An Exact Analysis of Heat and Mass Transfer Past a Vertical Plate with Newtonian Heating

Table 4

Inverse Laplace transform formulae.

	𝐹(𝑞)=𝐿{𝑓(𝑡)}	𝑓(𝑡)
1	1𝑞𝑒^√−𝑦𝑞	erf 𝑐𝑦2√𝑡
2	1𝑞^2𝑒^√−𝑦𝑞	𝑦^22+𝑡 erf c 𝑦2√𝑡−𝑦𝑡𝜋𝑒^−𝑦2/4𝑡
3	1𝑞√𝑒𝑞−𝑎^√−𝑦𝑞	𝑒^(𝑎2𝑡−𝑎𝑦) erf c 𝑦2√𝑡−𝑎√𝑡− erf c 𝑦2√𝑡
4	1𝑞^2√𝑒𝑞−𝑎^√−𝑦𝑞	14√𝑒𝜋𝑡^−𝑦2/4𝑡+𝑎𝑒^(𝑎2𝑡−𝑎𝑦) erf c 𝑦2√𝑡−𝑎√𝑡
5	1𝑒𝑞+𝑎^√−𝑦𝑞	𝑒^𝑎𝑡2𝑒^𝑦√𝑎 erf c 𝑦2√𝑡+√𝑎𝑡+𝑒^√−𝑦𝑎 erf c 𝑦2√𝑡−√𝑎𝑡