Position of peak temperature from fusion boundary Calculator

✖Melting Temperature of Base Metal is the temperature at which its phase changes to liquid to solid.ⓘ Melting Temperature of Base Metal [T_m]			+10% -10%
✖Temperature reached at a distance of y is the temperature reached at a distance of y from the fusion boundary.ⓘ Temperature Reached at a Distance of y [T_y]			+10% -10%
✖Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.ⓘ Net Heat Supplied per Unit Length [H_Net]			+10% -10%
✖Ambient Temperature is the temperature of the surrounding.ⓘ Ambient Temperature [t_a]			+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%
✖Thickness of the metal is the thickness of the base metal and is denoted by h symbol.ⓘ Thickness of the Metal [t]			+10% -10%

✖Distance from the Fusion Boundary is measured from the fusion boundary during welding.ⓘ Position of peak temperature from fusion boundary [y]

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Formula

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Position of peak temperature from fusion boundary

Formula

`"y" = (("T"_{"m"}-"T"_{"y"})*"H"_{"Net"})/(("T"_{"y"}-"t"_{"a"})*("T"_{"m"}-"t"_{"a"})*sqrt(2*pi*e)*"ρ"*"Q"_{"c"}*"t")`

Example

`"100.7983mm"=(("1500°C"-"143.7°C")*"1000J/mm")/(("143.7°C"-"37°C")*("1500°C"-"37°C")*sqrt(2*pi*e)*"997kg/m³"*"4.184kJ/kg*K"*"5mm")`

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Position of peak temperature from fusion boundary Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
y = ((T_m-T_y)*H_Net)/((T_y-t_a)*(T_m-t_a)*sqrt(2*pi*e)*ρ*Q_c*t)
This formula uses 2 Constants, 1 Functions, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

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

Distance from the Fusion Boundary - (Measured in Meter) - Distance from the Fusion Boundary is measured from the fusion boundary during welding.
Melting Temperature of Base Metal - (Measured in Kelvin) - Melting Temperature of Base Metal is the temperature at which its phase changes to liquid to solid.
Temperature Reached at a Distance of y - (Measured in Kelvin) - Temperature reached at a distance of y is the temperature reached at a distance of y from the fusion boundary.
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.
Ambient Temperature - (Measured in Kelvin) - Ambient Temperature is the temperature of the surrounding.
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.
Thickness of the Metal - (Measured in Meter) - Thickness of the metal is the thickness of the base metal and is denoted by h symbol.

STEP 1: Convert Input(s) to Base Unit

Melting Temperature of Base Metal: 1500 Celsius --> 1773.15 Kelvin (Check conversion here)
Temperature Reached at a Distance of y: 143.7 Celsius --> 416.85 Kelvin (Check conversion here)
Net Heat Supplied per Unit Length: 1000 Joule per Millimeter --> 1000000 Joule per Meter (Check conversion here)
Ambient Temperature: 37 Celsius --> 310.15 Kelvin (Check conversion here)
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)
Thickness of the Metal: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y = ((T_m-T_y)*H_Net)/((T_y-t_a)*(T_m-t_a)*sqrt(2*pi*e)*ρ*Q_c*t) --> ((1773.15-416.85)*1000000)/((416.85-310.15)*(1773.15-310.15)*sqrt(2*pi*e)*997*4184*0.005)

Evaluating ... ...

y = 0.100798252403894

STEP 3: Convert Result to Output's Unit

0.100798252403894 Meter -->100.798252403894 Millimeter (Check conversion here)

FINAL ANSWER

100.798252403894 ≈ 100.7983 Millimeter <-- Distance from the Fusion Boundary

(Calculation completed in 00.009 seconds)

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University Institute of Technology RGPV (UIT - RGPV), Bhopal

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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

Position of peak temperature from fusion boundary Formula

Why peak temperature reached in Heat Affected Zone is important to calculate ?

The peak temperature reached at any point in the material is another important parameter that needs to be calculated. This would help in identifying what type of metallurgical transformations are likely to takes place in the heat affected zone (HAZ).

How to Calculate Position of peak temperature from fusion boundary?

Position of peak temperature from fusion boundary calculator uses 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) to calculate the Distance from the Fusion Boundary, The Position of peak temperature from fusion boundary formula is defined as the distance from fusion boundary where given temp. is reached in heat affected zone. Distance from the Fusion Boundary is denoted by y symbol.

How to calculate Position of peak temperature from fusion boundary using this online calculator? To use this online calculator for Position of peak temperature from fusion boundary, enter Melting Temperature of Base Metal (T_m), Temperature Reached at a Distance of y (T_y), Net Heat Supplied per Unit Length (H_Net), Ambient Temperature (t_a), Density (ρ), Specific Heat Capacity (Q_c) & Thickness of the Metal (t) and hit the calculate button. Here is how the Position of peak temperature from fusion boundary calculation can be explained with given input values -> 100798.3 = ((1773.15-416.85)*1000000)/((416.85-310.15)*(1773.15-310.15)*sqrt(2*pi*e)*997*4184*0.005).

FAQ

What is Position of peak temperature from fusion boundary?

The Position of peak temperature from fusion boundary formula is defined as the distance from fusion boundary where given temp. is reached in heat affected zone and is represented as y = ((T_m-T_y)*H_Net)/((T_y-t_a)*(T_m-t_a)*sqrt(2*pi*e)*ρ*Q_c*t) or 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). Melting Temperature of Base Metal is the temperature at which its phase changes to liquid to solid, Temperature reached at a distance of y is the temperature reached at a distance of y from the fusion boundary, Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter, Ambient Temperature is the temperature of the surrounding, 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 & Thickness of the metal is the thickness of the base metal and is denoted by h symbol.

How to calculate Position of peak temperature from fusion boundary?

The Position of peak temperature from fusion boundary formula is defined as the distance from fusion boundary where given temp. is reached in heat affected zone is calculated using 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). To calculate Position of peak temperature from fusion boundary, you need Melting Temperature of Base Metal (T_m), Temperature Reached at a Distance of y (T_y), Net Heat Supplied per Unit Length (H_Net), Ambient Temperature (t_a), Density (ρ), Specific Heat Capacity (Q_c) & Thickness of the Metal (t). With our tool, you need to enter the respective value for Melting Temperature of Base Metal, Temperature Reached at a Distance of y, Net Heat Supplied per Unit Length, Ambient Temperature, Density, Specific Heat Capacity & Thickness of the Metal and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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