and convection account for about 10% of the heat loss of objects. The formula for calculating heat loss of a system can be calculated by adding in 10%.

Calculating Flat Surface Heat Loss

surface heat loss diagram

The term “heat loss” commonly refers to the thermal transfer of an object to its ambient environment. For example a wall is at a temperature above the ambient temperature. The formula for calculating heat loss of a system through conduction (Fourier's Law), expressed in BTU/hour is:

$$ Q = {(U)(A)(ΔT)}$$

Where U is the thermal conductance, BTU/(ft2)(Fº)(hr)
A is the surface area of object, ft2
ΔT is the temperature difference (T1 -T2), Fº
Conductance is the inverse of resistance, R, and can be expressed as U = 1/R  So, another equation for general heat loss in BTU/hr is:

$$ Q = {k(A)(ΔT)(1.1) \over L} $$

How Is Heat Loss Measured?

Heat loss is measured in kWs or BTUs. It is a function of heat transfer rates. Heat transfer rates in walls, floors and roofs are measured in U values. To calculate the U value of a wall, pipe, metal or water tank, you need to know the composition and thickness of each part.

Electricity is normally sold by kilowatt hours, but the equations above are BTU/hr. Just convert BTU to watts, where 1 watt equals 3.412142 BTU and multiply times (L).  The answer will be in W/hr.

$$ Q = {k(A)(ΔT)(1.1) \over (L)(3.412142)} $$

Conductive heat transfer can be expressed with:

q = (k / s) A dT  

   = U A dT                               (1)

where

q = heat transfer (W, J/s, Btu/hr)

k = Thermal Conductivity of material (W/m K or W/m Cº, Btu/(hr Fº ft2/ft))

s = material thickness (m, ft)

A = heat transfer area (m2, ft2)

U = k / s

  =  Coefficient of Heat Transfer (W/(m2K), Btu/(ft2 h Fº)

dT = t1 - t2

    = temperature gradient - difference - over the material (Fº)

Heat Loss in Water Tanks

polypro tank heat plating

Open water tanks like plating tanks, di water tanks, hot tubs or swimming pools lose excessive heat due to evaporation. SAVINGS TIP: Cover open water containers with insulation when not in use.  The overall heat loss from an open water tank can be expressed as:

Q = Qevaporation fluid + Qradiation fluid + Qtransmission through walls

The heat loss due to evaporation of water from a surface of an open tank is dominant at higher water temperatures. Any heat loss through insulated walls is minimal, this is especially try for polypro tanks. Polypropelne is an excellent insulator.

Remember– heat rises, so all the energy is being released on the top.

Water Temperature (Fº)
Heat Loss from Liquid Surface
(Btu/ft2hr)
Heat Loss Through Tank Walls
(Btu/ft2hr)
Evaporation LossRadiation LossTotalBare Steel UninsulatedInsulated (inches)
123
90 80 50 130 50 12 5 4
100 160 70 230 70 15 8 6
110 240 90 330 90 19 10 7
120 360 110 470 110 23 12 9
130 480 135 615 135 27 14 10
140 660 160 820 160 31 16 12
150 860 180 1040 180 34 18 13
160 1100 210 1310 210 38 21 15
170 1380 235 1615 235 42 23 16
180 1740 260 2000 260 46 25 17
190 2160 290 2450 290 50 27 19
200 2680 320 3000 320 53 29 20
210 3240 360 3600 360 57 31 22
  • the values above are for 60 Fº still ambient air

Example Formula Heat Loss From Open Water Tank

Here is a sample calculation of a water tank heat loss using the Table above (NOTE: the room temperature is at 60º F), where:

  • Water temperature: 150
  • Surface area: 10 ft2 (You calculate this by measuring the top open area; IE 4' x 2.5'=10 ft 2
  • Un-insulated steel tank walls area: 50 ft2 (Add up each area on a metal rectangle container; 10 ft 2 + 15 ft 2+ 10 ft 2+15 ft 2= 50 ft 2 )

 

Q(evaporation fluid + radiation fluid) = ( 1040 Btu/(ft 2 hr)) (10 ft2)

           = 10400 Btu/hr

Qtransmission through walls = ( 180 Btu/(ft Btu/(ft2 hr)) (50 ft2)

          = 9000 Btu/hr

Q = Q(evaporation fluid + radiation fluid) + Qtransmission through walls

         = (10400 Btu/hr) + (9000 Btu/hr)

         = 19400 Btu/hr

Need More Help?

When you become a customer, Skip Schaefer will put his almost 50 years of experience, designing heating processes, to work for you. His electric heaters are used by manufacturers worldwide. IHS offers a wide range of thermal products, including deep and large plating tank heaters. If you have a special manufacturing problem, Skip can solve it, talk to him today.

Works Cited

Ebadi-Dehaghani, Hassan, and Monireh Nazempour. "Thermal conductivity of nanoparticles filled polymers." Smart nanoparticles technology. IntechOpen, 2012. Fan, Jianhua, and Simon Furbo. "Thermal stratification in a hot water tank established by heat loss from the tank." Solar Energy 86.11 (2012): 3460-3469. Hot Water Storage Tank https://www.sciencedirect.com/topics/engineering/hot-water-storage-tank R-Value | EGEE 102: Energy Conservation and Environmental Protection https://www.e-education.psu.edu/egee102/node/2062 [3 September, 2019] Engineering ToolBox, (2003). Heat Loss from Open Water Tanks. [online] Available at: [3 September, 2019].https://www.engineeringtoolbox.com/heat-loss-open-water-tanks-d_286.html Incropera, Frank, and David DeWitt. "Introduction to heat transfer." (1985).

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