Net heat supplied to achieve given cooling rates for thin plates Calculator

✖Thickness of the metal is the thickness of the base metal and is denoted by h symbol.ⓘ Thickness of the Metal [t]			+10% -10%
✖Cooling Rate of Thinplate is the time rate of decrease of temperature of a particular material.ⓘ Cooling Rate of Thinplate [R_c]			+10% -10%
✖Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.ⓘ Thermal Conductivity [k]			+10% -10%
✖The Density of a material shows the denseness of that material in a specific given volume. This is taken as mass per unit volume of a given object.ⓘ Density [ρ]			+10% -10%
✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [Q_c]			+10% -10%
✖Temperature to calculate cooling rate is calculated is the temperature at which the cooling rate is calculated.ⓘ Temperature to Calculate Cooling Rate [T_c]			+10% -10%
✖Ambient Temperature is the temperature of the surrounding.ⓘ Ambient Temperature [t_a]			+10% -10%

✖Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.ⓘ Net heat supplied to achieve given cooling rates for thin plates [H_Net]

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Formula

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Net heat supplied to achieve given cooling rates for thin plates

Formula

`"H"_{"Net"} = "t"/sqrt("R"_{"c"}/(2*pi*"k"*"ρ"*"Q"_{"c"}*(("T"_{"c"}-"t"_{"a"})^3)))`

Example

`"1001.56J/mm"="5mm"/sqrt("0.66°C/s"/(2*pi*"10.18W/(m*K)"*"997kg/m³"*"4.184kJ/kg*K"*(("500°C"-"37°C")^3)))`

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Net heat supplied to achieve given cooling rates for thin plates Solution

STEP 0: Pre-Calculation Summary

Formula Used

Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))
H_Net = t/sqrt(R_c/(2*pi*k*ρ*Q_c*((T_c-t_a)^3)))
This formula uses 1 Constants, 1 Functions, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Net Heat Supplied per Unit Length - (Measured in Joule per Meter) - Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.
Thickness of the Metal - (Measured in Meter) - Thickness of the metal is the thickness of the base metal and is denoted by h symbol.
Cooling Rate of Thinplate - (Measured in Kelvin per Second) - Cooling Rate of Thinplate is the time rate of decrease of temperature of a particular material.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given volume. This is taken as mass per unit volume of a given object.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
Temperature to Calculate Cooling Rate - (Measured in Kelvin) - Temperature to calculate cooling rate is calculated is the temperature at which the cooling rate is calculated.
Ambient Temperature - (Measured in Kelvin) - Ambient Temperature is the temperature of the surrounding.

STEP 1: Convert Input(s) to Base Unit

Thickness of the Metal: 5 Millimeter --> 0.005 Meter (Check conversion here)
Cooling Rate of Thinplate: 0.66 Celsius per Second --> 0.66 Kelvin per Second (Check conversion here)
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
Temperature to Calculate Cooling Rate: 500 Celsius --> 773.15 Kelvin (Check conversion here)
Ambient Temperature: 37 Celsius --> 310.15 Kelvin (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_Net = t/sqrt(R_c/(2*pi*k*ρ*Q_c*((T_c-t_a)^3))) --> 0.005/sqrt(0.66/(2*pi*10.18*997*4184*((773.15-310.15)^3)))

Evaluating ... ...

H_Net = 1001559.52000553

STEP 3: Convert Result to Output's Unit

1001559.52000553 Joule per Meter -->1001.55952000553 Joule per Millimeter (Check conversion here)

FINAL ANSWER

1001.55952000553 ≈ 1001.56 Joule per Millimeter <-- Net Heat Supplied per Unit Length

(Calculation completed in 00.020 seconds)

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Home » Engineering » Production Engineering » Welding » Heat Flow in Welded Joints » Net heat supplied to achieve given cooling rates for thin plates

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< 13 Heat Flow in Welded Joints Calculators

Peak Temperature Reached at any Point in Material

Go Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length)

Position of peak temperature from fusion boundary

Go Distance from the Fusion Boundary = ((Melting Temperature of Base Metal-Temperature Reached at a Distance of y)*Net Heat Supplied per Unit Length)/((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal)

Net heat supplied to weld area to raise it to given temperature from fusion boundary

Go Net Heat Supplied per Unit Length = ((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal*Distance from the Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at a Distance of y)

Net heat supplied to achieve given cooling rates for thin plates

Go Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))

Thickness of base metal for desired cooling rate

Go Thickness = Net Heat Supplied per Unit Length*sqrt(Cooling Rate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))

Thermal conductivity of base metal using given cooling rate (thin plates)

Go Thermal Conductivity = Cooling Rate of Thinplate/(2*pi*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3))

Cooling rate for relatively thin plates

Go Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)

Relative plate thickness factor

Go Relative Plate Thickness Factor = Thickness of the Metal*sqrt(((Temperature to Calculate Cooling Rate-Ambient Temperature)*Density of Metal*Specific Heat Capacity)/Net Heat Supplied per Unit Length)

Thickness of Base Metal using Relative Thickness Factor

Go Thickness of the Base Metal = Relative Plate Thickness Factor*sqrt(Net Heat Supplied per Unit Length/((Temperature to Calculate Cooling Rate-Ambient Temperature)*Density*Specific Heat Capacity))

Net Heat supplied using Relative Thickness Factor

Go Net Heat Supplied = ((Thickness of the Metal/Relative Plate Thickness Factor)^2)*Density*Specific Heat Capacity*(Temperature to Calculate Cooling Rate-Ambient Temperature)

Thermal conductivity of base metal using given cooling rate (thick plates)

Go Thermal Conductivity = (Cooling Rate*Net Heat Supplied per Unit Length)/(2*pi*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))

Net heat supplied to achieve given cooling rates for thick plates

Go Net Heat Supplied per Unit Length = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Cooling Rate

Cooling Rate for Relatively Thick Plates

Go Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length

Net heat supplied to achieve given cooling rates for thin plates Formula

How heat transfer takes place near heat affected zone ?

Heat transfer in a welded joint is a complex phenomenon involving three dimensional movement of a heat source. Heat from the weld zone is transferred more to the other parts of the base metal by means of conduction. Similarly heat is also lost to surroundings by convection from the surface, with radiation component being relatively small except near the weld pool. Thus the analytical treatment of the weld zone is extremely difficult.

How to Calculate Net heat supplied to achieve given cooling rates for thin plates?

Net heat supplied to achieve given cooling rates for thin plates calculator uses Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3))) to calculate the Net Heat Supplied per Unit Length, The Net heat supplied to achieve given cooling rates for thin plates formula is defined as the energy that will result in given cooling of metal weld. Net Heat Supplied per Unit Length is denoted by H_Net symbol.

How to calculate Net heat supplied to achieve given cooling rates for thin plates using this online calculator? To use this online calculator for Net heat supplied to achieve given cooling rates for thin plates, enter Thickness of the Metal (t), Cooling Rate of Thinplate (R_c), Thermal Conductivity (k), Density (ρ), Specific Heat Capacity (Q_c), Temperature to Calculate Cooling Rate (T_c) & Ambient Temperature (t_a) and hit the calculate button. Here is how the Net heat supplied to achieve given cooling rates for thin plates calculation can be explained with given input values -> 1.00156 = 0.005/sqrt(0.66/(2*pi*10.18*997*4184*((773.15-310.15)^3))).

FAQ

What is Net heat supplied to achieve given cooling rates for thin plates?

The Net heat supplied to achieve given cooling rates for thin plates formula is defined as the energy that will result in given cooling of metal weld and is represented as H_Net = t/sqrt(R_c/(2*pi*k*ρ*Q_c*((T_c-t_a)^3))) or Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3))). Thickness of the metal is the thickness of the base metal and is denoted by h symbol, Cooling Rate of Thinplate is the time rate of decrease of temperature of a particular material, Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance, The Density of a material shows the denseness of that material in a specific given volume. This is taken as mass per unit volume of a given object, Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Temperature to calculate cooling rate is calculated is the temperature at which the cooling rate is calculated & Ambient Temperature is the temperature of the surrounding.

How to calculate Net heat supplied to achieve given cooling rates for thin plates?

The Net heat supplied to achieve given cooling rates for thin plates formula is defined as the energy that will result in given cooling of metal weld is calculated using Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3))). To calculate Net heat supplied to achieve given cooling rates for thin plates, you need Thickness of the Metal (t), Cooling Rate of Thinplate (R_c), Thermal Conductivity (k), Density (ρ), Specific Heat Capacity (Q_c), Temperature to Calculate Cooling Rate (T_c) & Ambient Temperature (t_a). With our tool, you need to enter the respective value for Thickness of the Metal, Cooling Rate of Thinplate, Thermal Conductivity, Density, Specific Heat Capacity, Temperature to Calculate Cooling Rate & Ambient Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Net Heat Supplied per Unit Length?

In this formula, Net Heat Supplied per Unit Length uses Thickness of the Metal, Cooling Rate of Thinplate, Thermal Conductivity, Density, Specific Heat Capacity, Temperature to Calculate Cooling Rate & Ambient Temperature. We can use 2 other way(s) to calculate the same, which is/are as follows -

Net Heat Supplied per Unit Length = ((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal*Distance from the Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at a Distance of y)
Net Heat Supplied per Unit Length = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Cooling Rate

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