Heat Transfer Equations and Calculators 

Advances in Heat Transfer  The serial publication “Advances in Heat Transfer” is designed to fill the information gap between the regularly scheduled journals and university level textbooks. 

Thermal Conductivity Theory, Properties, and Applications Premium resource membership 

Grashof Number (GR) The Grashof number is used to determine the heat transfer coefficient under free convection conditions. It is basically a ratio between the buoyancy forces and viscous forces. 

Heat Transfer, A Practical Approach  Heat transfer is a basic science that deals with the rate of transfer of thermal energy. 

Heat and Thermodynamics 341 pages, Premium Membership Required 

Hemispherical Emissivities of Various Surfaces Table  emissivities of various surfaces at several wavelengths and temperatures. 

Heat Loss Through Enclosure Walls Equations and Calculator Determine required wall thickness of an enclosure for temperature control and insulation requirements. Known Design Data: Size (thickness) of insulated enclosurewalls and inside and external surface temperatures 

Heat Loss Through a Wall Equation and Calculator Determine the steady state heat loss through a single wall. 

Heat Loss or Gain From Pipe Excel Spreadsheet Calculator 

Heat Loss through Aluminum Framed Window Equations and Calculator Design equations and calculator example Heat Loss through Aluminum Framed Window. 

Heat Loss through a SinglePane Window Equation and Calculator
Assumptions
1 Heat transfer through the window is steady since the surface temperatures remain constant at the specified values.
2 Heat transfer through the wall is onedimensional since any significant temperature gradients will exist in the direction from the indoors to the outdoors.
3 Thermal conductivity is constant. 

Heat Loss through a DoublePane Window Equation and Calculator A doublepane window is considered. The rate of heat transfer through the window and the inner surface temperature are to be determined. 

ConductionRectangular Coordinates Calculation Example Conduction  Rectangular Coordinates example calculation 

Conductive Heat Transfer Parallel Cylinders Equation and Calculator Conductive Heat Transfer of A row of equally spaced parallel isothermal cylinders buried in a semiinfinite medium (L >>D, z and w >1.5D) 

Conductive Heat Transfer Cylinder of Length Equation and Calculator Conductive Heat Transfer of Circular isothermal cylinder of length L in the midplane of an infinite wall (z > 0.5D) 

Conductive Heat Transfer Square Solid Equation and Calculator Conductive Heat Transfer of Circular isothermal cylinder of length L at the center of a square solid bar of the same length 

Conductive Heat Transfer Eccentric Cylinder Equation and Calculator Conductive Heat Transfer of Eccentric circular isothermal cylinder of length L in a cylinder of the same length (L > D2). 

Conductive Heat Transfer Large Plane Equation and Calculator Conductive Heat Transfer of Large plane wall equation and calculator. 

Conductive Heat Transfer of a Cylindrical Pipe or Layer Equation and Calculator Q = Rate of Steady State Heat Conductivity (W)
S = Conduction Shape Factor (ft) which has the dimension of length, and k is the thermal conductivity of the medium between the surfaces. The conduction shape factor depends on the geometry of the system only. 

Guide Manual of Cooling Methods for Electronic Equipment. Bureau of Ships Navy Department, 224 Pages, Free Membership Minimum Required to view Document/Book 

Heat loss from an insulated pipe calculations video This video solves a typical problem of determining the heat loss from an insulated pipe. 

Overall Heat Transfer Coefficient Development of a mathematical expression for overall heat transfer coefficient that includes conduction and convection Video. 

Conductive Heat Transfer of a Isothermal sphere buried in a semiinfinite medium Conductive Heat Transfer of a Isothermal sphere buried in a semiinfinite medium at T_{2} whose surface is insulated 

Conductive Heat Transfer of a Spherical Layer Equation and Calculator Conductive Heat Transfer of a spherical layer equation and calculator 

Conductive Heat Transfer of a Disk buried parallel to the surface Conductive Heat Transfer of a Disk buried parallel to the surface in a semiinfinite medium (z >> D) 

Conductive Heat Transfer of the edge of two adjoining walls of equal thickness Conductive Heat Transfer of the edge of two adjoining walls of equal thickness 

Conductive Heat Transfer Corner of three walls equal thickness equation and calculator Conductive Heat Transfer of a Corner of three walls of equal thickness equation and calculator 

Conductive Heat Transfer Isothermal sphere buried medium equation and calculator Conductive Heat Transfer of a Isothermal sphere buried in a semiinfinite medium equation and calculator 

Steady State Conduction Multi layer Cylinder Calculation Equation and calculator temperature on one side of an isothermal constant temperature multilayer cylinder. 

Heat Loss From an Insulated Electric Wire Equation and Calculator Heat transfer is steady since there is no indication of any change with time 

Maximum Power Dissipation of a Transistor Equation and Calculator
Assumptions:
1 Steady operating conditions exist.
2 The transistor case is isothermal at 85°C. 

Heat Loss of Two Cylinders at Known Separation Equation Steady State Rate of Heat Loss of Two Cylinders at Known Separation Equation and Calculator. Two parallel isothermal cylinders placed in an infinite medium (L >>D 1 , D 2 , z) 

Isothermal cylinder of length L buried in a semiinfinite medium calculator Steady State Rate of Heat Loss of Isothermal Cylinder. Isothermal cylinder of length L buried in a semiinfinite medium (L >>D and z >1.5D) 

Emissivity of Surface Table gives the emittance of various surfaces and emphasizes the variation possible in a single material. 

Heat Loss of cylinder buried in medium equation and calculator. Heat Loss of cylinder buried in a semiinfinite medium equation and calculator. Vertical isothermal cylinder of length L buried in a semiinfinite medium (L >>D) 

Linear Thermal Expansion Equation and Calculator Linear expansion is the change in length as opposed to change in volume. To a first approximation, the change in length measurements of an object due to thermal expansion is related to temperature change by a "linear expansion coefficient". 

Extruded ( Finned )Heat Sink Radiation Formulae Equation to calculate the radiation from an extruded (finned) heat sink. 

Selecting a Heat Sink for a Transistor Equation and Calculator
Assumptions:
1 Steady operating conditions exist.
2 The transistor case is isothermal at 90°C.
3 The contact resistance between the transistor and the heat sink is negligible. 

Forced Air Flow Convection Cooling. Fan Air Flow Required for Heat Sinking Formulas and Calculator. Forced air cooling with a fan of electronic components is often required over the heat transfer provided by natural convection cooling. 


Heat Loss from a Pipe Equation and calculator will determine the heat loss through a bare pipe 

Minimum Duct Insulation RValue, Cooling and HeatingOnly Supply Ducts and Return Ducts 

Minimum Pipe Insulation Thickness, in. per. ASHRAE Table, Formula and Calculator 

Heat Radiation of a Surface Calculator Heat Radiation of a Surface Calculator 

Estimating Junction Heat Transfer and Temperature of a Transistor Equation and Calculator 

Fan And Ventilation Requirements Procedure, Equations and Calculator. This webpage describes basic methods of selecting typical ventilation and cooling products based on their use and provides and example calculation and calculator. 

General Ventilation Rates Table Listed below are general ventilation rates for some common applications. Where more than one method is shown use the method that results in the higher airflow rate. 
Heat Transfer Application 

APM® Alloy Heating Tubes Review APM is ironchromiumaluminium (FeCrAI) powder metal alloy 

Bayonet Heating Elements Review Constructed with inline configurations and have electrical plugin "bayonet" connector to facilitate quick installation and removal. 

Coefficients Linear Thermal Expansion Thermal expansion is the tendency of matter to change in volume in response to a change in temperature, through heat transfer. 

Coil Heating Elements Review Heating elements work by converting electricity into heat energy, are rated in watts, however heat energy transfer varies by design. 

Compression Tension Stress Linear Thermal Expansion Equation and Calculator Compression or Tension Stress is the change in stress due to the material expansion by the change of temperature. 

Insulation Blanket Applications and Capabilities Overview When selecting the appropriate material for an insulation application, material galvanic capabilities, temperature range, and installation requirements should be understood 

Insulation Material Thermal Conductivity Chart Various Insulation Material Thermal Conductivity Table 

Heat Loss through a Insulated Pipe Equation and Calculator
1 Heat transfer is steady since there is no indication of any change with time.
2 Heat transfer is onedimensional since there is thermal symmetry about the centerline and no variation in the axial direction.
3 Thermal conductivities are constant. 4 The thermal contact resistance at the interface is negligible. 

Heat Losses From Bare and Insulated Pipe Heat Loss in Btu/h/ft Length of Fiberglass Insulation and Bare Pipe, ASJ Cover 150??F Temperature of Pipe Horizontal 

Heat Loss from Pipe Outdoors Heat Loss from Piping Chart For Piping Intended to Be Installed Outdoors 

Heat Loss Insulated Pipe Equation and Calculator Equation and calculator will determine the conductive heat loss through a cylinder or pipe wall insulation. 

Heat Transfer Coefficient Calculations This Worksheet will allow you to calculate heat transfer coefficients (h) for convection situations that involve internal flow in a tube of given crosssection. Premium membership required 

Ribbon Heating Elements Review Ribbon coil heating elements 

Rod Heating Elements Review Rod Heating Elements are cylindrical heating components of various lengths 

Thermal Energy Created by the Human Body he body is a heat engine. It converts chemical energy of the food consumed into both heat to sustain metabolism and work. 

Thermal Properties of Common Building Materials The materials' thermal properties govern the rate of heat transfer between the inside and outside of the building, the amount of heat that can be stored in the material. 
Convection Heat Transfer 

Convective Heat Transfer Coefficients Table Chart Convective Heat Transfer Coefficients Table Chart 

Heat Sink Convection with Fins Calculator Fins are used to increase heat transfer area and provide a cooling effect. 

Convection of Known Surface Area Calculator Convection of mass cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids. 

Vertical Plate Natural Convection Equation and Calculator 

Overall coefficient of heat transfer U of the wall calculator 

Overall Heat Leakage Coefficient Test Procedure, Equation and Calculator
Heat Leakage Test requirements Refrigeration System Design Equations and Calculator
Per. MILPRF3201 

Net Refrigeration Capacity System Design Equations and Calculator
Per. MILPRF32017 

Isothermal Square Rod Forced Air Convection Equation and Calculator 

Isothermal Circular Rod Forced Air Convection Equation and Calculator 

Convective Heat Transfer Convection Equation and Calculator is the transfer of heat from one place to another by the movement of fluids 

Vertical Parallel Plates Channel Natural Convection Equation and Calculator 

Natural Convection of a Horizontal Concentric Cylinders Equation and Calculator 

Convection Heat Transfer Coefficients Equations and Calculators Simplified relations for natural convection heat transfer coefficients for various geometries in air at atmospheric pressure for laminar flow conditions. 

Horizontal Plate Isothermal Heated Natural Convection Equation and Calculator 

Horizontal Heated Plate Facing Up Isothermal Natural Convection Equation and Calculator 

Natural Convection of a Horizontal Cylinder Equation and Calculator 

Overall Heat Transfer Coefficient Overall Heat Transfer Coefficient Equation 

Convection Heat Transfer Convection Heat Transfer calculation example 

Forced Convection Heat Transfer Printed Circuit board with Components Equation 

Flat Plate heat transfer coefficient and heat convected equation and calculator 

Round Duct Heat Transfer Coefficient and Wall Temperature Equation and Calculator 

Forced Convection Entry Region Circular Pipe / Tube Equation and Calculator 
Radiant Heat Transfer 

Thermal Radiation Radiant heat transfer involves the transfer of heat by electromagnetic radiation that arises due to the temperature of a body 

Black Body Radiation A body that emits the maximum amount of heat for its absolute temperature is called a black body. 

Emissivity and Heat Transfer Emissivity Equation 

Radiation Configuration Factor Radiative heat transfer rate between two gray bodies equation. 

Radiant Heat Exchange Parallel Flat Black Plates of Equal Size equation and calculator. 

Radiant heat exchange for two parallel flat black plates of different sizes equation and calculator. 

Solar Radiation Incident on the Surface of Earth Hourly variation of solar radiation incident on various surfaces and the daily totals throughout the year at 40?? latitude 

Radiant heat exchange for two parallel disks same size equations and calculator 

Radiant heat exchange for two perpendicular surfaces same size equation and calculator 
Heat Transfer Terminology 

Heat and Temperature Temperature is a measure of the amount of energy possessed by the molecules of a substance. 

Heat and Work Energy terms heat and work both represent energy in transition 

Modes of Transferring Heat Heat is always transferred when a temperature difference exists between two bodies. 

Heat Flux Heat Flux equation  The rate at which heat is transferred 

Thermal Conductivity Heat transfer characteristics of a solid material are measured by a property called the thermal conductivity (k) measured in Btu/hrft°F. 

Thermal Diffusivity Table is the thermal conductivity divided by density and specific heat capacity at constant pressure. 

Prandtl Number  The relative thickness of the velocity and the thermal boundary layers 

Dynamic Viscosity In fluid flow and heat transfer studies, the ratio of dynamic viscosity to density appears frequently. 

Log Mean Temperature Difference Temperature change between two fluids across the heat exchanger is best represented by the log mean temperature difference 

Convective Heat Transfer Coefficient Convective heat transfer coefficient is sometimes referred to as a film coefficient 

Overall Heat Transfer Coefficient Overall Heat Transfer Coefficient Equation 

Bulk Temperature Fluid temperature (Tb), referred to as the bulk temperature, varies according to the details of the situation. 

Water Boiling Graph Curve at 1 Atmosphere Typical Water Boiling Graph Curve at 1 Atmosphere 
Conduction Heat Transfer 

Conduction and Heat Transfer Conduction involves the transfer of heat by the interaction between adjacent molecules of a material. 

Equivalent Resistance Method Equivalent Resistance Method equation and calculation example 

Electrical Analogy Heat Transfer Electrical Analogy Heat Transfer equation and calculation 

Conduction Through a Uniform Material Calculator 

ConductionCylindrical Coordinates Heat transfer across a rectangular solid is the most direct application of Fouriers law. 

Overall Ufactors (heat transfer coefficients) for various windows and skylights Overall Ufactors (heat transfer coefficients) for various windows and skylights in W / (m 2 ?? ??C) 

Interior and Exterior Surface Heat Transfer Coefficients Equations for Windows Heat transfer through a window is also affected by the convection and radiation heat transfer coefficients between the glass surfaces and surroundings. 

Heat Loss from Ducts in a Building Equation and Calculator Heat Loss from Ducts in a Building Equation and Calculator and cost of energy lost. 

Heat Conduction through a Wall Equation and Calculator Heat Conduction through a wall equations and calculator. 

Steady State Conduction Multi layer Isothermal Walls Calculation Steady State Conduction Multilayer Isothermal Walls Calculation and equation 

Thermal Conductivity Conversions Calculator Conversions Factors for Thermal Conductivity Unit 

Thermal Conductivity of Gases Table of thermal conductivity of gases as a function of temperature. 

Thermal Conductivity of Common Metals and Alloys Table gives typical values of thermal several common commercial metals and alloys. 

Thermal Conductivity Common Liquids Thermal Conductivity of Liquids Table 
Heat Exchangers 

Heat Exchangers Transfer of heat is usually accomplished by means of a device known as a heat exchanger. 

Parallel and CounterFlow Designs Parallel and Counter Flow heat exchanger Designs 

NonRegenerative Heat Exchanger The nonregenerative application is the most frequent and involves two separate fluids. 

Regenerative Heat Exchanger Regenerative heat exchanger typically uses the fluid from a different area of the same system for both the hot and cold fluids. 

Cooling Towers Typical function of a cooling tower is to cool the water of a steam power plant by air that is brought into direct contact with the water. 

Log Mean Temperature Difference Application to Heat Exchangers To solve certain heat exchanger problems, a log mean temperature difference or must be evaluated. 

Overall Heat Transfer Coefficient Overall Heat Transfer Coefficient Across Heat Exchanger Tubes Equation 

Overall Heat Transfer Coefficients in Heat Exchangers Representative values of the overall heat transfer coefficients in heat exchangers. 

Empirical correlations for the average Nusselt number for forced convection over a flat plate and circular and noncircular cylinders in cross flow 
Heat Transfer Engineering Reference Data 

Thermal Properties of Metals 

Thermal Properties of NonMetals 

Saturated Liquids Thermal Properties 

Properties of air at 1 atm pressure Engineering properties of air at 1 atm pressure 

Thermal contact conductance of some metal surfaces in air (from various sources) table 

Thermal Properties of Gases 

Unit thermal resistance (the Rvalue) of common components used in buildings 

Unit thermal resistances (Rvalues) of wellsealed air spaces (from ASHRAE Handbook of Fundamentals, Ref. 1, Chap. 22, Table 2) 

Saturation pressure of water at various temperatures 

Boiling and freezing point properties of selected substances 

Thermal Properties of insulating materials (at a mean temperature of 24°C) 

Combined natural convection and radiation thermal resistance of various heat sinks used in the cooling of electronic devices between the heat sink and the surroundings. All fins are made of aluminum 6063T5, are black anodized. 

Thermal Linear Expansion of AISI 303 Stainless Steel AISI 303 stainless steel, which is a modification of the basic 188 austenitic stainless steel, contains higher amounts of phosphorous (0.20% max) and sulfur (0.15% min.). 

Heat Transfer and Evaporation Book
 General Theory of Heat Transmission  Conduction
 General Theory of Heat Transmission  Radiation
 Heat Transfer by Convection  General
 Heat Transfer Between Solids and Gases
 Heat Transfer Between Solid and Liquids


Heat and Thermodynamics, 684 Pages, Mark W. Zemansky, Ph.D. Membership (Minimum free) Required to view Document/Book 

Time to Freeze Outdoor / Indoor Piping Formulas and Calculator It is important to recognize that insulation reduces heat flow however it does not stop it completely. Piping located outdoors, or indoors in unheated areas, is subject to freezing. This is especially true for pipe systems containing standing water. Insulation will delay but not prevent freezing of still water or water flowing at a rate insufficient for the available heat content to offset the heat loss. 

Thermal Conductivity of Refractory Materials, 108 Pages, Pustovalov, V.V. Premium membership required 
Misc Heat Transfer resources
 Anti Freeze Ethylene Glycol Freezing and Boil Temperatures
 BenedictWebbRubin PVT
Formula and Calculator
 Brinkman Number Equation and Calculator

Building Sensible Heat Thermal Load with Air Exchange Calculator

Heat Loss by Free Convection from a Horizontal Pipe Formula and Calculator
 Glass or Frame Condensation Resistance Factor (CRF) or Temperature Index (I) Calculator
 Viscosity of Aqueous Solutions of Ethylene Glycol Antifreeze
 Inhibited Aqueous Solutions Ethylene Glycol Antifreeze Density
 Specific Heat of Aqueous Solutions of Propylene Glycol
 Thermal Conductivity of Aqueous Solutions of Propylene Glycol
 Viscosity of Aqueous Solutions of Propylene Glycol
 Convective Heat Gain from Unhooded Electric Appliances During Idle (ReadytoCook) Conditions
 Eckert Number Equation and Calculator
 Emittance Data of Commonly Used Materials

Effective Thermal Conductivity of Composite Solids
Formula and Calculator
 Emissivity of Surface Table
 Steady State Fenestration Heat Energy Flow and Loss
 Fourier's Law for Insulation Formula
 Freezing Point and Properties of Foods The following is the Unfrozen Composition Data, Initial Freezing Point, and Specific Heats of Foods
 Freezing Times for Food Using Plank's Equation
 Fuel Gas and Heating Values
 Heat Loss From House or Building
 Heat Loss from Bare Copper Tube to Still Air at 80°F, Btu/h· ft
 Heat Loss from Bare Steel Pipe to Still Air at 80°F, Btu/h· ft
 Heat Gain or Loss HVAC Duct ASHRAE Formula and Calculator. All HVAC ducts exposed to outdoor conditions, as well as those passing through unconditioned or semiconditioned spaces, should be insulated.
 Heat Gain from Typical Electric Motors
 Heat Gain from Lighting  The energy emitted by lighting and then absorbed by the structure and contents contributes to space cooling load only after a time lag, some still re radiatingafter the heat sources have been switched off.
 Heat Gain from Motors and their Loads Formula and Calculator Instantaneous rate of heat gain from equipment operated by electric motors within a space.
 Heats of Combustion for Common Compounds
 Heat Transfer Coefficient for Condensation Formula and Calculator
 Heating Capacity of a Radiator Formula and Calculator
 Humidity Ratio of Air Humidity ratio W is the ratio of the mass of water vapor to the mass of dry air:

Amount of Heat Required to Increase the Temperature of
Reservoir
Formula and Calculator
 Humidification Humidifier Load Calculations and Calculator
 Moisture Removal or Addition by HVAC Latent Energy Load Calculator
 Mean Radiant Temperature Formula and Calculator This is the uniform temperature of an imaginary black enclosure in which an occupant would exchange the same amount of radiant heat as in the actual nonuniform enclosure.
 Metabolic Rate Energy Burned Calculator and Formulas for Humans
 Radiative Heat Transfer Coefficient of a Human Calculator
 Thermal Conductivity of Soils and Rocks
 Thermal Expansion of Metal Pipe Temperature changes cause dimensional changes in all materials. Table 1.0 shows the coefficients of expansion for metallic piping materials. For systems operating at high temperatures, such as steam and hot water, the rate of expansion is high, and significant movements can occur in short runs of piping.
 Water Vapor Saturation Pressure Formulas and Calculator Increasing temperature of liquid (or any substance) enhances its evaporation that results in the increase of vapor pressure over the liquid.
 Vapor Saturation Pressure Over Ice Formulas and Calculator The saturation (sublimation) pressure over ice for the temperature range of –148 to 32°F
 Relative Humidity Calculator and Equation
 Relative Humidity and Weight per Cubic Foot Volume of Air
 Solid with Spherical Inclusions Effective Thermal Conductivity Equation and Calculator
 Specific Heat Capacity Table at Room Temperature Specific heat capacity c is the change in heat (energy) of a unit mass of material for a unit change of temperature in Btu/lb·°F or Btu/(lbm°R)
 Static Temperature Versus Total Temperature Formula and Calculator When a fluid stream impinges on a temperaturesensing element such as a thermometer or thermocouple, the element is at a temperature greater than the true stream temperature.
 Standard Atmospheric Data for Altitude and Temperature The standard atmosphere gives a standard of reference for estimating properties at various altitudes.
 Stanton Number Equation and Calculator
 Steam Enthalpy Quality and Volume Fraction of the Condensate can be estimated from:
 Temperature and Pressure Data for Refrigerants
 Thermal Conductivity of Aqueous Solutions of Antifreeze Ethylene Glycol
 Water Vapor Released by Human Activity and Plants Estimating moisture loads requires knowledge of occupancy patterns and releases per individual, activity, plant, and water surface present.
 WaterCooled Condenser Flow Requirements Calculator
 Wet and Dry Steam Mass and Volume Fraction Calculator Steam is a gaseous form of waterair vapor and there are two forms, wet steam and dry steam.
 Temperature Rise Across Fan Calculator
 Thermal Resistance of Floor Coverings
 Thermodynamic Functions, Typical Symbols and Units
